Update libsecp256k1

68 files changed, 7728 insertions, 1916 deletions

diff --git a/src/secp256k1/.gitignore b/src/secp256k1/.gitignore
index 076ff1295f..e0b7b7a48a 100644
--- a/src/secp256k1/.gitignore
+++ b/src/secp256k1/.gitignore
@@ -1,9 +1,12 @@
 bench_inv
+bench_ecdh
 bench_sign
 bench_verify
+bench_schnorr_verify
 bench_recover
 bench_internal
 tests
+gen_context
 *.exe
 *.so
 *.a
@@ -28,6 +31,7 @@ build-aux/
 *~
 src/libsecp256k1-config.h
 src/libsecp256k1-config.h.in
+src/ecmult_static_context.h
 m4/libtool.m4
 m4/ltoptions.m4
 m4/ltsugar.m4
diff --git a/src/secp256k1/.travis.yml b/src/secp256k1/.travis.yml
index 0d8089cfe4..4e1e73c39f 100644
--- a/src/secp256k1/.travis.yml
+++ b/src/secp256k1/.travis.yml
@@ -8,20 +8,24 @@ compiler:
   - gcc
 env:
   global:
-    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  ASM=no  BUILD=check  EXTRAFLAGS= HOST=
+    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  schnorr=no  RECOVERY=no
   matrix:
-    - SCALAR=32bit
+    - SCALAR=32bit    RECOVERY=yes
+    - SCALAR=32bit    FIELD=32bit       ECDH=yes
     - SCALAR=64bit
-    - FIELD=64bit
+    - FIELD=64bit     RECOVERY=yes
     - FIELD=64bit     ENDOMORPHISM=yes
+    - FIELD=64bit     ENDOMORPHISM=yes  ECDH=yes
     - FIELD=64bit                       ASM=x86_64
     - FIELD=64bit     ENDOMORPHISM=yes  ASM=x86_64
-    - FIELD=32bit
+    - FIELD=32bit     SCHNORR=yes
     - FIELD=32bit     ENDOMORPHISM=yes
     - BIGNUM=no
-    - BIGNUM=no       ENDOMORPHISM=yes
+    - BIGNUM=no       ENDOMORPHISM=yes SCHNORR=yes  RECOVERY=yes
+    - BIGNUM=no       STATICPRECOMPUTATION=no
     - BUILD=distcheck
-    - EXTRAFLAGS=CFLAGS=-DDETERMINISTIC
+    - EXTRAFLAGS=CPPFLAGS=-DDETERMINISTIC
+    - EXTRAFLAGS=CFLAGS=-O0
 matrix:
   fast_finish: true
   include:
@@ -55,5 +59,5 @@ before_script: ./autogen.sh
 script:
  - if [ -n "$HOST" ]; then export USE_HOST="--host=$HOST"; fi
  - if [ "x$HOST" = "xi686-linux-gnu" ]; then export CC="$CC -m32"; fi
- - ./configure --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
+ - ./configure --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-schnorr=$SCHNORR --enable-module-recovery=$RECOVERY $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
 os: linux
diff --git a/src/secp256k1/Makefile.am b/src/secp256k1/Makefile.am
index cc15338b7e..f4121f1705 100644
--- a/src/secp256k1/Makefile.am
+++ b/src/secp256k1/Makefile.am
@@ -19,6 +19,8 @@ noinst_HEADERS += src/eckey.h
 noinst_HEADERS += src/eckey_impl.h
 noinst_HEADERS += src/ecmult.h
 noinst_HEADERS += src/ecmult_impl.h
+noinst_HEADERS += src/ecmult_const.h
+noinst_HEADERS += src/ecmult_const_impl.h
 noinst_HEADERS += src/ecmult_gen.h
 noinst_HEADERS += src/ecmult_gen_impl.h
 noinst_HEADERS += src/num.h
@@ -38,40 +40,72 @@ noinst_HEADERS += src/hash_impl.h
 noinst_HEADERS += src/field.h
 noinst_HEADERS += src/field_impl.h
 noinst_HEADERS += src/bench.h
+noinst_HEADERS += contrib/lax_der_parsing.h
+noinst_HEADERS += contrib/lax_der_parsing.c
+noinst_HEADERS += contrib/lax_der_privatekey_parsing.h
+noinst_HEADERS += contrib/lax_der_privatekey_parsing.c
 
 pkgconfigdir = $(libdir)/pkgconfig
 pkgconfig_DATA = libsecp256k1.pc
 
 libsecp256k1_la_SOURCES = src/secp256k1.c
-libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include $(SECP_INCLUDES)
+libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
 libsecp256k1_la_LIBADD = $(SECP_LIBS)
 
 
 noinst_PROGRAMS =
 if USE_BENCHMARK
-noinst_PROGRAMS += bench_verify bench_recover bench_sign bench_internal
+noinst_PROGRAMS += bench_verify bench_sign bench_internal
 bench_verify_SOURCES = src/bench_verify.c
 bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
-bench_verify_LDFLAGS = -static
-bench_recover_SOURCES = src/bench_recover.c
-bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS)
-bench_recover_LDFLAGS = -static
 bench_sign_SOURCES = src/bench_sign.c
 bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS)
-bench_sign_LDFLAGS = -static
 bench_internal_SOURCES = src/bench_internal.c
 bench_internal_LDADD = $(SECP_LIBS)
-bench_internal_LDFLAGS = -static
 bench_internal_CPPFLAGS = $(SECP_INCLUDES)
 endif
 
 if USE_TESTS
 noinst_PROGRAMS += tests
 tests_SOURCES = src/tests.c
-tests_CPPFLAGS = -DVERIFY $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
+tests_CPPFLAGS = -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
 tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS)
 tests_LDFLAGS = -static
 TESTS = tests
 endif
 
-EXTRA_DIST = autogen.sh
+if USE_ECMULT_STATIC_PRECOMPUTATION
+CPPFLAGS_FOR_BUILD +=-I$(top_srcdir)/
+CFLAGS_FOR_BUILD += -Wall -Wextra -Wno-unused-function
+
+gen_context_OBJECTS = gen_context.o
+gen_context_BIN = gen_context$(BUILD_EXEEXT)
+gen_%.o: src/gen_%.c
+	$(CC_FOR_BUILD) $(CPPFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) -c $< -o $@
+
+$(gen_context_BIN): $(gen_context_OBJECTS)
+	$(CC_FOR_BUILD) $^ -o $@
+
+$(libsecp256k1_la_OBJECTS): src/ecmult_static_context.h
+$(tests_OBJECTS): src/ecmult_static_context.h
+$(bench_internal_OBJECTS): src/ecmult_static_context.h
+
+src/ecmult_static_context.h: $(gen_context_BIN)
+	./$(gen_context_BIN)
+
+CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h
+endif
+
+EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h
+
+if ENABLE_MODULE_ECDH
+include src/modules/ecdh/Makefile.am.include
+endif
+
+if ENABLE_MODULE_SCHNORR
+include src/modules/schnorr/Makefile.am.include
+endif
+
+if ENABLE_MODULE_RECOVERY
+include src/modules/recovery/Makefile.am.include
+endif
diff --git a/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4 b/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4
new file mode 100644
index 0000000000..77fd346a79
--- /dev/null
+++ b/src/secp256k1/build-aux/m4/ax_prog_cc_for_build.m4
@@ -0,0 +1,125 @@
+# ===========================================================================
+#   http://www.gnu.org/software/autoconf-archive/ax_prog_cc_for_build.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_PROG_CC_FOR_BUILD
+#
+# DESCRIPTION
+#
+#   This macro searches for a C compiler that generates native executables,
+#   that is a C compiler that surely is not a cross-compiler. This can be
+#   useful if you have to generate source code at compile-time like for
+#   example GCC does.
+#
+#   The macro sets the CC_FOR_BUILD and CPP_FOR_BUILD macros to anything
+#   needed to compile or link (CC_FOR_BUILD) and preprocess (CPP_FOR_BUILD).
+#   The value of these variables can be overridden by the user by specifying
+#   a compiler with an environment variable (like you do for standard CC).
+#
+#   It also sets BUILD_EXEEXT and BUILD_OBJEXT to the executable and object
+#   file extensions for the build platform, and GCC_FOR_BUILD to `yes' if
+#   the compiler we found is GCC. All these variables but GCC_FOR_BUILD are
+#   substituted in the Makefile.
+#
+# LICENSE
+#
+#   Copyright (c) 2008 Paolo Bonzini <bonzini@gnu.org>
+#
+#   Copying and distribution of this file, with or without modification, are
+#   permitted in any medium without royalty provided the copyright notice
+#   and this notice are preserved. This file is offered as-is, without any
+#   warranty.
+
+#serial 8
+
+AU_ALIAS([AC_PROG_CC_FOR_BUILD], [AX_PROG_CC_FOR_BUILD])
+AC_DEFUN([AX_PROG_CC_FOR_BUILD], [dnl
+AC_REQUIRE([AC_PROG_CC])dnl
+AC_REQUIRE([AC_PROG_CPP])dnl
+AC_REQUIRE([AC_EXEEXT])dnl
+AC_REQUIRE([AC_CANONICAL_HOST])dnl
+
+dnl Use the standard macros, but make them use other variable names
+dnl
+pushdef([ac_cv_prog_CPP], ac_cv_build_prog_CPP)dnl
+pushdef([ac_cv_prog_gcc], ac_cv_build_prog_gcc)dnl
+pushdef([ac_cv_prog_cc_works], ac_cv_build_prog_cc_works)dnl
+pushdef([ac_cv_prog_cc_cross], ac_cv_build_prog_cc_cross)dnl
+pushdef([ac_cv_prog_cc_g], ac_cv_build_prog_cc_g)dnl
+pushdef([ac_cv_exeext], ac_cv_build_exeext)dnl
+pushdef([ac_cv_objext], ac_cv_build_objext)dnl
+pushdef([ac_exeext], ac_build_exeext)dnl
+pushdef([ac_objext], ac_build_objext)dnl
+pushdef([CC], CC_FOR_BUILD)dnl
+pushdef([CPP], CPP_FOR_BUILD)dnl
+pushdef([CFLAGS], CFLAGS_FOR_BUILD)dnl
+pushdef([CPPFLAGS], CPPFLAGS_FOR_BUILD)dnl
+pushdef([LDFLAGS], LDFLAGS_FOR_BUILD)dnl
+pushdef([host], build)dnl
+pushdef([host_alias], build_alias)dnl
+pushdef([host_cpu], build_cpu)dnl
+pushdef([host_vendor], build_vendor)dnl
+pushdef([host_os], build_os)dnl
+pushdef([ac_cv_host], ac_cv_build)dnl
+pushdef([ac_cv_host_alias], ac_cv_build_alias)dnl
+pushdef([ac_cv_host_cpu], ac_cv_build_cpu)dnl
+pushdef([ac_cv_host_vendor], ac_cv_build_vendor)dnl
+pushdef([ac_cv_host_os], ac_cv_build_os)dnl
+pushdef([ac_cpp], ac_build_cpp)dnl
+pushdef([ac_compile], ac_build_compile)dnl
+pushdef([ac_link], ac_build_link)dnl
+
+save_cross_compiling=$cross_compiling
+save_ac_tool_prefix=$ac_tool_prefix
+cross_compiling=no
+ac_tool_prefix=
+
+AC_PROG_CC
+AC_PROG_CPP
+AC_EXEEXT
+
+ac_tool_prefix=$save_ac_tool_prefix
+cross_compiling=$save_cross_compiling
+
+dnl Restore the old definitions
+dnl
+popdef([ac_link])dnl
+popdef([ac_compile])dnl
+popdef([ac_cpp])dnl
+popdef([ac_cv_host_os])dnl
+popdef([ac_cv_host_vendor])dnl
+popdef([ac_cv_host_cpu])dnl
+popdef([ac_cv_host_alias])dnl
+popdef([ac_cv_host])dnl
+popdef([host_os])dnl
+popdef([host_vendor])dnl
+popdef([host_cpu])dnl
+popdef([host_alias])dnl
+popdef([host])dnl
+popdef([LDFLAGS])dnl
+popdef([CPPFLAGS])dnl
+popdef([CFLAGS])dnl
+popdef([CPP])dnl
+popdef([CC])dnl
+popdef([ac_objext])dnl
+popdef([ac_exeext])dnl
+popdef([ac_cv_objext])dnl
+popdef([ac_cv_exeext])dnl
+popdef([ac_cv_prog_cc_g])dnl
+popdef([ac_cv_prog_cc_cross])dnl
+popdef([ac_cv_prog_cc_works])dnl
+popdef([ac_cv_prog_gcc])dnl
+popdef([ac_cv_prog_CPP])dnl
+
+dnl Finally, set Makefile variables
+dnl
+BUILD_EXEEXT=$ac_build_exeext
+BUILD_OBJEXT=$ac_build_objext
+AC_SUBST(BUILD_EXEEXT)dnl
+AC_SUBST(BUILD_OBJEXT)dnl
+AC_SUBST([CFLAGS_FOR_BUILD])dnl
+AC_SUBST([CPPFLAGS_FOR_BUILD])dnl
+AC_SUBST([LDFLAGS_FOR_BUILD])dnl
+])
diff --git a/src/secp256k1/build-aux/m4/bitcoin_secp.m4 b/src/secp256k1/build-aux/m4/bitcoin_secp.m4
index 4a398d6c93..d41bbb6487 100644
--- a/src/secp256k1/build-aux/m4/bitcoin_secp.m4
+++ b/src/secp256k1/build-aux/m4/bitcoin_secp.m4
@@ -16,8 +16,7 @@ AC_MSG_RESULT([$has_64bit_asm])
 
 dnl
 AC_DEFUN([SECP_OPENSSL_CHECK],[
-if test x"$use_pkgconfig" = x"yes"; then
-    : #NOP
+  has_libcrypto=no
   m4_ifdef([PKG_CHECK_MODULES],[
     PKG_CHECK_MODULES([CRYPTO], [libcrypto], [has_libcrypto=yes],[has_libcrypto=no])
     if test x"$has_libcrypto" = x"yes"; then
@@ -27,11 +26,16 @@ if test x"$use_pkgconfig" = x"yes"; then
       LIBS="$TEMP_LIBS"
     fi
   ])
-else
-  AC_CHECK_HEADER(openssl/crypto.h,[AC_CHECK_LIB(crypto, main,[has_libcrypto=yes; CRYPTO_LIBS=-lcrypto; AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])]
-)])
-  LIBS=
-fi
+  if test x$has_libcrypto = xno; then
+    AC_CHECK_HEADER(openssl/crypto.h,[
+      AC_CHECK_LIB(crypto, main,[
+        has_libcrypto=yes
+        CRYPTO_LIBS=-lcrypto
+        AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])
+      ])
+    ])
+    LIBS=
+  fi
 if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then
   AC_MSG_CHECKING(for EC functions in libcrypto)
   AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
diff --git a/src/secp256k1/configure.ac b/src/secp256k1/configure.ac
index 3dc1829516..786d8dcfb9 100644
--- a/src/secp256k1/configure.ac
+++ b/src/secp256k1/configure.ac
@@ -17,25 +17,19 @@ PKG_PROG_PKG_CONFIG
 AC_PATH_TOOL(AR, ar)
 AC_PATH_TOOL(RANLIB, ranlib)
 AC_PATH_TOOL(STRIP, strip)
+AX_PROG_CC_FOR_BUILD
 
 if test "x$CFLAGS" = "x"; then
   CFLAGS="-O3 -g"
 fi
 
+AM_PROG_CC_C_O
+
 AC_PROG_CC_C89
 if test x"$ac_cv_prog_cc_c89" = x"no"; then
   AC_MSG_ERROR([c89 compiler support required])
 fi
 
-case $host in
-  *mingw*)
-     use_pkgconfig=no
-     ;;
-   *)
-     use_pkgconfig=yes
-     ;;
-esac
-
 case $host_os in
   *darwin*)
      if  test x$cross_compiling != xyes; then
@@ -80,6 +74,14 @@ AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
       CFLAGS="$saved_CFLAGS"
     ])
 
+saved_CFLAGS="$CFLAGS"
+CFLAGS="$CFLAGS -fvisibility=hidden"
+AC_MSG_CHECKING([if ${CC} supports -fvisibility=hidden])
+AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])],
+    [ AC_MSG_RESULT([yes]) ],
+    [ AC_MSG_RESULT([no])
+      CFLAGS="$saved_CFLAGS"
+    ])
 
 AC_ARG_ENABLE(benchmark,
     AS_HELP_STRING([--enable-benchmark],[compile benchmark (default is no)]),
@@ -95,6 +97,26 @@ AC_ARG_ENABLE(endomorphism,
     AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
     [use_endomorphism=$enableval],
     [use_endomorphism=no])
+    
+AC_ARG_ENABLE(ecmult_static_precomputation,
+    AS_HELP_STRING([--enable-ecmult-static-precomputation],[enable precomputed ecmult table for signing (default is yes)]),
+    [use_ecmult_static_precomputation=$enableval],
+    [use_ecmult_static_precomputation=yes])
+
+AC_ARG_ENABLE(module_ecdh,
+    AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation (default is no)]),
+    [enable_module_ecdh=$enableval],
+    [enable_module_ecdh=no])
+
+AC_ARG_ENABLE(module_schnorr,
+    AS_HELP_STRING([--enable-module-schnorr],[enable Schnorr signature module (default is no)]),
+    [enable_module_schnorr=$enableval],
+    [enable_module_schnorr=no])
+
+AC_ARG_ENABLE(module_recovery,
+    AS_HELP_STRING([--enable-module-recovery],[enable ECDSA pubkey recovery module (default is no)]),
+    [enable_module_recovery=$enableval],
+    [enable_module_recovery=no])
 
 AC_ARG_WITH([field], [AS_HELP_STRING([--with-field=64bit|32bit|auto],
 [Specify Field Implementation. Default is auto])],[req_field=$withval], [req_field=auto])
@@ -305,6 +327,22 @@ if test x"$use_endomorphism" = x"yes"; then
   AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization])
 fi
 
+if test x"$use_ecmult_static_precomputation" = x"yes"; then
+  AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table])
+fi
+
+if test x"$enable_module_ecdh" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_ECDH, 1, [Define this symbol to enable the ECDH module])
+fi
+
+if test x"$enable_module_schnorr" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_SCHNORR, 1, [Define this symbol to enable the Schnorr signature module])
+fi
+
+if test x"$enable_module_recovery" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_RECOVERY, 1, [Define this symbol to enable the ECDSA pubkey recovery module])
+fi
+
 AC_C_BIGENDIAN()
 
 AC_MSG_NOTICE([Using assembly optimizations: $set_asm])
@@ -312,6 +350,10 @@ AC_MSG_NOTICE([Using field implementation: $set_field])
 AC_MSG_NOTICE([Using bignum implementation: $set_bignum])
 AC_MSG_NOTICE([Using scalar implementation: $set_scalar])
 AC_MSG_NOTICE([Using endomorphism optimizations: $use_endomorphism])
+AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
+
+AC_MSG_NOTICE([Building Schnorr signatures module: $enable_module_schnorr])
+AC_MSG_NOTICE([Building ECDSA pubkey recovery module: $enable_module_recovery])
 
 AC_CONFIG_HEADERS([src/libsecp256k1-config.h])
 AC_CONFIG_FILES([Makefile libsecp256k1.pc])
@@ -321,6 +363,10 @@ AC_SUBST(SECP_TEST_LIBS)
 AC_SUBST(SECP_TEST_INCLUDES)
 AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
 AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
+AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$use_ecmult_static_precomputation" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_SCHNORR], [test x"$enable_module_schnorr" = x"yes"])
+AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"])
 
 dnl make sure nothing new is exported so that we don't break the cache
 PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH"
diff --git a/src/secp256k1/contrib/lax_der_parsing.c b/src/secp256k1/contrib/lax_der_parsing.c
new file mode 100644
index 0000000000..5b141a9948
--- /dev/null
+++ b/src/secp256k1/contrib/lax_der_parsing.c
@@ -0,0 +1,150 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+#include <secp256k1.h>
+
+#include "lax_der_parsing.h"
+
+int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) {
+    size_t rpos, rlen, spos, slen;
+    size_t pos = 0;
+    size_t lenbyte;
+    unsigned char tmpsig[64] = {0};
+    int overflow = 0;
+
+    /* Hack to initialize sig with a correctly-parsed but invalid signature. */
+    secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+
+    /* Sequence tag byte */
+    if (pos == inputlen || input[pos] != 0x30) {
+        return 0;
+    }
+    pos++;
+
+    /* Sequence length bytes */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        pos += lenbyte;
+    }
+
+    /* Integer tag byte for R */
+    if (pos == inputlen || input[pos] != 0x02) {
+        return 0;
+    }
+    pos++;
+
+    /* Integer length for R */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        while (lenbyte > 0 && input[pos] == 0) {
+            pos++;
+            lenbyte--;
+        }
+        if (lenbyte >= sizeof(size_t)) {
+            return 0;
+        }
+        rlen = 0;
+        while (lenbyte > 0) {
+            rlen = (rlen << 8) + input[pos];
+            pos++;
+            lenbyte--;
+        }
+    } else {
+        rlen = lenbyte;
+    }
+    if (rlen > inputlen - pos) {
+        return 0;
+    }
+    rpos = pos;
+    pos += rlen;
+
+    /* Integer tag byte for S */
+    if (pos == inputlen || input[pos] != 0x02) {
+        return 0;
+    }
+    pos++;
+
+    /* Integer length for S */
+    if (pos == inputlen) {
+        return 0;
+    }
+    lenbyte = input[pos++];
+    if (lenbyte & 0x80) {
+        lenbyte -= 0x80;
+        if (pos + lenbyte > inputlen) {
+            return 0;
+        }
+        while (lenbyte > 0 && input[pos] == 0) {
+            pos++;
+            lenbyte--;
+        }
+        if (lenbyte >= sizeof(size_t)) {
+            return 0;
+        }
+        slen = 0;
+        while (lenbyte > 0) {
+            slen = (slen << 8) + input[pos];
+            pos++;
+            lenbyte--;
+        }
+    } else {
+        slen = lenbyte;
+    }
+    if (slen > inputlen - pos) {
+        return 0;
+    }
+    spos = pos;
+    pos += slen;
+
+    /* Ignore leading zeroes in R */
+    while (rlen > 0 && input[rpos] == 0) {
+        rlen--;
+        rpos++;
+    }
+    /* Copy R value */
+    if (rlen > 32) {
+        overflow = 1;
+    } else {
+        memcpy(tmpsig + 32 - rlen, input + rpos, rlen);
+    }
+
+    /* Ignore leading zeroes in S */
+    while (slen > 0 && input[spos] == 0) {
+        slen--;
+        spos++;
+    }
+    /* Copy S value */
+    if (slen > 32) {
+        overflow = 1;
+    } else {
+        memcpy(tmpsig + 64 - slen, input + spos, slen);
+    }
+
+    if (!overflow) {
+        overflow = !secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+    }
+    if (overflow) {
+        memset(tmpsig, 0, 64);
+        secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig);
+    }
+    return 1;
+}
+
diff --git a/src/secp256k1/contrib/lax_der_parsing.h b/src/secp256k1/contrib/lax_der_parsing.h
new file mode 100644
index 0000000000..6d27871a7c
--- /dev/null
+++ b/src/secp256k1/contrib/lax_der_parsing.h
@@ -0,0 +1,91 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/****
+ * Please do not link this file directly. It is not part of the libsecp256k1
+ * project and does not promise any stability in its API, functionality or
+ * presence. Projects which use this code should instead copy this header
+ * and its accompanying .c file directly into their codebase.
+ ****/
+
+/* This file defines a function that parses DER with various errors and
+ * violations. This is not a part of the library itself, because the allowed
+ * violations are chosen arbitrarily and do not follow or establish any
+ * standard.
+ *
+ * In many places it matters that different implementations do not only accept
+ * the same set of valid signatures, but also reject the same set of signatures.
+ * The only means to accomplish that is by strictly obeying a standard, and not
+ * accepting anything else.
+ *
+ * Nonetheless, sometimes there is a need for compatibility with systems that
+ * use signatures which do not strictly obey DER. The snippet below shows how
+ * certain violations are easily supported. You may need to adapt it.
+ *
+ * Do not use this for new systems. Use well-defined DER or compact signatures
+ * instead if you have the choice (see secp256k1_ecdsa_signature_parse_der and
+ * secp256k1_ecdsa_signature_parse_compact).
+ *
+ * The supported violations are:
+ * - All numbers are parsed as nonnegative integers, even though X.609-0207
+ *   section 8.3.3 specifies that integers are always encoded as two's
+ *   complement.
+ * - Integers can have length 0, even though section 8.3.1 says they can't.
+ * - Integers with overly long padding are accepted, violation section
+ *   8.3.2.
+ * - 127-byte long length descriptors are accepted, even though section
+ *   8.1.3.5.c says that they are not.
+ * - Trailing garbage data inside or after the signature is ignored.
+ * - The length descriptor of the sequence is ignored.
+ *
+ * Compared to for example OpenSSL, many violations are NOT supported:
+ * - Using overly long tag descriptors for the sequence or integers inside,
+ *   violating section 8.1.2.2.
+ * - Encoding primitive integers as constructed values, violating section
+ *   8.3.1.
+ */
+
+#ifndef _SECP256K1_CONTRIB_LAX_DER_PARSING_H_
+#define _SECP256K1_CONTRIB_LAX_DER_PARSING_H_
+
+#include <secp256k1.h>
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Parse a signature in "lax DER" format
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input:    a pointer to the signature to be parsed
+ *        inputlen: the length of the array pointed to be input
+ *
+ *  This function will accept any valid DER encoded signature, even if the
+ *  encoded numbers are out of range. In addition, it will accept signatures
+ *  which violate the DER spec in various ways. Its purpose is to allow
+ *  validation of the Bitcoin blockchain, which includes non-DER signatures
+ *  from before the network rules were updated to enforce DER. Note that
+ *  the set of supported violations is a strict subset of what OpenSSL will
+ *  accept.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature validation with it is
+ *  guaranteed to fail for every message and public key.
+ */
+int ecdsa_signature_parse_der_lax(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/src/secp256k1/contrib/lax_der_privatekey_parsing.c b/src/secp256k1/contrib/lax_der_privatekey_parsing.c
new file mode 100644
index 0000000000..c2e63b4b8d
--- /dev/null
+++ b/src/secp256k1/contrib/lax_der_privatekey_parsing.c
@@ -0,0 +1,113 @@
+/**********************************************************************
+ * Copyright (c) 2014, 2015 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+#include <secp256k1.h>
+
+#include "lax_der_privatekey_parsing.h"
+
+int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *privkey, size_t privkeylen) {
+    const unsigned char *end = privkey + privkeylen;
+    int lenb = 0;
+    int len = 0;
+    memset(out32, 0, 32);
+    /* sequence header */
+    if (end < privkey+1 || *privkey != 0x30) {
+        return 0;
+    }
+    privkey++;
+    /* sequence length constructor */
+    if (end < privkey+1 || !(*privkey & 0x80)) {
+        return 0;
+    }
+    lenb = *privkey & ~0x80; privkey++;
+    if (lenb < 1 || lenb > 2) {
+        return 0;
+    }
+    if (end < privkey+lenb) {
+        return 0;
+    }
+    /* sequence length */
+    len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0);
+    privkey += lenb;
+    if (end < privkey+len) {
+        return 0;
+    }
+    /* sequence element 0: version number (=1) */
+    if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) {
+        return 0;
+    }
+    privkey += 3;
+    /* sequence element 1: octet string, up to 32 bytes */
+    if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) {
+        return 0;
+    }
+    memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]);
+    if (!secp256k1_ec_seckey_verify(ctx, out32)) {
+        memset(out32, 0, 32);
+        return 0;
+    }
+    return 1;
+}
+
+int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *key32, int compressed) {
+    secp256k1_pubkey pubkey;
+    size_t pubkeylen = 0;
+    if (!secp256k1_ec_pubkey_create(ctx, &pubkey, key32)) {
+        *privkeylen = 0;
+        return 0;
+    }
+    if (compressed) {
+        static const unsigned char begin[] = {
+            0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20
+        };
+        static const unsigned char middle[] = {
+            0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
+            0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
+            0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
+            0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
+            0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
+            0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00
+        };
+        unsigned char *ptr = privkey;
+        memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
+        memcpy(ptr, key32, 32); ptr += 32;
+        memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
+        pubkeylen = 33;
+        secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED);
+        ptr += pubkeylen;
+        *privkeylen = ptr - privkey;
+    } else {
+        static const unsigned char begin[] = {
+            0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20
+        };
+        static const unsigned char middle[] = {
+            0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
+            0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
+            0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
+            0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
+            0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11,
+            0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10,
+            0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+            0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
+            0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00
+        };
+        unsigned char *ptr = privkey;
+        memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
+        memcpy(ptr, key32, 32); ptr += 32;
+        memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
+        pubkeylen = 65;
+        secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_UNCOMPRESSED);
+        ptr += pubkeylen;
+        *privkeylen = ptr - privkey;
+    }
+    return 1;
+}
diff --git a/src/secp256k1/contrib/lax_der_privatekey_parsing.h b/src/secp256k1/contrib/lax_der_privatekey_parsing.h
new file mode 100644
index 0000000000..2fd088f8ab
--- /dev/null
+++ b/src/secp256k1/contrib/lax_der_privatekey_parsing.h
@@ -0,0 +1,90 @@
+/**********************************************************************
+ * Copyright (c) 2014, 2015 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/****
+ * Please do not link this file directly. It is not part of the libsecp256k1
+ * project and does not promise any stability in its API, functionality or
+ * presence. Projects which use this code should instead copy this header
+ * and its accompanying .c file directly into their codebase.
+ ****/
+
+/* This file contains code snippets that parse DER private keys with
+ * various errors and violations.  This is not a part of the library
+ * itself, because the allowed violations are chosen arbitrarily and
+ * do not follow or establish any standard.
+ *
+ * It also contains code to serialize private keys in a compatible
+ * manner.
+ *
+ * These functions are meant for compatibility with applications
+ * that require BER encoded keys. When working with secp256k1-specific
+ * code, the simple 32-byte private keys normally used by the
+ * library are sufficient.
+ */
+
+#ifndef _SECP256K1_CONTRIB_BER_PRIVATEKEY_H_
+#define _SECP256K1_CONTRIB_BER_PRIVATEKEY_H_
+
+#include <secp256k1.h>
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Export a private key in DER format.
+ *
+ *  Returns: 1 if the private key was valid.
+ *  Args: ctx:        pointer to a context object, initialized for signing (cannot
+ *                    be NULL)
+ *  Out: privkey:     pointer to an array for storing the private key in BER.
+ *                    Should have space for 279 bytes, and cannot be NULL.
+ *       privkeylen:  Pointer to an int where the length of the private key in
+ *                    privkey will be stored.
+ *  In:  seckey:      pointer to a 32-byte secret key to export.
+ *       compressed:  1 if the key should be exported in
+ *                    compressed format, 0 otherwise
+ *
+ *  This function is purely meant for compatibility with applications that
+ *  require BER encoded keys. When working with secp256k1-specific code, the
+ *  simple 32-byte private keys are sufficient.
+ *
+ *  Note that this function does not guarantee correct DER output. It is
+ *  guaranteed to be parsable by secp256k1_ec_privkey_import_der
+ */
+SECP256K1_WARN_UNUSED_RESULT int ec_privkey_export_der(
+    const secp256k1_context* ctx,
+    unsigned char *privkey,
+    size_t *privkeylen,
+    const unsigned char *seckey,
+    int compressed
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Import a private key in DER format.
+ * Returns: 1 if a private key was extracted.
+ * Args: ctx:        pointer to a context object (cannot be NULL).
+ * Out:  seckey:     pointer to a 32-byte array for storing the private key.
+ *                   (cannot be NULL).
+ * In:   privkey:    pointer to a private key in DER format (cannot be NULL).
+ *       privkeylen: length of the DER private key pointed to be privkey.
+ *
+ * This function will accept more than just strict DER, and even allow some BER
+ * violations. The public key stored inside the DER-encoded private key is not
+ * verified for correctness, nor are the curve parameters. Use this function
+ * only if you know in advance it is supposed to contain a secp256k1 private
+ * key.
+ */
+SECP256K1_WARN_UNUSED_RESULT int ec_privkey_import_der(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *privkey,
+    size_t privkeylen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/src/secp256k1/include/secp256k1.h b/src/secp256k1/include/secp256k1.h
index 06afd4c65b..7145dbcc54 100644
--- a/src/secp256k1/include/secp256k1.h
+++ b/src/secp256k1/include/secp256k1.h
@@ -5,6 +5,99 @@
 extern "C" {
 # endif
 
+#include <stddef.h>
+
+/* These rules specify the order of arguments in API calls:
+ *
+ * 1. Context pointers go first, followed by output arguments, combined
+ *    output/input arguments, and finally input-only arguments.
+ * 2. Array lengths always immediately the follow the argument whose length
+ *    they describe, even if this violates rule 1.
+ * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated
+ *    later go first. This means: signatures, public nonces, private nonces,
+ *    messages, public keys, secret keys, tweaks.
+ * 4. Arguments that are not data pointers go last, from more complex to less
+ *    complex: function pointers, algorithm names, messages, void pointers,
+ *    counts, flags, booleans.
+ * 5. Opaque data pointers follow the function pointer they are to be passed to.
+ */
+
+/** Opaque data structure that holds context information (precomputed tables etc.).
+ *
+ *  The purpose of context structures is to cache large precomputed data tables
+ *  that are expensive to construct, and also to maintain the randomization data
+ *  for blinding.
+ *
+ *  Do not create a new context object for each operation, as construction is
+ *  far slower than all other API calls (~100 times slower than an ECDSA
+ *  verification).
+ *
+ *  A constructed context can safely be used from multiple threads
+ *  simultaneously, but API call that take a non-const pointer to a context
+ *  need exclusive access to it. In particular this is the case for
+ *  secp256k1_context_destroy and secp256k1_context_randomize.
+ *
+ *  Regarding randomization, either do it once at creation time (in which case
+ *  you do not need any locking for the other calls), or use a read-write lock.
+ */
+typedef struct secp256k1_context_struct secp256k1_context;
+
+/** Opaque data structure that holds a parsed and valid public key.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse.
+ *
+ *  Furthermore, it is guaranteed that identical public keys (ignoring
+ *  compression) will have identical representation, so they can be memcmp'ed.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_pubkey;
+
+/** Opaque data structured that holds a parsed ECDSA signature.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_serialize_* functions.
+ *
+ *  Furthermore, it is guaranteed to identical signatures will have identical
+ *  representation, so they can be memcmp'ed.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_ecdsa_signature;
+
+/** A pointer to a function to deterministically generate a nonce.
+ *
+ * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail.
+ * Out:     nonce32:   pointer to a 32-byte array to be filled by the function.
+ * In:      msg32:     the 32-byte message hash being verified (will not be NULL)
+ *          key32:     pointer to a 32-byte secret key (will not be NULL)
+ *          algo16:    pointer to a 16-byte array describing the signature
+ *                     algorithm (will be NULL for ECDSA for compatibility).
+ *          data:      Arbitrary data pointer that is passed through.
+ *          attempt:   how many iterations we have tried to find a nonce.
+ *                     This will almost always be 0, but different attempt values
+ *                     are required to result in a different nonce.
+ *
+ * Except for test cases, this function should compute some cryptographic hash of
+ * the message, the algorithm, the key and the attempt.
+ */
+typedef int (*secp256k1_nonce_function)(
+    unsigned char *nonce32,
+    const unsigned char *msg32,
+    const unsigned char *key32,
+    const unsigned char *algo16,
+    void *data,
+    unsigned int attempt
+);
+
 # if !defined(SECP256K1_GNUC_PREREQ)
 #  if defined(__GNUC__)&&defined(__GNUC_MINOR__)
 #   define SECP256K1_GNUC_PREREQ(_maj,_min) \
@@ -26,6 +119,20 @@ extern "C" {
 #  define SECP256K1_INLINE inline
 # endif
 
+#ifndef SECP256K1_API
+# if defined(_WIN32)
+#  ifdef SECP256K1_BUILD
+#   define SECP256K1_API __declspec(dllexport)
+#  else
+#   define SECP256K1_API
+#  endif
+# elif defined(__GNUC__) && defined(SECP256K1_BUILD)
+#  define SECP256K1_API __attribute__ ((visibility ("default")))
+# else
+#  define SECP256K1_API
+# endif
+#endif
+
 /**Warning attributes
   * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
   * some paranoid null checks. */
@@ -40,305 +147,434 @@ extern "C" {
 #  define SECP256K1_ARG_NONNULL(_x)
 # endif
 
-/** Opaque data structure that holds context information (precomputed tables etc.).
- *  Only functions that take a pointer to a non-const context require exclusive
- *  access to it. Multiple functions that take a pointer to a const context may
- *  run simultaneously.
- */
-typedef struct secp256k1_context_struct secp256k1_context_t;
+/** All flags' lower 8 bits indicate what they're for. Do not use directly. */
+#define SECP256K1_FLAGS_TYPE_MASK ((1 << 8) - 1)
+#define SECP256K1_FLAGS_TYPE_CONTEXT (1 << 0)
+#define SECP256K1_FLAGS_TYPE_COMPRESSION (1 << 1)
+/** The higher bits contain the actual data. Do not use directly. */
+#define SECP256K1_FLAGS_BIT_CONTEXT_VERIFY (1 << 8)
+#define SECP256K1_FLAGS_BIT_CONTEXT_SIGN (1 << 9)
+#define SECP256K1_FLAGS_BIT_COMPRESSION (1 << 8)
 
 /** Flags to pass to secp256k1_context_create. */
-# define SECP256K1_CONTEXT_VERIFY (1 << 0)
-# define SECP256K1_CONTEXT_SIGN   (1 << 1)
+#define SECP256K1_CONTEXT_VERIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_VERIFY)
+#define SECP256K1_CONTEXT_SIGN (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_SIGN)
+#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT)
+
+/** Flag to pass to secp256k1_ec_pubkey_serialize and secp256k1_ec_privkey_export. */
+#define SECP256K1_EC_COMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION | SECP256K1_FLAGS_BIT_COMPRESSION)
+#define SECP256K1_EC_UNCOMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION)
 
 /** Create a secp256k1 context object.
+ *
  *  Returns: a newly created context object.
  *  In:      flags: which parts of the context to initialize.
  */
-secp256k1_context_t* secp256k1_context_create(
-  int flags
+SECP256K1_API secp256k1_context* secp256k1_context_create(
+    unsigned int flags
 ) SECP256K1_WARN_UNUSED_RESULT;
 
 /** Copies a secp256k1 context object.
+ *
  *  Returns: a newly created context object.
- *  In:      ctx: an existing context to copy
+ *  Args:    ctx: an existing context to copy (cannot be NULL)
  */
-secp256k1_context_t* secp256k1_context_clone(
-  const secp256k1_context_t* ctx
-) SECP256K1_WARN_UNUSED_RESULT;
+SECP256K1_API secp256k1_context* secp256k1_context_clone(
+    const secp256k1_context* ctx
+) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT;
 
 /** Destroy a secp256k1 context object.
+ *
  *  The context pointer may not be used afterwards.
+ *  Args:   ctx: an existing context to destroy (cannot be NULL)
+ */
+SECP256K1_API void secp256k1_context_destroy(
+    secp256k1_context* ctx
+);
+
+/** Set a callback function to be called when an illegal argument is passed to
+ *  an API call. It will only trigger for violations that are mentioned
+ *  explicitly in the header.
+ *
+ *  The philosophy is that these shouldn't be dealt with through a
+ *  specific return value, as calling code should not have branches to deal with
+ *  the case that this code itself is broken.
+ *
+ *  On the other hand, during debug stage, one would want to be informed about
+ *  such mistakes, and the default (crashing) may be inadvisable.
+ *  When this callback is triggered, the API function called is guaranteed not
+ *  to cause a crash, though its return value and output arguments are
+ *  undefined.
+ *
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   fun:  a pointer to a function to call when an illegal argument is
+ *              passed to the API, taking a message and an opaque pointer
+ *              (NULL restores a default handler that calls abort).
+ *        data: the opaque pointer to pass to fun above.
  */
-void secp256k1_context_destroy(
-  secp256k1_context_t* ctx
+SECP256K1_API void secp256k1_context_set_illegal_callback(
+    secp256k1_context* ctx,
+    void (*fun)(const char* message, void* data),
+    const void* data
 ) SECP256K1_ARG_NONNULL(1);
 
+/** Set a callback function to be called when an internal consistency check
+ *  fails. The default is crashing.
+ *
+ *  This can only trigger in case of a hardware failure, miscompilation,
+ *  memory corruption, serious bug in the library, or other error would can
+ *  otherwise result in undefined behaviour. It will not trigger due to mere
+ *  incorrect usage of the API (see secp256k1_context_set_illegal_callback
+ *  for that). After this callback returns, anything may happen, including
+ *  crashing.
+ *
+ *  Args: ctx:  an existing context object (cannot be NULL)
+ *  In:   fun:  a pointer to a function to call when an internal error occurs,
+ *              taking a message and an opaque pointer (NULL restores a default
+ *              handler that calls abort).
+ *        data: the opaque pointer to pass to fun above.
+ */
+SECP256K1_API void secp256k1_context_set_error_callback(
+    secp256k1_context* ctx,
+    void (*fun)(const char* message, void* data),
+    const void* data
+) SECP256K1_ARG_NONNULL(1);
+
+/** Parse a variable-length public key into the pubkey object.
+ *
+ *  Returns: 1 if the public key was fully valid.
+ *           0 if the public key could not be parsed or is invalid.
+ *  Args: ctx:      a secp256k1 context object.
+ *  Out:  pubkey:   pointer to a pubkey object. If 1 is returned, it is set to a
+ *                  parsed version of input. If not, its value is undefined.
+ *  In:   input:    pointer to a serialized public key
+ *        inputlen: length of the array pointed to by input
+ *
+ *  This function supports parsing compressed (33 bytes, header byte 0x02 or
+ *  0x03), uncompressed (65 bytes, header byte 0x04), or hybrid (65 bytes, header
+ *  byte 0x06 or 0x07) format public keys.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_parse(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey* pubkey,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize a pubkey object into a serialized byte sequence.
+ *
+ *  Returns: 1 always.
+ *  Args:   ctx:        a secp256k1 context object.
+ *  Out:    output:     a pointer to a 65-byte (if compressed==0) or 33-byte (if
+ *                      compressed==1) byte array to place the serialized key
+ *                      in.
+ *  In/Out: outputlen:  a pointer to an integer which is initially set to the
+ *                      size of output, and is overwritten with the written
+ *                      size.
+ *  In:     pubkey:     a pointer to a secp256k1_pubkey containing an
+ *                      initialized public key.
+ *          flags:      SECP256K1_EC_COMPRESSED if serialization should be in
+ *                      compressed format, otherwise SECP256K1_EC_UNCOMPRESSED.
+ */
+SECP256K1_API int secp256k1_ec_pubkey_serialize(
+    const secp256k1_context* ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_pubkey* pubkey,
+    unsigned int flags
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Parse an ECDSA signature in compact (64 bytes) format.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input64:  a pointer to the 64-byte array to parse
+ *
+ *  The signature must consist of a 32-byte big endian R value, followed by a
+ *  32-byte big endian S value. If R or S fall outside of [0..order-1], the
+ *  encoding is invalid. R and S with value 0 are allowed in the encoding.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or R or
+ *  S are zero, the resulting sig value is guaranteed to fail validation for any
+ *  message and public key.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_compact(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input64
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse a DER ECDSA signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  sig:      a pointer to a signature object
+ *  In:   input:    a pointer to the signature to be parsed
+ *        inputlen: the length of the array pointed to be input
+ *
+ *  This function will accept any valid DER encoded signature, even if the
+ *  encoded numbers are out of range.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature validation with it is
+ *  guaranteed to fail for every message and public key.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_der(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in DER format.
+ *
+ *  Returns: 1 if enough space was available to serialize, 0 otherwise
+ *  Args:   ctx:       a secp256k1 context object
+ *  Out:    output:    a pointer to an array to store the DER serialization
+ *  In/Out: outputlen: a pointer to a length integer. Initially, this integer
+ *                     should be set to the length of output. After the call
+ *                     it will be set to the length of the serialization (even
+ *                     if 0 was returned).
+ *  In:     sig:       a pointer to an initialized signature object
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_der(
+    const secp256k1_context* ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_ecdsa_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Serialize an ECDSA signature in compact (64 byte) format.
+ *
+ *  Returns: 1
+ *  Args:   ctx:       a secp256k1 context object
+ *  Out:    output64:  a pointer to a 64-byte array to store the compact serialization
+ *  In:     sig:       a pointer to an initialized signature object
+ *
+ *  See secp256k1_ecdsa_signature_parse_compact for details about the encoding.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact(
+    const secp256k1_context* ctx,
+    unsigned char *output64,
+    const secp256k1_ecdsa_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
 /** Verify an ECDSA signature.
+ *
  *  Returns: 1: correct signature
- *           0: incorrect signature
- *          -1: invalid public key
- *          -2: invalid signature
- * In:       ctx:       a secp256k1 context object, initialized for verification.
+ *           0: incorrect or unparseable signature
+ *  Args:    ctx:       a secp256k1 context object, initialized for verification.
+ *  In:      sig:       the signature being verified (cannot be NULL)
  *           msg32:     the 32-byte message hash being verified (cannot be NULL)
- *           sig:       the signature being verified (cannot be NULL)
- *           siglen:    the length of the signature
- *           pubkey:    the public key to verify with (cannot be NULL)
- *           pubkeylen: the length of pubkey
+ *           pubkey:    pointer to an initialized public key to verify with (cannot be NULL)
+ *
+ * To avoid accepting malleable signatures, only ECDSA signatures in lower-S
+ * form are accepted.
+ *
+ * If you need to accept ECDSA signatures from sources that do not obey this
+ * rule, apply secp256k1_ecdsa_signature_normalize to the signature prior to
+ * validation, but be aware that doing so results in malleable signatures.
+ *
+ * For details, see the comments for that function.
  */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
-  const secp256k1_context_t* ctx,
-  const unsigned char *msg32,
-  const unsigned char *sig,
-  int siglen,
-  const unsigned char *pubkey,
-  int pubkeylen
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(5);
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
+    const secp256k1_context* ctx,
+    const secp256k1_ecdsa_signature *sig,
+    const unsigned char *msg32,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
 
-/** A pointer to a function to deterministically generate a nonce.
- * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail.
- * In:      msg32:     the 32-byte message hash being verified (will not be NULL)
- *          key32:     pointer to a 32-byte secret key (will not be NULL)
- *          attempt:   how many iterations we have tried to find a nonce.
- *                     This will almost always be 0, but different attempt values
- *                     are required to result in a different nonce.
- *          data:      Arbitrary data pointer that is passed through.
- * Out:     nonce32:   pointer to a 32-byte array to be filled by the function.
- * Except for test cases, this function should compute some cryptographic hash of
- * the message, the key and the attempt.
+/** Convert a signature to a normalized lower-S form.
+ *
+ *  Returns: 1 if sigin was not normalized, 0 if it already was.
+ *  Args: ctx:    a secp256k1 context object
+ *  Out:  sigout: a pointer to a signature to fill with the normalized form,
+ *                or copy if the input was already normalized. (can be NULL if
+ *                you're only interested in whether the input was already
+ *                normalized).
+ *  In:   sigin:  a pointer to a signature to check/normalize (cannot be NULL,
+ *                can be identical to sigout)
+ *
+ *  With ECDSA a third-party can forge a second distinct signature of the same
+ *  message, given a single initial signature, but without knowing the key. This
+ *  is done by negating the S value modulo the order of the curve, 'flipping'
+ *  the sign of the random point R which is not included in the signature.
+ *
+ *  Forgery of the same message isn't universally problematic, but in systems
+ *  where message malleability or uniqueness of signatures is important this can
+ *  cause issues. This forgery can be blocked by all verifiers forcing signers
+ *  to use a normalized form.
+ *
+ *  The lower-S form reduces the size of signatures slightly on average when
+ *  variable length encodings (such as DER) are used and is cheap to verify,
+ *  making it a good choice. Security of always using lower-S is assured because
+ *  anyone can trivially modify a signature after the fact to enforce this
+ *  property anyway.
+ *
+ *  The lower S value is always between 0x1 and
+ *  0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
+ *  inclusive.
+ *
+ *  No other forms of ECDSA malleability are known and none seem likely, but
+ *  there is no formal proof that ECDSA, even with this additional restriction,
+ *  is free of other malleability. Commonly used serialization schemes will also
+ *  accept various non-unique encodings, so care should be taken when this
+ *  property is required for an application.
+ *
+ *  The secp256k1_ecdsa_sign function will by default create signatures in the
+ *  lower-S form, and secp256k1_ecdsa_verify will not accept others. In case
+ *  signatures come from a system that cannot enforce this property,
+ *  secp256k1_ecdsa_signature_normalize must be called before verification.
  */
-typedef int (*secp256k1_nonce_function_t)(
-  unsigned char *nonce32,
-  const unsigned char *msg32,
-  const unsigned char *key32,
-  unsigned int attempt,
-  const void *data
-);
+SECP256K1_API int secp256k1_ecdsa_signature_normalize(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature *sigout,
+    const secp256k1_ecdsa_signature *sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3);
 
 /** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function.
  * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
  * extra entropy.
  */
-extern const secp256k1_nonce_function_t secp256k1_nonce_function_rfc6979;
+SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_rfc6979;
 
 /** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */
-extern const secp256k1_nonce_function_t secp256k1_nonce_function_default;
-
+SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_default;
 
 /** Create an ECDSA signature.
+ *
  *  Returns: 1: signature created
- *           0: the nonce generation function failed, the private key was invalid, or there is not
- *              enough space in the signature (as indicated by siglen).
- *  In:      ctx:    pointer to a context object, initialized for signing (cannot be NULL)
- *           msg32:  the 32-byte message hash being signed (cannot be NULL)
- *           seckey: pointer to a 32-byte secret key (cannot be NULL)
- *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
- *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
+ *           0: the nonce generation function failed, or the private key was invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing (cannot be NULL)
  *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
- *  In/Out:  siglen: pointer to an int with the length of sig, which will be updated
- *                   to contain the actual signature length (<=72).
- *
- * The sig always has an s value in the lower half of the range (From 0x1
- * to 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
- * inclusive), unlike many other implementations.
- * With ECDSA a third-party can can forge a second distinct signature
- * of the same message given a single initial signature without knowing
- * the key by setting s to its additive inverse mod-order, 'flipping' the
- * sign of the random point R which is not included in the signature.
- * Since the forgery is of the same message this isn't universally
- * problematic, but in systems where message malleability or uniqueness
- * of signatures is important this can cause issues.  This forgery can be
- * blocked by all verifiers forcing signers to use a canonical form. The
- * lower-S form reduces the size of signatures slightly on average when
- * variable length encodings (such as DER) are used and is cheap to
- * verify, making it a good choice. Security of always using lower-S is
- * assured because anyone can trivially modify a signature after the
- * fact to enforce this property.  Adjusting it inside the signing
- * function avoids the need to re-serialize or have curve specific
- * constants outside of the library.  By always using a canonical form
- * even in applications where it isn't needed it becomes possible to
- * impose a requirement later if a need is discovered.
- * No other forms of ECDSA malleability are known and none seem likely,
- * but there is no formal proof that ECDSA, even with this additional
- * restriction, is free of other malleability.  Commonly used serialization
- * schemes will also accept various non-unique encodings, so care should
- * be taken when this property is required for an application.
- */
-int secp256k1_ecdsa_sign(
-  const secp256k1_context_t* ctx,
-  const unsigned char *msg32,
-  unsigned char *sig,
-  int *siglen,
-  const unsigned char *seckey,
-  secp256k1_nonce_function_t noncefp,
-  const void *ndata
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
-
-/** Create a compact ECDSA signature (64 byte + recovery id).
- *  Returns: 1: signature created
- *           0: the nonce generation function failed, or the secret key was invalid.
- *  In:      ctx:    pointer to a context object, initialized for signing (cannot be NULL)
- *           msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
  *           seckey: pointer to a 32-byte secret key (cannot be NULL)
  *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
  *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
- *  Out:     sig:    pointer to a 64-byte array where the signature will be placed (cannot be NULL)
- *                   In case 0 is returned, the returned signature length will be zero.
- *           recid:  pointer to an int, which will be updated to contain the recovery id (can be NULL)
+ *
+ * The created signature is always in lower-S form. See
+ * secp256k1_ecdsa_signature_normalize for more details.
  */
-int secp256k1_ecdsa_sign_compact(
-  const secp256k1_context_t* ctx,
-  const unsigned char *msg32,
-  unsigned char *sig64,
-  const unsigned char *seckey,
-  secp256k1_nonce_function_t noncefp,
-  const void *ndata,
-  int *recid
+SECP256K1_API int secp256k1_ecdsa_sign(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature *sig,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
 
-/** Recover an ECDSA public key from a compact signature.
- *  Returns: 1: public key successfully recovered (which guarantees a correct signature).
- *           0: otherwise.
- *  In:      ctx:        pointer to a context object, initialized for verification (cannot be NULL)
- *           msg32:      the 32-byte message hash assumed to be signed (cannot be NULL)
- *           sig64:      signature as 64 byte array (cannot be NULL)
- *           compressed: whether to recover a compressed or uncompressed pubkey
- *           recid:      the recovery id (0-3, as returned by ecdsa_sign_compact)
- *  Out:     pubkey:     pointer to a 33 or 65 byte array to put the pubkey (cannot be NULL)
- *           pubkeylen:  pointer to an int that will contain the pubkey length (cannot be NULL)
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover_compact(
-  const secp256k1_context_t* ctx,
-  const unsigned char *msg32,
-  const unsigned char *sig64,
-  unsigned char *pubkey,
-  int *pubkeylen,
-  int compressed,
-  int recid
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
-
 /** Verify an ECDSA secret key.
+ *
  *  Returns: 1: secret key is valid
  *           0: secret key is invalid
- *  In:      ctx: pointer to a context object (cannot be NULL)
- *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *  Args:    ctx: pointer to a context object (cannot be NULL)
+ *  In:      seckey: pointer to a 32-byte secret key (cannot be NULL)
  */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(
-  const secp256k1_context_t* ctx,
-  const unsigned char *seckey
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
-
-/** Just validate a public key.
- *  Returns: 1: public key is valid
- *           0: public key is invalid
- *  In:      ctx:       pointer to a context object (cannot be NULL)
- *           pubkey:    pointer to a 33-byte or 65-byte public key (cannot be NULL).
- *           pubkeylen: length of pubkey
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_verify(
-  const secp256k1_context_t* ctx,
-  const unsigned char *pubkey,
-  int pubkeylen
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(
+    const secp256k1_context* ctx,
+    const unsigned char *seckey
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
 
 /** Compute the public key for a secret key.
- *  In:     ctx:        pointer to a context object, initialized for signing (cannot be NULL)
- *          compressed: whether the computed public key should be compressed
- *          seckey:     pointer to a 32-byte private key (cannot be NULL)
- *  Out:    pubkey:     pointer to a 33-byte (if compressed) or 65-byte (if uncompressed)
- *                      area to store the public key (cannot be NULL)
- *          pubkeylen:  pointer to int that will be updated to contains the pubkey's
- *                      length (cannot be NULL)
+ *
  *  Returns: 1: secret was valid, public key stores
  *           0: secret was invalid, try again
+ *  Args:   ctx:        pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:    pubkey:     pointer to the created public key (cannot be NULL)
+ *  In:     seckey:     pointer to a 32-byte private key (cannot be NULL)
  */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
-  const secp256k1_context_t* ctx,
-  unsigned char *pubkey,
-  int *pubkeylen,
-  const unsigned char *seckey,
-  int compressed
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
-
-/** Decompress a public key.
- * In:     ctx:       pointer to a context object (cannot be NULL)
- * In/Out: pubkey:    pointer to a 65-byte array to put the decompressed public key.
- *                    It must contain a 33-byte or 65-byte public key already (cannot be NULL)
- *         pubkeylen: pointer to the size of the public key pointed to by pubkey (cannot be NULL)
- *                    It will be updated to reflect the new size.
- * Returns: 0: pubkey was invalid
- *          1: pubkey was valid, and was replaced with its decompressed version
- */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_decompress(
-  const secp256k1_context_t* ctx,
-  unsigned char *pubkey,
-  int *pubkeylen
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *seckey
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
-/** Export a private key in DER format.
- * In: ctx: pointer to a context object, initialized for signing (cannot be NULL)
+/** Tweak a private key by adding tweak to it.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or if the resulting private key
+ *          would be invalid (only when the tweak is the complement of the
+ *          private key). 1 otherwise.
+ * Args:    ctx:    pointer to a context object (cannot be NULL).
+ * In/Out:  seckey: pointer to a 32-byte private key.
+ * In:      tweak:  pointer to a 32-byte tweak.
  */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_export(
-  const secp256k1_context_t* ctx,
-  const unsigned char *seckey,
-  unsigned char *privkey,
-  int *privkeylen,
-  int compressed
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
-
-/** Import a private key in DER format. */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_import(
-  const secp256k1_context_t* ctx,
-  unsigned char *seckey,
-  const unsigned char *privkey,
-  int privkeylen
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
-/** Tweak a private key by adding tweak to it. */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
-  const secp256k1_context_t* ctx,
-  unsigned char *seckey,
-  const unsigned char *tweak
+/** Tweak a public key by adding tweak times the generator to it.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or if the resulting public key
+ *          would be invalid (only when the tweak is the complement of the
+ *          corresponding private key). 1 otherwise.
+ * Args:    ctx:    pointer to a context object initialized for validation
+ *                  (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key object.
+ * In:      tweak:  pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
-/** Tweak a public key by adding tweak times the generator to it.
- * In: ctx: pointer to a context object, initialized for verification (cannot be NULL)
+/** Tweak a private key by multiplying it by a tweak.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Args:   ctx:    pointer to a context object (cannot be NULL).
+ * In/Out: seckey: pointer to a 32-byte private key.
+ * In:     tweak:  pointer to a 32-byte tweak.
  */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
-  const secp256k1_context_t* ctx,
-  unsigned char *pubkey,
-  int pubkeylen,
-  const unsigned char *tweak
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4);
-
-/** Tweak a private key by multiplying it with tweak. */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
-  const secp256k1_context_t* ctx,
-  unsigned char *seckey,
-  const unsigned char *tweak
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
+    const secp256k1_context* ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
-/** Tweak a public key by multiplying it with tweak.
- * In: ctx: pointer to a context object, initialized for verification (cannot be NULL)
+/** Tweak a public key by multiplying it by a tweak value.
+ * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
+ *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Args:    ctx:    pointer to a context object initialized for validation
+ *                 (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key obkect.
+ * In:      tweak:  pointer to a 32-byte tweak.
  */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
-  const secp256k1_context_t* ctx,
-  unsigned char *pubkey,
-  int pubkeylen,
-  const unsigned char *tweak
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4);
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
 /** Updates the context randomization.
  *  Returns: 1: randomization successfully updated
  *           0: error
- *  In:      ctx:       pointer to a context object (cannot be NULL)
- *           seed32:    pointer to a 32-byte random seed (NULL resets to initial state)
+ *  Args:    ctx:       pointer to a context object (cannot be NULL)
+ *  In:      seed32:    pointer to a 32-byte random seed (NULL resets to initial state)
  */
-SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
-  secp256k1_context_t* ctx,
-  const unsigned char *seed32
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
+    secp256k1_context* ctx,
+    const unsigned char *seed32
 ) SECP256K1_ARG_NONNULL(1);
 
+/** Add a number of public keys together.
+ *  Returns: 1: the sum of the public keys is valid.
+ *           0: the sum of the public keys is not valid.
+ *  Args:   ctx:        pointer to a context object
+ *  Out:    out:        pointer to a public key object for placing the resulting public key
+ *                      (cannot be NULL)
+ *  In:     ins:        pointer to array of pointers to public keys (cannot be NULL)
+ *          n:          the number of public keys to add together (must be at least 1)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *out,
+    const secp256k1_pubkey * const * ins,
+    size_t n
+) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
 # ifdef __cplusplus
 }
diff --git a/src/secp256k1/include/secp256k1_ecdh.h b/src/secp256k1/include/secp256k1_ecdh.h
new file mode 100644
index 0000000000..4b84d7a963
--- /dev/null
+++ b/src/secp256k1/include/secp256k1_ecdh.h
@@ -0,0 +1,31 @@
+#ifndef _SECP256K1_ECDH_
+# define _SECP256K1_ECDH_
+
+# include "secp256k1.h"
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Compute an EC Diffie-Hellman secret in constant time
+ *  Returns: 1: exponentiation was successful
+ *           0: scalar was invalid (zero or overflow)
+ *  Args:    ctx:        pointer to a context object (cannot be NULL)
+ *  Out:     result:     a 32-byte array which will be populated by an ECDH
+ *                       secret computed from the point and scalar
+ *  In:      pubkey:     a pointer to a secp256k1_pubkey containing an
+ *                       initialized public key
+ *           privkey:    a 32-byte scalar with which to multiply the point
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdh(
+  const secp256k1_context* ctx,
+  unsigned char *result,
+  const secp256k1_pubkey *pubkey,
+  const unsigned char *privkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif
diff --git a/src/secp256k1/include/secp256k1_recovery.h b/src/secp256k1/include/secp256k1_recovery.h
new file mode 100644
index 0000000000..0553797253
--- /dev/null
+++ b/src/secp256k1/include/secp256k1_recovery.h
@@ -0,0 +1,110 @@
+#ifndef _SECP256K1_RECOVERY_
+# define _SECP256K1_RECOVERY_
+
+# include "secp256k1.h"
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Opaque data structured that holds a parsed ECDSA signature,
+ *  supporting pubkey recovery.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 65 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_parse_* functions.
+ *
+ *  Furthermore, it is guaranteed that identical signatures (including their
+ *  recoverability) will have identical representation, so they can be
+ *  memcmp'ed.
+ */
+typedef struct {
+    unsigned char data[65];
+} secp256k1_ecdsa_recoverable_signature;
+
+/** Parse a compact ECDSA signature (64 bytes + recovery id).
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise
+ *  Args: ctx:     a secp256k1 context object
+ *  Out:  sig:     a pointer to a signature object
+ *  In:   input64: a pointer to a 64-byte compact signature
+ *        recid:   the recovery id (0, 1, 2 or 3)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_recoverable_signature* sig,
+    const unsigned char *input64,
+    int recid
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Convert a recoverable signature into a normal signature.
+ *
+ *  Returns: 1
+ *  Out: sig:    a pointer to a normal signature (cannot be NULL).
+ *  In:  sigin:  a pointer to a recoverable signature (cannot be NULL).
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature* sig,
+    const secp256k1_ecdsa_recoverable_signature* sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in compact format (64 bytes + recovery id).
+ *
+ *  Returns: 1
+ *  Args: ctx:      a secp256k1 context object
+ *  Out:  output64: a pointer to a 64-byte array of the compact signature (cannot be NULL)
+ *        recid:    a pointer to an integer to hold the recovery id (can be NULL).
+ *  In:   sig:      a pointer to an initialized signature object (cannot be NULL)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact(
+    const secp256k1_context* ctx,
+    unsigned char *output64,
+    int *recid,
+    const secp256k1_ecdsa_recoverable_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Create a recoverable ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:     sig:    pointer to an array where the signature will be placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation function (can be NULL)
+ */
+SECP256K1_API int secp256k1_ecdsa_sign_recoverable(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Recover an ECDSA public key from a signature.
+ *
+ *  Returns: 1: public key successfully recovered (which guarantees a correct signature).
+ *           0: otherwise.
+ *  Args:    ctx:        pointer to a context object, initialized for verification (cannot be NULL)
+ *  Out:     pubkey:     pointer to the recovered public key (cannot be NULL)
+ *  In:      sig:        pointer to initialized signature that supports pubkey recovery (cannot be NULL)
+ *           msg32:      the 32-byte message hash assumed to be signed (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover(
+    const secp256k1_context* ctx,
+    secp256k1_pubkey *pubkey,
+    const secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msg32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif
diff --git a/src/secp256k1/include/secp256k1_schnorr.h b/src/secp256k1/include/secp256k1_schnorr.h
new file mode 100644
index 0000000000..dc32fec1ea
--- /dev/null
+++ b/src/secp256k1/include/secp256k1_schnorr.h
@@ -0,0 +1,173 @@
+#ifndef _SECP256K1_SCHNORR_
+# define _SECP256K1_SCHNORR_
+
+# include "secp256k1.h"
+
+# ifdef __cplusplus
+extern "C" {
+# endif
+
+/** Create a signature using a custom EC-Schnorr-SHA256 construction. It
+ *  produces non-malleable 64-byte signatures which support public key recovery
+ *  batch validation, and multiparty signing.
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was
+ *              invalid.
+ *  Args:    ctx:    pointer to a context object, initialized for signing
+ *                   (cannot be NULL)
+ *  Out:     sig64:  pointer to a 64-byte array where the signature will be
+ *                   placed (cannot be NULL)
+ *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL,
+ *                   secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation
+ *                   function (can be NULL)
+ */
+SECP256K1_API int secp256k1_schnorr_sign(
+  const secp256k1_context* ctx,
+  unsigned char *sig64,
+  const unsigned char *msg32,
+  const unsigned char *seckey,
+  secp256k1_nonce_function noncefp,
+  const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verify a signature created by secp256k1_schnorr_sign.
+ *  Returns: 1: correct signature
+ *           0: incorrect signature
+ *  Args:    ctx:       a secp256k1 context object, initialized for verification.
+ *  In:      sig64:     the 64-byte signature being verified (cannot be NULL)
+ *           msg32:     the 32-byte message hash being verified (cannot be NULL)
+ *           pubkey:    the public key to verify with (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_verify(
+  const secp256k1_context* ctx,
+  const unsigned char *sig64,
+  const unsigned char *msg32,
+  const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Recover an EC public key from a Schnorr signature created using
+ *  secp256k1_schnorr_sign.
+ *  Returns: 1: public key successfully recovered (which guarantees a correct
+ *           signature).
+ *           0: otherwise.
+ *  Args:    ctx:        pointer to a context object, initialized for
+ *                       verification (cannot be NULL)
+ *  Out:     pubkey:     pointer to a pubkey to set to the recovered public key
+ *                       (cannot be NULL).
+ *  In:      sig64:      signature as 64 byte array (cannot be NULL)
+ *           msg32:      the 32-byte message hash assumed to be signed (cannot
+ *                       be NULL)
+ */
+SECP256K1_API int secp256k1_schnorr_recover(
+  const secp256k1_context* ctx,
+  secp256k1_pubkey *pubkey,
+  const unsigned char *sig64,
+  const unsigned char *msg32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Generate a nonce pair deterministically for use with
+ *  secp256k1_schnorr_partial_sign.
+ *  Returns: 1: valid nonce pair was generated.
+ *           0: otherwise (nonce generation function failed)
+ *  Args:    ctx:         pointer to a context object, initialized for signing
+ *                        (cannot be NULL)
+ *  Out:     pubnonce:    public side of the nonce (cannot be NULL)
+ *           privnonce32: private side of the nonce (32 byte) (cannot be NULL)
+ *  In:      msg32:       the 32-byte message hash assumed to be signed (cannot
+ *                        be NULL)
+ *           sec32:       the 32-byte private key (cannot be NULL)
+ *           noncefp:     pointer to a nonce generation function. If NULL,
+ *                        secp256k1_nonce_function_default is used
+ *           noncedata:   pointer to arbitrary data used by the nonce generation
+ *                        function (can be NULL)
+ *
+ *  Do not use the output as a private/public key pair for signing/validation.
+ */
+SECP256K1_API int secp256k1_schnorr_generate_nonce_pair(
+  const secp256k1_context* ctx,
+  secp256k1_pubkey *pubnonce,
+  unsigned char *privnonce32,
+  const unsigned char *msg32,
+  const unsigned char *sec32,
+  secp256k1_nonce_function noncefp,
+  const void* noncedata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Produce a partial Schnorr signature, which can be combined using
+ *  secp256k1_schnorr_partial_combine, to end up with a full signature that is
+ *  verifiable using secp256k1_schnorr_verify.
+ *  Returns: 1: signature created successfully.
+ *           0: no valid signature exists with this combination of keys, nonces
+ *              and message (chance around 1 in 2^128)
+ *          -1: invalid private key, nonce, or public nonces.
+ *  Args: ctx:             pointer to context object, initialized for signing (cannot
+ *                         be NULL)
+ *  Out:  sig64:           pointer to 64-byte array to put partial signature in
+ *  In:   msg32:           pointer to 32-byte message to sign
+ *        sec32:           pointer to 32-byte private key
+ *        pubnonce_others: pointer to pubkey containing the sum of the other's
+ *                         nonces (see secp256k1_ec_pubkey_combine)
+ *        secnonce32:      pointer to 32-byte array containing our nonce
+ *
+ * The intended procedure for creating a multiparty signature is:
+ * - Each signer S[i] with private key x[i] and public key Q[i] runs
+ *   secp256k1_schnorr_generate_nonce_pair to produce a pair (k[i],R[i]) of
+ *   private/public nonces.
+ * - All signers communicate their public nonces to each other (revealing your
+ *   private nonce can lead to discovery of your private key, so it should be
+ *   considered secret).
+ * - All signers combine all the public nonces they received (excluding their
+ *   own) using secp256k1_ec_pubkey_combine to obtain an
+ *   Rall[i] = sum(R[0..i-1,i+1..n]).
+ * - All signers produce a partial signature using
+ *   secp256k1_schnorr_partial_sign, passing in their own private key x[i],
+ *   their own private nonce k[i], and the sum of the others' public nonces
+ *   Rall[i].
+ * - All signers communicate their partial signatures to each other.
+ * - Someone combines all partial signatures using
+ *   secp256k1_schnorr_partial_combine, to obtain a full signature.
+ * - The resulting signature is validatable using secp256k1_schnorr_verify, with
+ *   public key equal to the result of secp256k1_ec_pubkey_combine of the
+ *   signers' public keys (sum(Q[0..n])).
+ *
+ *  Note that secp256k1_schnorr_partial_combine and secp256k1_ec_pubkey_combine
+ *  function take their arguments in any order, and it is possible to
+ *  pre-combine several inputs already with one call, and add more inputs later
+ *  by calling the function again (they are commutative and associative).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_partial_sign(
+  const secp256k1_context* ctx,
+  unsigned char *sig64,
+  const unsigned char *msg32,
+  const unsigned char *sec32,
+  const secp256k1_pubkey *pubnonce_others,
+  const unsigned char *secnonce32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(6);
+
+/** Combine multiple Schnorr partial signatures.
+ * Returns: 1: the passed signatures were successfully combined.
+ *          0: the resulting signature is not valid (chance of 1 in 2^256)
+ *         -1: some inputs were invalid, or the signatures were not created
+ *             using the same set of nonces
+ * Args:   ctx:      pointer to a context object
+ * Out:    sig64:    pointer to a 64-byte array to place the combined signature
+ *                   (cannot be NULL)
+ * In:     sig64sin: pointer to an array of n pointers to 64-byte input
+ *                   signatures
+ *         n:        the number of signatures to combine (at least 1)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_partial_combine(
+  const secp256k1_context* ctx,
+  unsigned char *sig64,
+  const unsigned char * const * sig64sin,
+  size_t n
+) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+# ifdef __cplusplus
+}
+# endif
+
+#endif
diff --git a/src/secp256k1/src/basic-config.h b/src/secp256k1/src/basic-config.h
new file mode 100644
index 0000000000..c4c16eb7ca
--- /dev/null
+++ b/src/secp256k1/src/basic-config.h
@@ -0,0 +1,32 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_BASIC_CONFIG_
+#define _SECP256K1_BASIC_CONFIG_
+
+#ifdef USE_BASIC_CONFIG
+
+#undef USE_ASM_X86_64
+#undef USE_ENDOMORPHISM
+#undef USE_FIELD_10X26
+#undef USE_FIELD_5X52
+#undef USE_FIELD_INV_BUILTIN
+#undef USE_FIELD_INV_NUM
+#undef USE_NUM_GMP
+#undef USE_NUM_NONE
+#undef USE_SCALAR_4X64
+#undef USE_SCALAR_8X32
+#undef USE_SCALAR_INV_BUILTIN
+#undef USE_SCALAR_INV_NUM
+
+#define USE_NUM_NONE 1
+#define USE_FIELD_INV_BUILTIN 1
+#define USE_SCALAR_INV_BUILTIN 1
+#define USE_FIELD_10X26 1
+#define USE_SCALAR_8X32 1
+
+#endif // USE_BASIC_CONFIG
+#endif // _SECP256K1_BASIC_CONFIG_
diff --git a/src/secp256k1/src/bench.h b/src/secp256k1/src/bench.h
index db5f68cee1..3a71b4aafa 100644
--- a/src/secp256k1/src/bench.h
+++ b/src/secp256k1/src/bench.h
@@ -20,7 +20,9 @@ static double gettimedouble(void) {
 void print_number(double x) {
     double y = x;
     int c = 0;
-    if (y < 0.0) y = -y;
+    if (y < 0.0) {
+        y = -y;
+    }
     while (y < 100.0) {
         y *= 10.0;
         c++;
@@ -35,13 +37,21 @@ void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), v
     double max = 0.0;
     for (i = 0; i < count; i++) {
         double begin, total;
-        if (setup) setup(data);
+        if (setup != NULL) {
+            setup(data);
+        }
         begin = gettimedouble();
         benchmark(data);
         total = gettimedouble() - begin;
-        if (teardown) teardown(data);
-        if (total < min) min = total;
-        if (total > max) max = total;
+        if (teardown != NULL) {
+            teardown(data);
+        }
+        if (total < min) {
+            min = total;
+        }
+        if (total > max) {
+            max = total;
+        }
         sum += total;
     }
     printf("%s: min ", name);
diff --git a/src/secp256k1/src/bench_ecdh.c b/src/secp256k1/src/bench_ecdh.c
new file mode 100644
index 0000000000..5a7c6376e0
--- /dev/null
+++ b/src/secp256k1/src/bench_ecdh.c
@@ -0,0 +1,53 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <string.h>
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_ecdh.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    secp256k1_context *ctx;
+    secp256k1_pubkey point;
+    unsigned char scalar[32];
+} bench_ecdh_t;
+
+static void bench_ecdh_setup(void* arg) {
+    int i;
+    bench_ecdh_t *data = (bench_ecdh_t*)arg;
+    const unsigned char point[] = {
+        0x03,
+        0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06,
+        0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd,
+        0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb,
+        0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f
+    };
+
+    data->ctx = secp256k1_context_create(0);
+    for (i = 0; i < 32; i++) {
+        data->scalar[i] = i + 1;
+    }
+    CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1);
+}
+
+static void bench_ecdh(void* arg) {
+    int i;
+    unsigned char res[32];
+    bench_ecdh_t *data = (bench_ecdh_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        CHECK(secp256k1_ecdh(data->ctx, res, &data->point, data->scalar) == 1);
+    }
+}
+
+int main(void) {
+    bench_ecdh_t data;
+
+    run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, 20000);
+    return 0;
+}
diff --git a/src/secp256k1/src/bench_internal.c b/src/secp256k1/src/bench_internal.c
index a960549b94..7809f5f8cf 100644
--- a/src/secp256k1/src/bench_internal.c
+++ b/src/secp256k1/src/bench_internal.c
@@ -13,15 +13,17 @@
 #include "field_impl.h"
 #include "group_impl.h"
 #include "scalar_impl.h"
+#include "ecmult_const_impl.h"
 #include "ecmult_impl.h"
 #include "bench.h"
+#include "secp256k1.c"
 
 typedef struct {
-    secp256k1_scalar_t scalar_x, scalar_y;
-    secp256k1_fe_t fe_x, fe_y;
-    secp256k1_ge_t ge_x, ge_y;
-    secp256k1_gej_t gej_x, gej_y;
-    unsigned char data[32];
+    secp256k1_scalar scalar_x, scalar_y;
+    secp256k1_fe fe_x, fe_y;
+    secp256k1_ge ge_x, ge_y;
+    secp256k1_gej gej_x, gej_y;
+    unsigned char data[64];
     int wnaf[256];
 } bench_inv_t;
 
@@ -51,6 +53,7 @@ void bench_setup(void* arg) {
     secp256k1_gej_set_ge(&data->gej_x, &data->ge_x);
     secp256k1_gej_set_ge(&data->gej_y, &data->ge_y);
     memcpy(data->data, init_x, 32);
+    memcpy(data->data + 32, init_y, 32);
 }
 
 void bench_scalar_add(void* arg) {
@@ -95,8 +98,8 @@ void bench_scalar_split(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_scalar_t l, r;
-        secp256k1_scalar_split_lambda_var(&l, &r, &data->scalar_x);
+        secp256k1_scalar l, r;
+        secp256k1_scalar_split_lambda(&l, &r, &data->scalar_x);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
@@ -193,7 +196,7 @@ void bench_group_double_var(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 200000; i++) {
-        secp256k1_gej_double_var(&data->gej_x, &data->gej_x);
+        secp256k1_gej_double_var(&data->gej_x, &data->gej_x, NULL);
     }
 }
 
@@ -202,7 +205,7 @@ void bench_group_add_var(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 200000; i++) {
-        secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y);
+        secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y, NULL);
     }
 }
 
@@ -220,7 +223,7 @@ void bench_group_add_affine_var(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 200000; i++) {
-        secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y);
+        secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y, NULL);
     }
 }
 
@@ -229,7 +232,17 @@ void bench_ecmult_wnaf(void* arg) {
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_ecmult_wnaf(data->wnaf, &data->scalar_x, WINDOW_A);
+        secp256k1_ecmult_wnaf(data->wnaf, 256, &data->scalar_x, WINDOW_A);
+        secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
+    }
+}
+
+void bench_wnaf_const(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_wnaf_const(data->wnaf, data->scalar_x, WINDOW_A);
         secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y);
     }
 }
@@ -265,11 +278,27 @@ void bench_rfc6979_hmac_sha256(void* arg) {
     secp256k1_rfc6979_hmac_sha256_t rng;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 32, data->data, 32, NULL, 0);
+        secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 64);
         secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32);
     }
 }
 
+void bench_context_verify(void* arg) {
+    int i;
+    (void)arg;
+    for (i = 0; i < 20; i++) {
+        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_VERIFY));
+    }
+}
+
+void bench_context_sign(void* arg) {
+    int i;
+    (void)arg;
+    for (i = 0; i < 200; i++) {
+        secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_SIGN));
+    }
+}
+
 
 int have_flag(int argc, char** argv, char *flag) {
     char** argm = argv + argc;
@@ -278,7 +307,9 @@ int have_flag(int argc, char** argv, char *flag) {
         return 1;
     }
     while (argv != NULL && argv != argm) {
-        if (strcmp(*argv, flag) == 0) return 1;
+        if (strcmp(*argv, flag) == 0) {
+            return 1;
+        }
         argv++;
     }
     return 0;
@@ -309,10 +340,15 @@ int main(int argc, char **argv) {
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, 200000);
 
+    if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, 20000);
 
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, 20000);
+
+    if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 20);
+    if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 200);
+
     return 0;
 }
diff --git a/src/secp256k1/src/bench_recover.c b/src/secp256k1/src/bench_recover.c
index 56faed11a0..6489378cc6 100644
--- a/src/secp256k1/src/bench_recover.c
+++ b/src/secp256k1/src/bench_recover.c
@@ -1,15 +1,16 @@
 /**********************************************************************
- * Copyright (c) 2014 Pieter Wuille                                   *
+ * Copyright (c) 2014-2015 Pieter Wuille                              *
  * Distributed under the MIT software license, see the accompanying   *
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
 
 #include "include/secp256k1.h"
+#include "include/secp256k1_recovery.h"
 #include "util.h"
 #include "bench.h"
 
 typedef struct {
-    secp256k1_context_t *ctx;
+    secp256k1_context *ctx;
     unsigned char msg[32];
     unsigned char sig[64];
 } bench_recover_t;
@@ -17,16 +18,20 @@ typedef struct {
 void bench_recover(void* arg) {
     int i;
     bench_recover_t *data = (bench_recover_t*)arg;
-    unsigned char pubkey[33];
+    secp256k1_pubkey pubkey;
+    unsigned char pubkeyc[33];
 
     for (i = 0; i < 20000; i++) {
         int j;
-        int pubkeylen = 33;
-        CHECK(secp256k1_ecdsa_recover_compact(data->ctx, data->msg, data->sig, pubkey, &pubkeylen, 1, i % 2));
+        size_t pubkeylen = 33;
+        secp256k1_ecdsa_recoverable_signature sig;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(data->ctx, &sig, data->sig, i % 2));
+        CHECK(secp256k1_ecdsa_recover(data->ctx, &pubkey, &sig, data->msg));
+        CHECK(secp256k1_ec_pubkey_serialize(data->ctx, pubkeyc, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
         for (j = 0; j < 32; j++) {
             data->sig[j + 32] = data->msg[j];    /* Move former message to S. */
             data->msg[j] = data->sig[j];         /* Move former R to message. */
-            data->sig[j] = pubkey[j + 1];        /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */
+            data->sig[j] = pubkeyc[j + 1];       /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */
         }
     }
 }
@@ -35,8 +40,12 @@ void bench_recover_setup(void* arg) {
     int i;
     bench_recover_t *data = (bench_recover_t*)arg;
 
-    for (i = 0; i < 32; i++) data->msg[i] = 1 + i;
-    for (i = 0; i < 64; i++) data->sig[i] = 65 + i;
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = 1 + i;
+    }
+    for (i = 0; i < 64; i++) {
+        data->sig[i] = 65 + i;
+    }
 }
 
 int main(void) {
diff --git a/src/secp256k1/src/bench_schnorr_verify.c b/src/secp256k1/src/bench_schnorr_verify.c
new file mode 100644
index 0000000000..5f137dda23
--- /dev/null
+++ b/src/secp256k1/src/bench_schnorr_verify.c
@@ -0,0 +1,73 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <stdio.h>
+#include <string.h>
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_schnorr.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    unsigned char key[32];
+    unsigned char sig[64];
+    unsigned char pubkey[33];
+    size_t pubkeylen;
+} benchmark_schnorr_sig_t;
+
+typedef struct {
+    secp256k1_context *ctx;
+    unsigned char msg[32];
+    benchmark_schnorr_sig_t sigs[64];
+    int numsigs;
+} benchmark_schnorr_verify_t;
+
+static void benchmark_schnorr_init(void* arg) {
+    int i, k;
+    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
+
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = 1 + i;
+    }
+    for (k = 0; k < data->numsigs; k++) {
+        secp256k1_pubkey pubkey;
+        for (i = 0; i < 32; i++) {
+            data->sigs[k].key[i] = 33 + i + k;
+        }
+        secp256k1_schnorr_sign(data->ctx, data->sigs[k].sig, data->msg, data->sigs[k].key, NULL, NULL);
+        data->sigs[k].pubkeylen = 33;
+        CHECK(secp256k1_ec_pubkey_create(data->ctx, &pubkey, data->sigs[k].key));
+        CHECK(secp256k1_ec_pubkey_serialize(data->ctx, data->sigs[k].pubkey, &data->sigs[k].pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED));
+    }
+}
+
+static void benchmark_schnorr_verify(void* arg) {
+    int i;
+    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
+
+    for (i = 0; i < 20000 / data->numsigs; i++) {
+        secp256k1_pubkey pubkey;
+        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
+        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->sigs[0].pubkey, data->sigs[0].pubkeylen));
+        CHECK(secp256k1_schnorr_verify(data->ctx, data->sigs[0].sig, data->msg, &pubkey) == ((i & 0xFF) == 0));
+        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
+    }
+}
+
+
+
+int main(void) {
+    benchmark_schnorr_verify_t data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    data.numsigs = 1;
+    run_benchmark("schnorr_verify", benchmark_schnorr_verify, benchmark_schnorr_init, NULL, &data, 10, 20000);
+
+    secp256k1_context_destroy(data.ctx);
+    return 0;
+}
diff --git a/src/secp256k1/src/bench_sign.c b/src/secp256k1/src/bench_sign.c
index 072a37af51..ed7224d757 100644
--- a/src/secp256k1/src/bench_sign.c
+++ b/src/secp256k1/src/bench_sign.c
@@ -9,7 +9,7 @@
 #include "bench.h"
 
 typedef struct {
-    secp256k1_context_t* ctx;
+    secp256k1_context* ctx;
     unsigned char msg[32];
     unsigned char key[32];
 } bench_sign_t;
@@ -18,22 +18,28 @@ static void bench_sign_setup(void* arg) {
     int i;
     bench_sign_t *data = (bench_sign_t*)arg;
 
-    for (i = 0; i < 32; i++) data->msg[i] = i + 1;
-    for (i = 0; i < 32; i++) data->key[i] = i + 65;
+    for (i = 0; i < 32; i++) {
+        data->msg[i] = i + 1;
+    }
+    for (i = 0; i < 32; i++) {
+        data->key[i] = i + 65;
+    }
 }
 
 static void bench_sign(void* arg) {
     int i;
     bench_sign_t *data = (bench_sign_t*)arg;
 
-    unsigned char sig[64];
+    unsigned char sig[74];
     for (i = 0; i < 20000; i++) {
+        size_t siglen = 74;
         int j;
-        int recid = 0;
-        CHECK(secp256k1_ecdsa_sign_compact(data->ctx, data->msg, sig, data->key, NULL, NULL, &recid));
+        secp256k1_ecdsa_signature signature;
+        CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL));
+        CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature));
         for (j = 0; j < 32; j++) {
-            data->msg[j] = sig[j];             /* Move former R to message. */
-            data->key[j] = sig[j + 32];        /* Move former S to key.     */
+            data->msg[j] = sig[j];
+            data->key[j] = sig[j + 32];
         }
     }
 }
diff --git a/src/secp256k1/src/bench_verify.c b/src/secp256k1/src/bench_verify.c
index c8c82752ce..5718320cda 100644
--- a/src/secp256k1/src/bench_verify.c
+++ b/src/secp256k1/src/bench_verify.c
@@ -12,13 +12,13 @@
 #include "bench.h"
 
 typedef struct {
-    secp256k1_context_t *ctx;
+    secp256k1_context *ctx;
     unsigned char msg[32];
     unsigned char key[32];
     unsigned char sig[72];
-    int siglen;
+    size_t siglen;
     unsigned char pubkey[33];
-    int pubkeylen;
+    size_t pubkeylen;
 } benchmark_verify_t;
 
 static void benchmark_verify(void* arg) {
@@ -26,10 +26,14 @@ static void benchmark_verify(void* arg) {
     benchmark_verify_t* data = (benchmark_verify_t*)arg;
 
     for (i = 0; i < 20000; i++) {
+        secp256k1_pubkey pubkey;
+        secp256k1_ecdsa_signature sig;
         data->sig[data->siglen - 1] ^= (i & 0xFF);
         data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
         data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
-        CHECK(secp256k1_ecdsa_verify(data->ctx, data->msg, data->sig, data->siglen, data->pubkey, data->pubkeylen) == (i == 0));
+        CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1);
+        CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0));
         data->sig[data->siglen - 1] ^= (i & 0xFF);
         data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
         data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
@@ -38,16 +42,24 @@ static void benchmark_verify(void* arg) {
 
 int main(void) {
     int i;
+    secp256k1_pubkey pubkey;
+    secp256k1_ecdsa_signature sig;
     benchmark_verify_t data;
 
     data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
 
-    for (i = 0; i < 32; i++) data.msg[i] = 1 + i;
-    for (i = 0; i < 32; i++) data.key[i] = 33 + i;
+    for (i = 0; i < 32; i++) {
+        data.msg[i] = 1 + i;
+    }
+    for (i = 0; i < 32; i++) {
+        data.key[i] = 33 + i;
+    }
     data.siglen = 72;
-    secp256k1_ecdsa_sign(data.ctx, data.msg, data.sig, &data.siglen, data.key, NULL, NULL);
+    CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL));
+    CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig));
+    CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key));
     data.pubkeylen = 33;
-    CHECK(secp256k1_ec_pubkey_create(data.ctx, data.pubkey, &data.pubkeylen, data.key, 1));
+    CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
 
     run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, 20000);
 
diff --git a/src/secp256k1/src/ecdsa.h b/src/secp256k1/src/ecdsa.h
index 4ef78e8afb..54ae101b92 100644
--- a/src/secp256k1/src/ecdsa.h
+++ b/src/secp256k1/src/ecdsa.h
@@ -7,18 +7,15 @@
 #ifndef _SECP256K1_ECDSA_
 #define _SECP256K1_ECDSA_
 
+#include <stddef.h>
+
 #include "scalar.h"
 #include "group.h"
 #include "ecmult.h"
 
-typedef struct {
-    secp256k1_scalar_t r, s;
-} secp256k1_ecdsa_sig_t;
-
-static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size);
-static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a);
-static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context_t *ctx, const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message);
-static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context_t *ctx, secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *seckey, const secp256k1_scalar_t *message, const secp256k1_scalar_t *nonce, int *recid);
-static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context_t *ctx, const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message, int recid);
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size);
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s);
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid);
 
 #endif
diff --git a/src/secp256k1/src/ecdsa_impl.h b/src/secp256k1/src/ecdsa_impl.h
index ed1d228189..d110b4bb1d 100644
--- a/src/secp256k1/src/ecdsa_impl.h
+++ b/src/secp256k1/src/ecdsa_impl.h
@@ -1,5 +1,5 @@
 /**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                               *
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
  * Distributed under the MIT software license, see the accompanying   *
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
@@ -28,7 +28,7 @@
  *  sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
  *   'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
  */
-static const secp256k1_fe_t secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
+static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
     0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
     0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
 );
@@ -42,82 +42,150 @@ static const secp256k1_fe_t secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CON
  *  sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
  *   '14551231950b75fc4402da1722fc9baee'
  */
-static const secp256k1_fe_t secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
+static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
     0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
 );
 
-static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size) {
-    unsigned char ra[32] = {0}, sa[32] = {0};
-    const unsigned char *rp;
-    const unsigned char *sp;
-    int lenr;
-    int lens;
-    int overflow;
-    if (sig[0] != 0x30) {
-        return 0;
+static int secp256k1_der_read_len(const unsigned char **sigp, const unsigned char *sigend) {
+    int lenleft, b1;
+    size_t ret = 0;
+    if (*sigp >= sigend) {
+        return -1;
     }
-    lenr = sig[3];
-    if (5+lenr >= size) {
-        return 0;
+    b1 = *((*sigp)++);
+    if (b1 == 0xFF) {
+        /* X.690-0207 8.1.3.5.c the value 0xFF shall not be used. */
+        return -1;
     }
-    lens = sig[lenr+5];
-    if (sig[1] != lenr+lens+4) {
-        return 0;
+    if ((b1 & 0x80) == 0) {
+        /* X.690-0207 8.1.3.4 short form length octets */
+        return b1;
     }
-    if (lenr+lens+6 > size) {
-        return 0;
+    if (b1 == 0x80) {
+        /* Indefinite length is not allowed in DER. */
+        return -1;
+    }
+    /* X.690-207 8.1.3.5 long form length octets */
+    lenleft = b1 & 0x7F;
+    if (lenleft > sigend - *sigp) {
+        return -1;
+    }
+    if (**sigp == 0) {
+        /* Not the shortest possible length encoding. */
+        return -1;
+    }
+    if ((size_t)lenleft > sizeof(size_t)) {
+        /* The resulting length would exceed the range of a size_t, so
+         * certainly longer than the passed array size.
+         */
+        return -1;
+    }
+    while (lenleft > 0) {
+        if ((ret >> ((sizeof(size_t) - 1) * 8)) != 0) {
+        }
+        ret = (ret << 8) | **sigp;
+        if (ret + lenleft > (size_t)(sigend - *sigp)) {
+            /* Result exceeds the length of the passed array. */
+            return -1;
+        }
+        (*sigp)++;
+        lenleft--;
+    }
+    if (ret < 128) {
+        /* Not the shortest possible length encoding. */
+        return -1;
     }
-    if (sig[2] != 0x02) {
+    return ret;
+}
+
+static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char **sig, const unsigned char *sigend) {
+    int overflow = 0;
+    unsigned char ra[32] = {0};
+    int rlen;
+
+    if (*sig == sigend || **sig != 0x02) {
+        /* Not a primitive integer (X.690-0207 8.3.1). */
         return 0;
     }
-    if (lenr == 0) {
+    (*sig)++;
+    rlen = secp256k1_der_read_len(sig, sigend);
+    if (rlen <= 0 || (*sig) + rlen > sigend) {
+        /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1).  */
         return 0;
     }
-    if (sig[lenr+4] != 0x02) {
+    if (**sig == 0x00 && rlen > 1 && (((*sig)[1]) & 0x80) == 0x00) {
+        /* Excessive 0x00 padding. */
         return 0;
     }
-    if (lens == 0) {
+    if (**sig == 0xFF && rlen > 1 && (((*sig)[1]) & 0x80) == 0x80) {
+        /* Excessive 0xFF padding. */
         return 0;
     }
-    sp = sig + 6 + lenr;
-    while (lens > 0 && sp[0] == 0) {
-        lens--;
-        sp++;
+    if ((**sig & 0x80) == 0x80) {
+        /* Negative. */
+        overflow = 1;
+    }
+    while (rlen > 0 && **sig == 0) {
+        /* Skip leading zero bytes */
+        rlen--;
+        (*sig)++;
     }
-    if (lens > 32) {
+    if (rlen > 32) {
+        overflow = 1;
+    }
+    if (!overflow) {
+        memcpy(ra + 32 - rlen, *sig, rlen);
+        secp256k1_scalar_set_b32(r, ra, &overflow);
+    }
+    if (overflow) {
+        secp256k1_scalar_set_int(r, 0);
+    }
+    (*sig) += rlen;
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) {
+    const unsigned char *sigend = sig + size;
+    int rlen;
+    if (sig == sigend || *(sig++) != 0x30) {
+        /* The encoding doesn't start with a constructed sequence (X.690-0207 8.9.1). */
         return 0;
     }
-    rp = sig + 4;
-    while (lenr > 0 && rp[0] == 0) {
-        lenr--;
-        rp++;
+    rlen = secp256k1_der_read_len(&sig, sigend);
+    if (rlen < 0 || sig + rlen > sigend) {
+        /* Tuple exceeds bounds */
+        return 0;
     }
-    if (lenr > 32) {
+    if (sig + rlen != sigend) {
+        /* Garbage after tuple. */
         return 0;
     }
-    memcpy(ra + 32 - lenr, rp, lenr);
-    memcpy(sa + 32 - lens, sp, lens);
-    overflow = 0;
-    secp256k1_scalar_set_b32(&r->r, ra, &overflow);
-    if (overflow) {
+
+    if (!secp256k1_der_parse_integer(rr, &sig, sigend)) {
         return 0;
     }
-    secp256k1_scalar_set_b32(&r->s, sa, &overflow);
-    if (overflow) {
+    if (!secp256k1_der_parse_integer(rs, &sig, sigend)) {
         return 0;
     }
+
+    if (sig != sigend) {
+        /* Trailing garbage inside tuple. */
+        return 0;
+    }
+
     return 1;
 }
 
-static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a) {
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) {
     unsigned char r[33] = {0}, s[33] = {0};
     unsigned char *rp = r, *sp = s;
-    int lenR = 33, lenS = 33;
-    secp256k1_scalar_get_b32(&r[1], &a->r);
-    secp256k1_scalar_get_b32(&s[1], &a->s);
+    size_t lenR = 33, lenS = 33;
+    secp256k1_scalar_get_b32(&r[1], ar);
+    secp256k1_scalar_get_b32(&s[1], as);
     while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; }
     while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; }
     if (*size < 6+lenS+lenR) {
+        *size = 6 + lenS + lenR;
         return 0;
     }
     *size = 6 + lenS + lenR;
@@ -132,26 +200,26 @@ static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const se
     return 1;
 }
 
-static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context_t *ctx, const secp256k1_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message) {
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
     unsigned char c[32];
-    secp256k1_scalar_t sn, u1, u2;
-    secp256k1_fe_t xr;
-    secp256k1_gej_t pubkeyj;
-    secp256k1_gej_t pr;
+    secp256k1_scalar sn, u1, u2;
+    secp256k1_fe xr;
+    secp256k1_gej pubkeyj;
+    secp256k1_gej pr;
 
-    if (secp256k1_scalar_is_zero(&sig->r) || secp256k1_scalar_is_zero(&sig->s)) {
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
         return 0;
     }
 
-    secp256k1_scalar_inverse_var(&sn, &sig->s);
+    secp256k1_scalar_inverse_var(&sn, sigs);
     secp256k1_scalar_mul(&u1, &sn, message);
-    secp256k1_scalar_mul(&u2, &sn, &sig->r);
+    secp256k1_scalar_mul(&u2, &sn, sigr);
     secp256k1_gej_set_ge(&pubkeyj, pubkey);
     secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1);
     if (secp256k1_gej_is_infinity(&pr)) {
         return 0;
     }
-    secp256k1_scalar_get_b32(c, &sig->r);
+    secp256k1_scalar_get_b32(c, sigr);
     secp256k1_fe_set_b32(&xr, c);
 
     /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
@@ -171,11 +239,11 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context_t *ctx, con
      *  secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test.
      */
     if (secp256k1_gej_eq_x_var(&xr, &pr)) {
-        /* xr.x == xr * xr.z^2 mod p, so the signature is valid. */
+        /* xr * pr.z^2 mod p == pr.x, so the signature is valid. */
         return 1;
     }
     if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
-        /* xr + p >= n, so we can skip testing the second case. */
+        /* xr + n >= p, so we can skip testing the second case. */
         return 0;
     }
     secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe);
@@ -186,44 +254,11 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context_t *ctx, con
     return 0;
 }
 
-static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context_t *ctx, const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message, int recid) {
-    unsigned char brx[32];
-    secp256k1_fe_t fx;
-    secp256k1_ge_t x;
-    secp256k1_gej_t xj;
-    secp256k1_scalar_t rn, u1, u2;
-    secp256k1_gej_t qj;
-
-    if (secp256k1_scalar_is_zero(&sig->r) || secp256k1_scalar_is_zero(&sig->s)) {
-        return 0;
-    }
-
-    secp256k1_scalar_get_b32(brx, &sig->r);
-    VERIFY_CHECK(secp256k1_fe_set_b32(&fx, brx)); /* brx comes from a scalar, so is less than the order; certainly less than p */
-    if (recid & 2) {
-        if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
-            return 0;
-        }
-        secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
-    }
-    if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) {
-        return 0;
-    }
-    secp256k1_gej_set_ge(&xj, &x);
-    secp256k1_scalar_inverse_var(&rn, &sig->r);
-    secp256k1_scalar_mul(&u1, &rn, message);
-    secp256k1_scalar_negate(&u1, &u1);
-    secp256k1_scalar_mul(&u2, &rn, &sig->s);
-    secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1);
-    secp256k1_ge_set_gej_var(pubkey, &qj);
-    return !secp256k1_gej_is_infinity(&qj);
-}
-
-static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context_t *ctx, secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *seckey, const secp256k1_scalar_t *message, const secp256k1_scalar_t *nonce, int *recid) {
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
     unsigned char b[32];
-    secp256k1_gej_t rp;
-    secp256k1_ge_t r;
-    secp256k1_scalar_t n;
+    secp256k1_gej rp;
+    secp256k1_ge r;
+    secp256k1_scalar n;
     int overflow = 0;
 
     secp256k1_ecmult_gen(ctx, &rp, nonce);
@@ -231,28 +266,33 @@ static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context_t *ctx, s
     secp256k1_fe_normalize(&r.x);
     secp256k1_fe_normalize(&r.y);
     secp256k1_fe_get_b32(b, &r.x);
-    secp256k1_scalar_set_b32(&sig->r, b, &overflow);
-    if (secp256k1_scalar_is_zero(&sig->r)) {
-        /* P.x = order is on the curve, so technically sig->r could end up zero, which would be an invalid signature. */
+    secp256k1_scalar_set_b32(sigr, b, &overflow);
+    if (secp256k1_scalar_is_zero(sigr)) {
+        /* P.x = order is on the curve, so technically sig->r could end up zero, which would be an invalid signature.
+         * This branch is cryptographically unreachable as hitting it requires finding the discrete log of P.x = N.
+         */
         secp256k1_gej_clear(&rp);
         secp256k1_ge_clear(&r);
         return 0;
     }
     if (recid) {
+        /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log
+         * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria.
+         */
         *recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
     }
-    secp256k1_scalar_mul(&n, &sig->r, seckey);
+    secp256k1_scalar_mul(&n, sigr, seckey);
     secp256k1_scalar_add(&n, &n, message);
-    secp256k1_scalar_inverse(&sig->s, nonce);
-    secp256k1_scalar_mul(&sig->s, &sig->s, &n);
+    secp256k1_scalar_inverse(sigs, nonce);
+    secp256k1_scalar_mul(sigs, sigs, &n);
     secp256k1_scalar_clear(&n);
     secp256k1_gej_clear(&rp);
     secp256k1_ge_clear(&r);
-    if (secp256k1_scalar_is_zero(&sig->s)) {
+    if (secp256k1_scalar_is_zero(sigs)) {
         return 0;
     }
-    if (secp256k1_scalar_is_high(&sig->s)) {
-        secp256k1_scalar_negate(&sig->s, &sig->s);
+    if (secp256k1_scalar_is_high(sigs)) {
+        secp256k1_scalar_negate(sigs, sigs);
         if (recid) {
             *recid ^= 1;
         }
diff --git a/src/secp256k1/src/eckey.h b/src/secp256k1/src/eckey.h
index 53b818485e..42739a3bea 100644
--- a/src/secp256k1/src/eckey.h
+++ b/src/secp256k1/src/eckey.h
@@ -7,20 +7,19 @@
 #ifndef _SECP256K1_ECKEY_
 #define _SECP256K1_ECKEY_
 
+#include <stddef.h>
+
 #include "group.h"
 #include "scalar.h"
 #include "ecmult.h"
 #include "ecmult_gen.h"
 
-static int secp256k1_eckey_pubkey_parse(secp256k1_ge_t *elem, const unsigned char *pub, int size);
-static int secp256k1_eckey_pubkey_serialize(secp256k1_ge_t *elem, unsigned char *pub, int *size, int compressed);
-
-static int secp256k1_eckey_privkey_parse(secp256k1_scalar_t *key, const unsigned char *privkey, int privkeylen);
-static int secp256k1_eckey_privkey_serialize(const secp256k1_ecmult_gen_context_t *ctx, unsigned char *privkey, int *privkeylen, const secp256k1_scalar_t *key, int compressed);
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size);
+static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed);
 
-static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak);
-static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context_t *ctx, secp256k1_ge_t *key, const secp256k1_scalar_t *tweak);
-static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak);
-static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context_t *ctx, secp256k1_ge_t *key, const secp256k1_scalar_t *tweak);
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak);
 
 #endif
diff --git a/src/secp256k1/src/eckey_impl.h b/src/secp256k1/src/eckey_impl.h
index a332bd34ec..ce38071ac2 100644
--- a/src/secp256k1/src/eckey_impl.h
+++ b/src/secp256k1/src/eckey_impl.h
@@ -14,12 +14,12 @@
 #include "group.h"
 #include "ecmult_gen.h"
 
-static int secp256k1_eckey_pubkey_parse(secp256k1_ge_t *elem, const unsigned char *pub, int size) {
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) {
     if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) {
-        secp256k1_fe_t x;
+        secp256k1_fe x;
         return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == 0x03);
     } else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) {
-        secp256k1_fe_t x, y;
+        secp256k1_fe x, y;
         if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) {
             return 0;
         }
@@ -33,7 +33,7 @@ static int secp256k1_eckey_pubkey_parse(secp256k1_ge_t *elem, const unsigned cha
     }
 }
 
-static int secp256k1_eckey_pubkey_serialize(secp256k1_ge_t *elem, unsigned char *pub, int *size, int compressed) {
+static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed) {
     if (secp256k1_ge_is_infinity(elem)) {
         return 0;
     }
@@ -51,110 +51,7 @@ static int secp256k1_eckey_pubkey_serialize(secp256k1_ge_t *elem, unsigned char
     return 1;
 }
 
-static int secp256k1_eckey_privkey_parse(secp256k1_scalar_t *key, const unsigned char *privkey, int privkeylen) {
-    unsigned char c[32] = {0};
-    const unsigned char *end = privkey + privkeylen;
-    int lenb = 0;
-    int len = 0;
-    int overflow = 0;
-    /* sequence header */
-    if (end < privkey+1 || *privkey != 0x30) {
-        return 0;
-    }
-    privkey++;
-    /* sequence length constructor */
-    if (end < privkey+1 || !(*privkey & 0x80)) {
-        return 0;
-    }
-    lenb = *privkey & ~0x80; privkey++;
-    if (lenb < 1 || lenb > 2) {
-        return 0;
-    }
-    if (end < privkey+lenb) {
-        return 0;
-    }
-    /* sequence length */
-    len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0);
-    privkey += lenb;
-    if (end < privkey+len) {
-        return 0;
-    }
-    /* sequence element 0: version number (=1) */
-    if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) {
-        return 0;
-    }
-    privkey += 3;
-    /* sequence element 1: octet string, up to 32 bytes */
-    if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) {
-        return 0;
-    }
-    memcpy(c + 32 - privkey[1], privkey + 2, privkey[1]);
-    secp256k1_scalar_set_b32(key, c, &overflow);
-    memset(c, 0, 32);
-    return !overflow;
-}
-
-static int secp256k1_eckey_privkey_serialize(const secp256k1_ecmult_gen_context_t *ctx, unsigned char *privkey, int *privkeylen, const secp256k1_scalar_t *key, int compressed) {
-    secp256k1_gej_t rp;
-    secp256k1_ge_t r;
-    int pubkeylen = 0;
-    secp256k1_ecmult_gen(ctx, &rp, key);
-    secp256k1_ge_set_gej(&r, &rp);
-    if (compressed) {
-        static const unsigned char begin[] = {
-            0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20
-        };
-        static const unsigned char middle[] = {
-            0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
-            0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
-            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
-            0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
-            0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
-            0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
-            0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
-            0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
-            0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00
-        };
-        unsigned char *ptr = privkey;
-        memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
-        secp256k1_scalar_get_b32(ptr, key); ptr += 32;
-        memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
-        if (!secp256k1_eckey_pubkey_serialize(&r, ptr, &pubkeylen, 1)) {
-            return 0;
-        }
-        ptr += pubkeylen;
-        *privkeylen = ptr - privkey;
-    } else {
-        static const unsigned char begin[] = {
-            0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20
-        };
-        static const unsigned char middle[] = {
-            0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48,
-            0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
-            0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
-            0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04,
-            0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87,
-            0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8,
-            0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11,
-            0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10,
-            0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
-            0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,
-            0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00
-        };
-        unsigned char *ptr = privkey;
-        memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin);
-        secp256k1_scalar_get_b32(ptr, key); ptr += 32;
-        memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle);
-        if (!secp256k1_eckey_pubkey_serialize(&r, ptr, &pubkeylen, 0)) {
-            return 0;
-        }
-        ptr += pubkeylen;
-        *privkeylen = ptr - privkey;
-    }
-    return 1;
-}
-
-static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak) {
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
     secp256k1_scalar_add(key, key, tweak);
     if (secp256k1_scalar_is_zero(key)) {
         return 0;
@@ -162,9 +59,9 @@ static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar_t *key, const secp
     return 1;
 }
 
-static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context_t *ctx, secp256k1_ge_t *key, const secp256k1_scalar_t *tweak) {
-    secp256k1_gej_t pt;
-    secp256k1_scalar_t one;
+static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_gej pt;
+    secp256k1_scalar one;
     secp256k1_gej_set_ge(&pt, key);
     secp256k1_scalar_set_int(&one, 1);
     secp256k1_ecmult(ctx, &pt, &pt, &one, tweak);
@@ -176,7 +73,7 @@ static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context_t *ct
     return 1;
 }
 
-static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar_t *key, const secp256k1_scalar_t *tweak) {
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
     if (secp256k1_scalar_is_zero(tweak)) {
         return 0;
     }
@@ -185,9 +82,9 @@ static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar_t *key, const secp
     return 1;
 }
 
-static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context_t *ctx, secp256k1_ge_t *key, const secp256k1_scalar_t *tweak) {
-    secp256k1_scalar_t zero;
-    secp256k1_gej_t pt;
+static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_scalar zero;
+    secp256k1_gej pt;
     if (secp256k1_scalar_is_zero(tweak)) {
         return 0;
     }
diff --git a/src/secp256k1/src/ecmult.h b/src/secp256k1/src/ecmult.h
index bab9e4ef52..20484134f5 100644
--- a/src/secp256k1/src/ecmult.h
+++ b/src/secp256k1/src/ecmult.h
@@ -12,20 +12,20 @@
 
 typedef struct {
     /* For accelerating the computation of a*P + b*G: */
-    secp256k1_ge_storage_t (*pre_g)[];    /* odd multiples of the generator */
+    secp256k1_ge_storage (*pre_g)[];    /* odd multiples of the generator */
 #ifdef USE_ENDOMORPHISM
-    secp256k1_ge_storage_t (*pre_g_128)[]; /* odd multiples of 2^128*generator */
+    secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */
 #endif
-} secp256k1_ecmult_context_t;
+} secp256k1_ecmult_context;
 
-static void secp256k1_ecmult_context_init(secp256k1_ecmult_context_t *ctx);
-static void secp256k1_ecmult_context_build(secp256k1_ecmult_context_t *ctx);
-static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context_t *dst,
-                                           const secp256k1_ecmult_context_t *src);
-static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context_t *ctx);
-static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context_t *ctx);
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx);
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+                                           const secp256k1_ecmult_context *src, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx);
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx);
 
 /** Double multiply: R = na*A + ng*G */
-static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng);
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
 
 #endif
diff --git a/src/secp256k1/src/ecmult_const.h b/src/secp256k1/src/ecmult_const.h
new file mode 100644
index 0000000000..2b0097655c
--- /dev/null
+++ b/src/secp256k1/src/ecmult_const.h
@@ -0,0 +1,15 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_CONST_
+#define _SECP256K1_ECMULT_CONST_
+
+#include "scalar.h"
+#include "group.h"
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
+
+#endif
diff --git a/src/secp256k1/src/ecmult_const_impl.h b/src/secp256k1/src/ecmult_const_impl.h
new file mode 100644
index 0000000000..90ac94770e
--- /dev/null
+++ b/src/secp256k1/src/ecmult_const_impl.h
@@ -0,0 +1,260 @@
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_CONST_IMPL_
+#define _SECP256K1_ECMULT_CONST_IMPL_
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_const.h"
+#include "ecmult_impl.h"
+
+#ifdef USE_ENDOMORPHISM
+    #define WNAF_BITS 128
+#else
+    #define WNAF_BITS 256
+#endif
+#define WNAF_SIZE(w) ((WNAF_BITS + (w) - 1) / (w))
+
+/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
+#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
+    int m; \
+    int abs_n = (n) * (((n) > 0) * 2 - 1); \
+    int idx_n = abs_n / 2; \
+    secp256k1_fe neg_y; \
+    VERIFY_CHECK(((n) & 1) == 1); \
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+    VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
+    VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
+    for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
+        /* This loop is used to avoid secret data in array indices. See
+         * the comment in ecmult_gen_impl.h for rationale. */ \
+        secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
+        secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
+    } \
+    (r)->infinity = 0; \
+    secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
+    secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
+} while(0)
+
+
+/** Convert a number to WNAF notation. The number becomes represented by sum(2^{wi} * wnaf[i], i=0..return_val)
+ *  with the following guarantees:
+ *  - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
+ *  - each wnaf[i] is nonzero
+ *  - the number of words set is returned; this is always (WNAF_BITS + w - 1) / w
+ *
+ *  Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
+ *  Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
+ *  CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
+ *
+ *  Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
+ */
+static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
+    int global_sign;
+    int skew = 0;
+    int word = 0;
+    /* 1 2 3 */
+    int u_last;
+    int u;
+
+#ifdef USE_ENDOMORPHISM
+    int flip;
+    int bit;
+    secp256k1_scalar neg_s;
+    int not_neg_one;
+    /* If we are using the endomorphism, we cannot handle even numbers by negating
+     * them, since we are working with 128-bit numbers whose negations would be 256
+     * bits, eliminating the performance advantage. Instead we use a technique from
+     * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
+     * or 2 (for odd) to the number we are encoding, then compensating after the
+     * multiplication. */
+    /* Negative 128-bit numbers will be negated, since otherwise they are 256-bit */
+    flip = secp256k1_scalar_is_high(&s);
+    /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
+    bit = flip ^ (s.d[0] & 1);
+    /* We check for negative one, since adding 2 to it will cause an overflow */
+    secp256k1_scalar_negate(&neg_s, &s);
+    not_neg_one = !secp256k1_scalar_is_one(&neg_s);
+    secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
+    /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
+     * that we added two to it and flipped it. In fact for -1 these operations are
+     * identical. We only flipped, but since skewing is required (in the sense that
+     * the skew must be 1 or 2, never zero) and flipping is not, we need to change
+     * our flags to claim that we only skewed. */
+    global_sign = secp256k1_scalar_cond_negate(&s, flip);
+    global_sign *= not_neg_one * 2 - 1;
+    skew = 1 << bit;
+#else
+    /* Otherwise, we just negate to force oddness */
+    int is_even = secp256k1_scalar_is_even(&s);
+    global_sign = secp256k1_scalar_cond_negate(&s, is_even);
+#endif
+
+    /* 4 */
+    u_last = secp256k1_scalar_shr_int(&s, w);
+    while (word * w < WNAF_BITS) {
+        int sign;
+        int even;
+
+        /* 4.1 4.4 */
+        u = secp256k1_scalar_shr_int(&s, w);
+        /* 4.2 */
+        even = ((u & 1) == 0);
+        sign = 2 * (u_last > 0) - 1;
+        u += sign * even;
+        u_last -= sign * even * (1 << w);
+
+        /* 4.3, adapted for global sign change */
+        wnaf[word++] = u_last * global_sign;
+
+        u_last = u;
+    }
+    wnaf[word] = u * global_sign;
+
+    VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
+    VERIFY_CHECK(word == WNAF_SIZE(w));
+    return skew;
+}
+
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar) {
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
+
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+    int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
+    int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
+    int skew_1;
+    int skew_lam;
+    secp256k1_scalar q_1, q_lam;
+#else
+    int wnaf[1 + WNAF_SIZE(WINDOW_A - 1)];
+#endif
+
+    int i;
+    secp256k1_scalar sc = *scalar;
+
+    /* build wnaf representation for q. */
+#ifdef USE_ENDOMORPHISM
+    /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
+    secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
+    /* no need for zero correction when using endomorphism since even
+     * numbers have one added to them anyway */
+    skew_1   = secp256k1_wnaf_const(wnaf_1,   q_1,   WINDOW_A - 1);
+    skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1);
+#else
+    int is_zero = secp256k1_scalar_is_zero(scalar);
+    /* the wNAF ladder cannot handle zero, so bump this to one .. we will
+     * correct the result after the fact */
+    sc.d[0] += is_zero;
+    VERIFY_CHECK(!secp256k1_scalar_is_zero(&sc));
+
+    secp256k1_wnaf_const(wnaf, sc, WINDOW_A - 1);
+#endif
+
+    /* Calculate odd multiples of a.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     */
+    secp256k1_gej_set_ge(r, a);
+    secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_fe_normalize_weak(&pre_a[i].y);
+    }
+#ifdef USE_ENDOMORPHISM
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+    }
+#endif
+
+    /* first loop iteration (separated out so we can directly set r, rather
+     * than having it start at infinity, get doubled several times, then have
+     * its new value added to it) */
+#ifdef USE_ENDOMORPHISM
+    i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+    secp256k1_gej_set_ge(r, &tmpa);
+
+    i = wnaf_lam[WNAF_SIZE(WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
+    secp256k1_gej_add_ge(r, r, &tmpa);
+#else
+    i = wnaf[WNAF_SIZE(WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+    secp256k1_gej_set_ge(r, &tmpa);
+#endif
+    /* remaining loop iterations */
+    for (i = WNAF_SIZE(WINDOW_A - 1) - 1; i >= 0; i--) {
+        int n;
+        int j;
+        for (j = 0; j < WINDOW_A - 1; ++j) {
+            secp256k1_gej_double_nonzero(r, r, NULL);
+        }
+#ifdef USE_ENDOMORPHISM
+        n = wnaf_1[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+
+        n = wnaf_lam[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+#else
+        n = wnaf[i];
+        VERIFY_CHECK(n != 0);
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+#endif
+    }
+
+    secp256k1_fe_mul(&r->z, &r->z, &Z);
+
+#ifdef USE_ENDOMORPHISM
+    {
+        /* Correct for wNAF skew */
+        secp256k1_ge correction = *a;
+        secp256k1_ge_storage correction_1_stor;
+        secp256k1_ge_storage correction_lam_stor;
+        secp256k1_ge_storage a2_stor;
+        secp256k1_gej tmpj;
+        secp256k1_gej_set_ge(&tmpj, &correction);
+        secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
+        secp256k1_ge_set_gej(&correction, &tmpj);
+        secp256k1_ge_to_storage(&correction_1_stor, a);
+        secp256k1_ge_to_storage(&correction_lam_stor, a);
+        secp256k1_ge_to_storage(&a2_stor, &correction);
+
+        /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
+        secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
+        secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
+
+        /* Apply the correction */
+        secp256k1_ge_from_storage(&correction, &correction_1_stor);
+        secp256k1_ge_neg(&correction, &correction);
+        secp256k1_gej_add_ge(r, r, &correction);
+
+        secp256k1_ge_from_storage(&correction, &correction_lam_stor);
+        secp256k1_ge_neg(&correction, &correction);
+        secp256k1_ge_mul_lambda(&correction, &correction);
+        secp256k1_gej_add_ge(r, r, &correction);
+    }
+#else
+    /* correct for zero */
+    r->infinity |= is_zero;
+#endif
+}
+
+#endif
diff --git a/src/secp256k1/src/ecmult_gen.h b/src/secp256k1/src/ecmult_gen.h
index 3745633c47..eb2cc9ead6 100644
--- a/src/secp256k1/src/ecmult_gen.h
+++ b/src/secp256k1/src/ecmult_gen.h
@@ -23,21 +23,21 @@ typedef struct {
      * None of the resulting prec group elements have a known scalar, and neither do any of
      * the intermediate sums while computing a*G.
      */
-    secp256k1_ge_storage_t (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
-    secp256k1_scalar_t blind;
-    secp256k1_gej_t initial;
-} secp256k1_ecmult_gen_context_t;
+    secp256k1_ge_storage (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
+    secp256k1_scalar blind;
+    secp256k1_gej initial;
+} secp256k1_ecmult_gen_context;
 
-static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context_t* ctx);
-static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context_t* ctx);
-static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context_t *dst,
-                                               const secp256k1_ecmult_gen_context_t* src);
-static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context_t* ctx);
-static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context_t* ctx);
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx);
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, const secp256k1_callback* cb);
+static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
+                                               const secp256k1_ecmult_gen_context* src, const secp256k1_callback* cb);
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx);
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx);
 
 /** Multiply with the generator: R = a*G */
-static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context_t* ctx, secp256k1_gej_t *r, const secp256k1_scalar_t *a);
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a);
 
-static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context_t *ctx, const unsigned char *seed32);
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32);
 
 #endif
diff --git a/src/secp256k1/src/ecmult_gen_impl.h b/src/secp256k1/src/ecmult_gen_impl.h
index 4697753ac8..b63c4d8662 100644
--- a/src/secp256k1/src/ecmult_gen_impl.h
+++ b/src/secp256k1/src/ecmult_gen_impl.h
@@ -11,22 +11,26 @@
 #include "group.h"
 #include "ecmult_gen.h"
 #include "hash_impl.h"
-
-static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context_t *ctx) {
+#ifdef USE_ECMULT_STATIC_PRECOMPUTATION
+#include "ecmult_static_context.h"
+#endif
+static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) {
     ctx->prec = NULL;
 }
 
-static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context_t *ctx) {
-    secp256k1_ge_t prec[1024];
-    secp256k1_gej_t gj;
-    secp256k1_gej_t nums_gej;
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_callback* cb) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    secp256k1_ge prec[1024];
+    secp256k1_gej gj;
+    secp256k1_gej nums_gej;
     int i, j;
+#endif
 
     if (ctx->prec != NULL) {
         return;
     }
-
-    ctx->prec = (secp256k1_ge_storage_t (*)[64][16])checked_malloc(sizeof(*ctx->prec));
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+    ctx->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*ctx->prec));
 
     /* get the generator */
     secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
@@ -34,77 +38,93 @@ static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context_t *c
     /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
     {
         static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
-        secp256k1_fe_t nums_x;
-        secp256k1_ge_t nums_ge;
-        VERIFY_CHECK(secp256k1_fe_set_b32(&nums_x, nums_b32));
-        VERIFY_CHECK(secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0));
+        secp256k1_fe nums_x;
+        secp256k1_ge nums_ge;
+        int r;
+        r = secp256k1_fe_set_b32(&nums_x, nums_b32);
+        (void)r;
+        VERIFY_CHECK(r);
+        r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0);
+        (void)r;
+        VERIFY_CHECK(r);
         secp256k1_gej_set_ge(&nums_gej, &nums_ge);
         /* Add G to make the bits in x uniformly distributed. */
-        secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g);
+        secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL);
     }
 
     /* compute prec. */
     {
-        secp256k1_gej_t precj[1024]; /* Jacobian versions of prec. */
-        secp256k1_gej_t gbase;
-        secp256k1_gej_t numsbase;
+        secp256k1_gej precj[1024]; /* Jacobian versions of prec. */
+        secp256k1_gej gbase;
+        secp256k1_gej numsbase;
         gbase = gj; /* 16^j * G */
         numsbase = nums_gej; /* 2^j * nums. */
         for (j = 0; j < 64; j++) {
             /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
             precj[j*16] = numsbase;
             for (i = 1; i < 16; i++) {
-                secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
+                secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
             }
             /* Multiply gbase by 16. */
             for (i = 0; i < 4; i++) {
-                secp256k1_gej_double_var(&gbase, &gbase);
+                secp256k1_gej_double_var(&gbase, &gbase, NULL);
             }
             /* Multiply numbase by 2. */
-            secp256k1_gej_double_var(&numsbase, &numsbase);
+            secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
             if (j == 62) {
                 /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
                 secp256k1_gej_neg(&numsbase, &numsbase);
-                secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej);
+                secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
             }
         }
-        secp256k1_ge_set_all_gej_var(1024, prec, precj);
+        secp256k1_ge_set_all_gej_var(1024, prec, precj, cb);
     }
     for (j = 0; j < 64; j++) {
         for (i = 0; i < 16; i++) {
             secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
         }
     }
+#else
+    (void)cb;
+    ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
+#endif
     secp256k1_ecmult_gen_blind(ctx, NULL);
 }
 
-static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context_t* ctx) {
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
     return ctx->prec != NULL;
 }
 
-static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context_t *dst,
-                                               const secp256k1_ecmult_gen_context_t *src) {
+static void secp256k1_ecmult_gen_context_clone(secp256k1_ecmult_gen_context *dst,
+                                               const secp256k1_ecmult_gen_context *src, const secp256k1_callback* cb) {
     if (src->prec == NULL) {
         dst->prec = NULL;
     } else {
-        dst->prec = (secp256k1_ge_storage_t (*)[64][16])checked_malloc(sizeof(*dst->prec));
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
+        dst->prec = (secp256k1_ge_storage (*)[64][16])checked_malloc(cb, sizeof(*dst->prec));
         memcpy(dst->prec, src->prec, sizeof(*dst->prec));
+#else
+        (void)cb;
+        dst->prec = src->prec;
+#endif
         dst->initial = src->initial;
         dst->blind = src->blind;
     }
 }
 
-static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context_t *ctx) {
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
+#ifndef USE_ECMULT_STATIC_PRECOMPUTATION
     free(ctx->prec);
+#endif
     secp256k1_scalar_clear(&ctx->blind);
     secp256k1_gej_clear(&ctx->initial);
     ctx->prec = NULL;
 }
 
-static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context_t *ctx, secp256k1_gej_t *r, const secp256k1_scalar_t *gn) {
-    secp256k1_ge_t add;
-    secp256k1_ge_storage_t adds;
-    secp256k1_scalar_t gnb;
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
+    secp256k1_ge add;
+    secp256k1_ge_storage adds;
+    secp256k1_scalar gnb;
     int bits;
     int i, j;
     memset(&adds, 0, sizeof(adds));
@@ -136,14 +156,15 @@ static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context_t *ctx, secp
 }
 
 /* Setup blinding values for secp256k1_ecmult_gen. */
-static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context_t *ctx, const unsigned char *seed32) {
-    secp256k1_scalar_t b;
-    secp256k1_gej_t gb;
-    secp256k1_fe_t s;
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) {
+    secp256k1_scalar b;
+    secp256k1_gej gb;
+    secp256k1_fe s;
     unsigned char nonce32[32];
     secp256k1_rfc6979_hmac_sha256_t rng;
     int retry;
-    if (!seed32) {
+    unsigned char keydata[64] = {0};
+    if (seed32 == NULL) {
         /* When seed is NULL, reset the initial point and blinding value. */
         secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g);
         secp256k1_gej_neg(&ctx->initial, &ctx->initial);
@@ -155,13 +176,18 @@ static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context_t *ctx, cons
      *   and guards against weak or adversarial seeds.  This is a simpler and safer interface than
      *   asking the caller for blinding values directly and expecting them to retry on failure.
      */
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, seed32 ? seed32 : nonce32, 32, nonce32, 32, NULL, 0);
+    memcpy(keydata, nonce32, 32);
+    if (seed32 != NULL) {
+        memcpy(keydata + 32, seed32, 32);
+    }
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32);
+    memset(keydata, 0, sizeof(keydata));
     /* Retry for out of range results to achieve uniformity. */
     do {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
         retry = !secp256k1_fe_set_b32(&s, nonce32);
         retry |= secp256k1_fe_is_zero(&s);
-    } while (retry);
+    } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > Fp. */
     /* Randomize the projection to defend against multiplier sidechannels. */
     secp256k1_gej_rescale(&ctx->initial, &s);
     secp256k1_fe_clear(&s);
@@ -170,7 +196,7 @@ static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context_t *ctx, cons
         secp256k1_scalar_set_b32(&b, nonce32, &retry);
         /* A blinding value of 0 works, but would undermine the projection hardening. */
         retry |= secp256k1_scalar_is_zero(&b);
-    } while (retry);
+    } while (retry); /* This branch true is cryptographically unreachable. Requires sha256_hmac output > order. */
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
     memset(nonce32, 0, 32);
     secp256k1_ecmult_gen(ctx, &gb, &b);
diff --git a/src/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h
index 1b2856f83d..e6e5f47188 100644
--- a/src/secp256k1/src/ecmult_impl.h
+++ b/src/secp256k1/src/ecmult_impl.h
@@ -24,62 +24,107 @@
 #define WINDOW_G 16
 #endif
 
-/** Fill a table 'pre' with precomputed odd multiples of a. W determines the size of the table.
- *  pre will contains the values [1*a,3*a,5*a,...,(2^(w-1)-1)*a], so it needs place for
- *  2^(w-2) entries.
- *
- *  There are two versions of this function:
- *  - secp256k1_ecmult_precomp_wnaf_gej, which operates on group elements in jacobian notation,
- *    fast to precompute, but slower to use in later additions.
- *  - secp256k1_ecmult_precomp_wnaf_ge, which operates on group elements in affine notations,
- *    (much) slower to precompute, but a bit faster to use in later additions.
- *  To compute a*P + b*G, we use the jacobian version for P, and the affine version for G, as
- *  G is constant, so it only needs to be done once in advance.
+/** The number of entries a table with precomputed multiples needs to have. */
+#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
+
+/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
+ *  the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
+ *  contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
+ *  Prej's Z values are undefined, except for the last value.
  */
-static void secp256k1_ecmult_table_precomp_gej_var(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) {
-    secp256k1_gej_t d;
+static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) {
+    secp256k1_gej d;
+    secp256k1_ge a_ge, d_ge;
     int i;
-    pre[0] = *a;
-    secp256k1_gej_double_var(&d, &pre[0]);
-    for (i = 1; i < (1 << (w-2)); i++) {
-        secp256k1_gej_add_var(&pre[i], &d, &pre[i-1]);
+
+    VERIFY_CHECK(!a->infinity);
+
+    secp256k1_gej_double_var(&d, a, NULL);
+
+    /*
+     * Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
+     * of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
+     */
+    d_ge.x = d.x;
+    d_ge.y = d.y;
+    d_ge.infinity = 0;
+
+    secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
+    prej[0].x = a_ge.x;
+    prej[0].y = a_ge.y;
+    prej[0].z = a->z;
+    prej[0].infinity = 0;
+
+    zr[0] = d.z;
+    for (i = 1; i < n; i++) {
+        secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
     }
+
+    /*
+     * Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
+     * the final point's z coordinate is actually used though, so just update that.
+     */
+    secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
+}
+
+/** Fill a table 'pre' with precomputed odd multiples of a.
+ *
+ *  There are two versions of this function:
+ *  - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
+ *    resulting point set to a single constant Z denominator, stores the X and Y
+ *    coordinates as ge_storage points in pre, and stores the global Z in rz.
+ *    It only operates on tables sized for WINDOW_A wnaf multiples.
+ *  - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
+ *    resulting point set to actually affine points, and stores those in pre.
+ *    It operates on tables of any size, but uses heap-allocated temporaries.
+ *
+ *  To compute a*P + b*G, we compute a table for P using the first function,
+ *  and for G using the second (which requires an inverse, but it only needs to
+ *  happen once).
+ */
+static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
+    secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
+
+    /* Compute the odd multiples in Jacobian form. */
+    secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
+    /* Bring them to the same Z denominator. */
+    secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
 }
 
-static void secp256k1_ecmult_table_precomp_ge_storage_var(secp256k1_ge_storage_t *pre, const secp256k1_gej_t *a, int w) {
-    secp256k1_gej_t d;
+static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage *pre, const secp256k1_gej *a, const secp256k1_callback *cb) {
+    secp256k1_gej *prej = (secp256k1_gej*)checked_malloc(cb, sizeof(secp256k1_gej) * n);
+    secp256k1_ge *prea = (secp256k1_ge*)checked_malloc(cb, sizeof(secp256k1_ge) * n);
+    secp256k1_fe *zr = (secp256k1_fe*)checked_malloc(cb, sizeof(secp256k1_fe) * n);
     int i;
-    const int table_size = 1 << (w-2);
-    secp256k1_gej_t *prej = (secp256k1_gej_t *)checked_malloc(sizeof(secp256k1_gej_t) * table_size);
-    secp256k1_ge_t *prea = (secp256k1_ge_t *)checked_malloc(sizeof(secp256k1_ge_t) * table_size);
-    prej[0] = *a;
-    secp256k1_gej_double_var(&d, a);
-    for (i = 1; i < table_size; i++) {
-        secp256k1_gej_add_var(&prej[i], &d, &prej[i-1]);
-    }
-    secp256k1_ge_set_all_gej_var(table_size, prea, prej);
-    for (i = 0; i < table_size; i++) {
+
+    /* Compute the odd multiples in Jacobian form. */
+    secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
+    /* Convert them in batch to affine coordinates. */
+    secp256k1_ge_set_table_gej_var(n, prea, prej, zr);
+    /* Convert them to compact storage form. */
+    for (i = 0; i < n; i++) {
         secp256k1_ge_to_storage(&pre[i], &prea[i]);
     }
-    free(prej);
+
     free(prea);
+    free(prej);
+    free(zr);
 }
 
-/** The number of entries a table with precomputed multiples needs to have. */
-#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
-
 /** The following two macro retrieves a particular odd multiple from a table
  *  of precomputed multiples. */
-#define ECMULT_TABLE_GET_GEJ(r,pre,n,w) do { \
+#define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \
     VERIFY_CHECK(((n) & 1) == 1); \
     VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
     VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
     if ((n) > 0) { \
         *(r) = (pre)[((n)-1)/2]; \
     } else { \
-        secp256k1_gej_neg((r), &(pre)[(-(n)-1)/2]); \
+        secp256k1_ge_neg((r), &(pre)[(-(n)-1)/2]); \
     } \
 } while(0)
+
 #define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
     VERIFY_CHECK(((n) & 1) == 1); \
     VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
@@ -92,15 +137,15 @@ static void secp256k1_ecmult_table_precomp_ge_storage_var(secp256k1_ge_storage_t
     } \
 } while(0)
 
-static void secp256k1_ecmult_context_init(secp256k1_ecmult_context_t *ctx) {
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
     ctx->pre_g = NULL;
 #ifdef USE_ENDOMORPHISM
     ctx->pre_g_128 = NULL;
 #endif
 }
 
-static void secp256k1_ecmult_context_build(secp256k1_ecmult_context_t *ctx) {
-    secp256k1_gej_t gj;
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb) {
+    secp256k1_gej gj;
 
     if (ctx->pre_g != NULL) {
         return;
@@ -109,35 +154,35 @@ static void secp256k1_ecmult_context_build(secp256k1_ecmult_context_t *ctx) {
     /* get the generator */
     secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
 
-    ctx->pre_g = (secp256k1_ge_storage_t (*)[])checked_malloc(sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
+    ctx->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
 
     /* precompute the tables with odd multiples */
-    secp256k1_ecmult_table_precomp_ge_storage_var(*ctx->pre_g, &gj, WINDOW_G);
+    secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb);
 
 #ifdef USE_ENDOMORPHISM
     {
-        secp256k1_gej_t g_128j;
+        secp256k1_gej g_128j;
         int i;
 
-        ctx->pre_g_128 = (secp256k1_ge_storage_t (*)[])checked_malloc(sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
+        ctx->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
 
         /* calculate 2^128*generator */
         g_128j = gj;
         for (i = 0; i < 128; i++) {
-            secp256k1_gej_double_var(&g_128j, &g_128j);
+            secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
         }
-        secp256k1_ecmult_table_precomp_ge_storage_var(*ctx->pre_g_128, &g_128j, WINDOW_G);
+        secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb);
     }
 #endif
 }
 
-static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context_t *dst,
-                                           const secp256k1_ecmult_context_t *src) {
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+                                           const secp256k1_ecmult_context *src, const secp256k1_callback *cb) {
     if (src->pre_g == NULL) {
         dst->pre_g = NULL;
     } else {
         size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
-        dst->pre_g = (secp256k1_ge_storage_t (*)[])checked_malloc(size);
+        dst->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
         memcpy(dst->pre_g, src->pre_g, size);
     }
 #ifdef USE_ENDOMORPHISM
@@ -145,17 +190,17 @@ static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context_t *dst,
         dst->pre_g_128 = NULL;
     } else {
         size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
-        dst->pre_g_128 = (secp256k1_ge_storage_t (*)[])checked_malloc(size);
+        dst->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
         memcpy(dst->pre_g_128, src->pre_g_128, size);
     }
 #endif
 }
 
-static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context_t *ctx) {
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
     return ctx->pre_g != NULL;
 }
 
-static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context_t *ctx) {
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
     free(ctx->pre_g);
 #ifdef USE_ENDOMORPHISM
     free(ctx->pre_g_128);
@@ -168,54 +213,68 @@ static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context_t *ctx) {
  *  - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
  *  - two non-zero entries in wnaf are separated by at least w-1 zeroes.
  *  - the number of set values in wnaf is returned. This number is at most 256, and at most one more
- *  - than the number of bits in the (absolute value) of the input.
+ *    than the number of bits in the (absolute value) of the input.
  */
-static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_scalar_t *a, int w) {
-    secp256k1_scalar_t s = *a;
-    int set_bits = 0;
+static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) {
+    secp256k1_scalar s = *a;
+    int last_set_bit = -1;
     int bit = 0;
     int sign = 1;
+    int carry = 0;
+
+    VERIFY_CHECK(wnaf != NULL);
+    VERIFY_CHECK(0 <= len && len <= 256);
+    VERIFY_CHECK(a != NULL);
+    VERIFY_CHECK(2 <= w && w <= 31);
+
+    memset(wnaf, 0, len * sizeof(wnaf[0]));
 
     if (secp256k1_scalar_get_bits(&s, 255, 1)) {
         secp256k1_scalar_negate(&s, &s);
         sign = -1;
     }
 
-    while (bit < 256) {
+    while (bit < len) {
         int now;
         int word;
-        if (secp256k1_scalar_get_bits(&s, bit, 1) == 0) {
+        if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
             bit++;
             continue;
         }
-        while (set_bits < bit) {
-            wnaf[set_bits++] = 0;
-        }
+
         now = w;
-        if (bit + now > 256) {
-            now = 256 - bit;
-        }
-        word = secp256k1_scalar_get_bits_var(&s, bit, now);
-        if (word & (1 << (w-1))) {
-            secp256k1_scalar_add_bit(&s, bit + w);
-            wnaf[set_bits++] = sign * (word - (1 << w));
-        } else {
-            wnaf[set_bits++] = sign * word;
+        if (now > len - bit) {
+            now = len - bit;
         }
+
+        word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
+
+        carry = (word >> (w-1)) & 1;
+        word -= carry << w;
+
+        wnaf[bit] = sign * word;
+        last_set_bit = bit;
+
         bit += now;
     }
-    return set_bits;
+#ifdef VERIFY
+    CHECK(carry == 0);
+    while (bit < 256) {
+        CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
+    } 
+#endif
+    return last_set_bit + 1;
 }
 
-static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng) {
-    secp256k1_gej_t tmpj;
-    secp256k1_gej_t pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
-    secp256k1_ge_t tmpa;
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
 #ifdef USE_ENDOMORPHISM
-    secp256k1_gej_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
-    secp256k1_scalar_t na_1, na_lam;
+    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_scalar na_1, na_lam;
     /* Splitted G factors. */
-    secp256k1_scalar_t ng_1, ng_128;
+    secp256k1_scalar ng_1, ng_128;
     int wnaf_na_1[130];
     int wnaf_na_lam[130];
     int bits_na_1;
@@ -227,7 +286,7 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge
 #else
     int wnaf_na[256];
     int bits_na;
-    int wnaf_ng[257];
+    int wnaf_ng[256];
     int bits_ng;
 #endif
     int i;
@@ -235,11 +294,11 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge
 
 #ifdef USE_ENDOMORPHISM
     /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
-    secp256k1_scalar_split_lambda_var(&na_1, &na_lam, na);
+    secp256k1_scalar_split_lambda(&na_1, &na_lam, na);
 
     /* build wnaf representation for na_1 and na_lam. */
-    bits_na_1   = secp256k1_ecmult_wnaf(wnaf_na_1,   &na_1,   WINDOW_A);
-    bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
+    bits_na_1   = secp256k1_ecmult_wnaf(wnaf_na_1,   130, &na_1,   WINDOW_A);
+    bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, 130, &na_lam, WINDOW_A);
     VERIFY_CHECK(bits_na_1 <= 130);
     VERIFY_CHECK(bits_na_lam <= 130);
     bits = bits_na_1;
@@ -248,24 +307,33 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge
     }
 #else
     /* build wnaf representation for na. */
-    bits_na     = secp256k1_ecmult_wnaf(wnaf_na,     na,      WINDOW_A);
+    bits_na     = secp256k1_ecmult_wnaf(wnaf_na,     256, na,      WINDOW_A);
     bits = bits_na;
 #endif
 
-    /* calculate odd multiples of a */
-    secp256k1_ecmult_table_precomp_gej_var(pre_a, a, WINDOW_A);
+    /* Calculate odd multiples of a.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     * The exception is the precomputed G table points, which are actually
+     * affine. Compared to the base used for other points, they have a Z ratio
+     * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
+     * isomorphism to efficiently add with a known Z inverse.
+     */
+    secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, a);
 
 #ifdef USE_ENDOMORPHISM
     for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
-        secp256k1_gej_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+        secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
     }
 
     /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
     secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
 
     /* Build wnaf representation for ng_1 and ng_128 */
-    bits_ng_1   = secp256k1_ecmult_wnaf(wnaf_ng_1,   &ng_1,   WINDOW_G);
-    bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, &ng_128, WINDOW_G);
+    bits_ng_1   = secp256k1_ecmult_wnaf(wnaf_ng_1,   129, &ng_1,   WINDOW_G);
+    bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
     if (bits_ng_1 > bits) {
         bits = bits_ng_1;
     }
@@ -273,7 +341,7 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge
         bits = bits_ng_128;
     }
 #else
-    bits_ng     = secp256k1_ecmult_wnaf(wnaf_ng,     ng,      WINDOW_G);
+    bits_ng     = secp256k1_ecmult_wnaf(wnaf_ng,     256, ng,      WINDOW_G);
     if (bits_ng > bits) {
         bits = bits_ng;
     }
@@ -281,37 +349,41 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_ge
 
     secp256k1_gej_set_infinity(r);
 
-    for (i = bits-1; i >= 0; i--) {
+    for (i = bits - 1; i >= 0; i--) {
         int n;
-        secp256k1_gej_double_var(r, r);
+        secp256k1_gej_double_var(r, r, NULL);
 #ifdef USE_ENDOMORPHISM
         if (i < bits_na_1 && (n = wnaf_na_1[i])) {
-            ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
-            secp256k1_gej_add_var(r, r, &tmpj);
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
         }
         if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
-            ECMULT_TABLE_GET_GEJ(&tmpj, pre_a_lam, n, WINDOW_A);
-            secp256k1_gej_add_var(r, r, &tmpj);
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
         }
         if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
             ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
-            secp256k1_gej_add_ge_var(r, r, &tmpa);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
         }
         if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
             ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
-            secp256k1_gej_add_ge_var(r, r, &tmpa);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
         }
 #else
         if (i < bits_na && (n = wnaf_na[i])) {
-            ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
-            secp256k1_gej_add_var(r, r, &tmpj);
+            ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+            secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
         }
         if (i < bits_ng && (n = wnaf_ng[i])) {
             ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
-            secp256k1_gej_add_ge_var(r, r, &tmpa);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
         }
 #endif
     }
+
+    if (!r->infinity) {
+        secp256k1_fe_mul(&r->z, &r->z, &Z);
+    }
 }
 
 #endif
diff --git a/src/secp256k1/src/field.h b/src/secp256k1/src/field.h
index 41b280892d..2d52af5e36 100644
--- a/src/secp256k1/src/field.h
+++ b/src/secp256k1/src/field.h
@@ -10,7 +10,7 @@
 /** Field element module.
  *
  *  Field elements can be represented in several ways, but code accessing
- *  it (and implementations) need to take certain properaties into account:
+ *  it (and implementations) need to take certain properties into account:
  *  - Each field element can be normalized or not.
  *  - Each field element has a magnitude, which represents how far away
  *    its representation is away from normalization. Normalized elements
@@ -31,89 +31,91 @@
 #endif
 
 /** Normalize a field element. */
-static void secp256k1_fe_normalize(secp256k1_fe_t *r);
+static void secp256k1_fe_normalize(secp256k1_fe *r);
 
 /** Weakly normalize a field element: reduce it magnitude to 1, but don't fully normalize. */
-static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r);
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
 
 /** Normalize a field element, without constant-time guarantee. */
-static void secp256k1_fe_normalize_var(secp256k1_fe_t *r);
+static void secp256k1_fe_normalize_var(secp256k1_fe *r);
 
 /** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
  *  implementation may optionally normalize the input, but this should not be relied upon. */
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r);
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r);
 
 /** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
  *  implementation may optionally normalize the input, but this should not be relied upon. */
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r);
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
 
 /** Set a field element equal to a small integer. Resulting field element is normalized. */
-static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a);
+static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
 
 /** Verify whether a field element is zero. Requires the input to be normalized. */
-static int secp256k1_fe_is_zero(const secp256k1_fe_t *a);
+static int secp256k1_fe_is_zero(const secp256k1_fe *a);
 
 /** Check the "oddness" of a field element. Requires the input to be normalized. */
-static int secp256k1_fe_is_odd(const secp256k1_fe_t *a);
+static int secp256k1_fe_is_odd(const secp256k1_fe *a);
 
 /** Compare two field elements. Requires magnitude-1 inputs. */
-static int secp256k1_fe_equal_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
+static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
 
 /** Compare two field elements. Requires both inputs to be normalized */
-static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
 
-/** Set a field element equal to 32-byte big endian value. If succesful, the resulting field element is normalized. */
-static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a);
+/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a);
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
 
 /** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
  *  as an argument. The magnitude of the output is one higher. */
-static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m);
+static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
 
 /** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
  *  small integer. */
-static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a);
+static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
 
 /** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
-static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
  *  The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b);
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
 
 /** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
  *  The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
 
-/** Sets a field element to be the (modular) square root (if any exist) of another. Requires the
- *  input's magnitude to be at most 8. The output magnitude is 1 (but not guaranteed to be
- *  normalized). Return value indicates whether a square root was found. */
-static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+/** If a has a square root, it is computed in r and 1 is returned. If a does not
+ *  have a square root, the root of its negation is computed and 0 is returned.
+ *  The input's magnitude can be at most 8. The output magnitude is 1 (but not
+ *  guaranteed to be normalized). The result in r will always be a square
+ *  itself. */
+static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be
  *  at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
-static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be
  *  at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and
  *  outputs must not overlap in memory. */
-static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Convert a field element to the storage type. */
-static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t*);
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
 
 /** Convert a field element back from the storage type. */
-static void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t*);
+static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
 
 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
-static void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r, const secp256k1_fe_storage_t *a, int flag);
+static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
 
 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
-static void secp256k1_fe_cmov(secp256k1_fe_t *r, const secp256k1_fe_t *a, int flag);
+static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
 
 #endif
diff --git a/src/secp256k1/src/field_10x26.h b/src/secp256k1/src/field_10x26.h
index 44bce6525d..61ee1e0965 100644
--- a/src/secp256k1/src/field_10x26.h
+++ b/src/secp256k1/src/field_10x26.h
@@ -16,20 +16,20 @@ typedef struct {
     int magnitude;
     int normalized;
 #endif
-} secp256k1_fe_t;
+} secp256k1_fe;
 
 /* Unpacks a constant into a overlapping multi-limbed FE element. */
 #define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
     (d0) & 0x3FFFFFFUL, \
-    ((d0) >> 26) | ((d1) & 0xFFFFFUL) << 6, \
-    ((d1) >> 20) | ((d2) & 0x3FFFUL) << 12, \
-    ((d2) >> 14) | ((d3) & 0xFFUL) << 18, \
-    ((d3) >> 8) | ((d4) & 0x3) << 24, \
-    ((d4) >> 2) & 0x3FFFFFFUL, \
-    ((d4) >> 28) | ((d5) & 0x3FFFFFUL) << 4, \
-    ((d5) >> 22) | ((d6) & 0xFFFF) << 10, \
-    ((d6) >> 16) | ((d7) & 0x3FF) << 16, \
-    ((d7) >> 10) \
+    (((uint32_t)d0) >> 26) | (((uint32_t)(d1) & 0xFFFFFUL) << 6), \
+    (((uint32_t)d1) >> 20) | (((uint32_t)(d2) & 0x3FFFUL) << 12), \
+    (((uint32_t)d2) >> 14) | (((uint32_t)(d3) & 0xFFUL) << 18), \
+    (((uint32_t)d3) >> 8) | (((uint32_t)(d4) & 0x3UL) << 24), \
+    (((uint32_t)d4) >> 2) & 0x3FFFFFFUL, \
+    (((uint32_t)d4) >> 28) | (((uint32_t)(d5) & 0x3FFFFFUL) << 4), \
+    (((uint32_t)d5) >> 22) | (((uint32_t)(d6) & 0xFFFFUL) << 10), \
+    (((uint32_t)d6) >> 16) | (((uint32_t)(d7) & 0x3FFUL) << 16), \
+    (((uint32_t)d7) >> 10) \
 }
 
 #ifdef VERIFY
@@ -40,8 +40,8 @@ typedef struct {
 
 typedef struct {
     uint32_t n[8];
-} secp256k1_fe_storage_t;
+} secp256k1_fe_storage;
 
 #define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }}
-
+#define SECP256K1_FE_STORAGE_CONST_GET(d) d.n[7], d.n[6], d.n[5], d.n[4],d.n[3], d.n[2], d.n[1], d.n[0]
 #endif
diff --git a/src/secp256k1/src/field_10x26_impl.h b/src/secp256k1/src/field_10x26_impl.h
index 871b91f912..212cc5396a 100644
--- a/src/secp256k1/src/field_10x26_impl.h
+++ b/src/secp256k1/src/field_10x26_impl.h
@@ -14,7 +14,7 @@
 #include "field.h"
 
 #ifdef VERIFY
-static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
     const uint32_t *d = a->n;
     int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
     r &= (d[0] <= 0x3FFFFFFUL * m);
@@ -41,12 +41,12 @@ static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
     VERIFY_CHECK(r == 1);
 }
 #else
-static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
     (void)a;
 }
 #endif
 
-static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -101,7 +101,7 @@ static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
 #endif
 }
 
-static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -132,7 +132,7 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
 #endif
 }
 
-static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -188,7 +188,7 @@ static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
 #endif
 }
 
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
     uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
              t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
 
@@ -217,7 +217,7 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
     return (z0 == 0) | (z1 == 0x3FFFFFFUL);
 }
 
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
     uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
     uint32_t z0, z1;
     uint32_t x;
@@ -252,7 +252,7 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
     t9 &= 0x03FFFFFUL;
     t1 += (x << 6);
 
-    t1 += (t0 >> 26); t0  = z0;
+    t1 += (t0 >> 26);
     t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
     t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
     t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
@@ -269,7 +269,7 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
     return (z0 == 0) | (z1 == 0x3FFFFFFUL);
 }
 
-SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
 #ifdef VERIFY
@@ -279,7 +279,7 @@ SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
     const uint32_t *t = a->n;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -288,7 +288,7 @@ SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
     return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
     secp256k1_fe_verify(a);
@@ -296,7 +296,7 @@ SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
     return a->n[0] & 1;
 }
 
-SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
     int i;
 #ifdef VERIFY
     a->magnitude = 0;
@@ -307,7 +307,7 @@ SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
     }
 }
 
-static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -326,7 +326,7 @@ static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b
     return 0;
 }
 
-static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
     int i;
     r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
     r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
@@ -350,7 +350,7 @@ static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
 }
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
     int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -368,7 +368,7 @@ static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
     }
 }
 
-SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= m);
     secp256k1_fe_verify(a);
@@ -390,7 +390,7 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp25
 #endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
     r->n[0] *= a;
     r->n[1] *= a;
     r->n[2] *= a;
@@ -408,7 +408,7 @@ SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     secp256k1_fe_verify(a);
 #endif
@@ -1039,7 +1039,7 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t
 }
 
 
-static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b) {
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= 8);
     VERIFY_CHECK(b->magnitude <= 8);
@@ -1055,7 +1055,7 @@ static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const s
 #endif
 }
 
-static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= 8);
     secp256k1_fe_verify(a);
@@ -1068,7 +1068,7 @@ static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
 #endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe_t *r, const secp256k1_fe_t *a, int flag) {
+static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
     uint32_t mask0, mask1;
     mask0 = flag + ~((uint32_t)0);
     mask1 = ~mask0;
@@ -1083,12 +1083,14 @@ static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe_t *r, const secp256k
     r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
     r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
 #ifdef VERIFY
-    r->magnitude = (r->magnitude & mask0) | (a->magnitude & mask1);
-    r->normalized = (r->normalized & mask0) | (a->normalized & mask1);
+    if (a->magnitude > r->magnitude) {
+        r->magnitude = a->magnitude;
+    }
+    r->normalized &= a->normalized;
 #endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r, const secp256k1_fe_storage_t *a, int flag) {
+static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
     uint32_t mask0, mask1;
     mask0 = flag + ~((uint32_t)0);
     mask1 = ~mask0;
@@ -1102,7 +1104,7 @@ static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r
     r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
 }
 
-static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
 #endif
@@ -1116,7 +1118,7 @@ static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_f
     r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
 }
 
-static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t *a) {
+static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
     r->n[0] = a->n[0] & 0x3FFFFFFUL;
     r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
     r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
diff --git a/src/secp256k1/src/field_5x52.h b/src/secp256k1/src/field_5x52.h
index 4513d36f49..8e69a560dc 100644
--- a/src/secp256k1/src/field_5x52.h
+++ b/src/secp256k1/src/field_5x52.h
@@ -16,15 +16,15 @@ typedef struct {
     int magnitude;
     int normalized;
 #endif
-} secp256k1_fe_t;
+} secp256k1_fe;
 
 /* Unpacks a constant into a overlapping multi-limbed FE element. */
 #define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
-    (d0) | ((uint64_t)(d1) & 0xFFFFFUL) << 32, \
-    ((d1) >> 20) | ((uint64_t)(d2)) << 12 | ((uint64_t)(d3) & 0xFFUL) << 44, \
-    ((d3) >> 8) | ((uint64_t)(d4) & 0xFFFFFFFUL) << 24, \
-    ((d4) >> 28) | ((uint64_t)(d5)) << 4 | ((uint64_t)(d6) & 0xFFFFUL) << 36, \
-    ((d6) >> 16) | ((uint64_t)(d7)) << 16 \
+    (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \
+    ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \
+    ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \
+    ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \
+    ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \
 }
 
 #ifdef VERIFY
@@ -35,13 +35,13 @@ typedef struct {
 
 typedef struct {
     uint64_t n[4];
-} secp256k1_fe_storage_t;
+} secp256k1_fe_storage;
 
 #define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \
-    (d0) | ((uint64_t)(d1)) << 32, \
-    (d2) | ((uint64_t)(d3)) << 32, \
-    (d4) | ((uint64_t)(d5)) << 32, \
-    (d6) | ((uint64_t)(d7)) << 32 \
+    (d0) | (((uint64_t)(d1)) << 32), \
+    (d2) | (((uint64_t)(d3)) << 32), \
+    (d4) | (((uint64_t)(d5)) << 32), \
+    (d6) | (((uint64_t)(d7)) << 32) \
 }}
 
 #endif
diff --git a/src/secp256k1/src/field_5x52_impl.h b/src/secp256k1/src/field_5x52_impl.h
index bda4c3dfc2..b31e24ab81 100644
--- a/src/secp256k1/src/field_5x52_impl.h
+++ b/src/secp256k1/src/field_5x52_impl.h
@@ -31,7 +31,7 @@
  */
 
 #ifdef VERIFY
-static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
     const uint64_t *d = a->n;
     int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
    /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
@@ -51,12 +51,12 @@ static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
     VERIFY_CHECK(r == 1);
 }
 #else
-static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
     (void)a;
 }
 #endif
 
-static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -99,7 +99,7 @@ static void secp256k1_fe_normalize(secp256k1_fe_t *r) {
 #endif
 }
 
-static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -123,7 +123,7 @@ static void secp256k1_fe_normalize_weak(secp256k1_fe_t *r) {
 #endif
 }
 
-static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
+static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* Reduce t4 at the start so there will be at most a single carry from the first pass */
@@ -167,7 +167,7 @@ static void secp256k1_fe_normalize_var(secp256k1_fe_t *r) {
 #endif
 }
 
-static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) {
     uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
 
     /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
@@ -190,7 +190,7 @@ static int secp256k1_fe_normalizes_to_zero(secp256k1_fe_t *r) {
     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 }
 
-static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) {
     uint64_t t0, t1, t2, t3, t4;
     uint64_t z0, z1;
     uint64_t x;
@@ -219,7 +219,7 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
 
     t4 &= 0x0FFFFFFFFFFFFULL;
 
-    t1 += (t0 >> 52); t0  = z0;
+    t1 += (t0 >> 52);
     t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
     t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
     t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
@@ -231,7 +231,7 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe_t *r) {
     return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
 }
 
-SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
 #ifdef VERIFY
@@ -241,7 +241,7 @@ SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
     const uint64_t *t = a->n;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -250,7 +250,7 @@ SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe_t *a) {
     return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
 }
 
-SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
     secp256k1_fe_verify(a);
@@ -258,7 +258,7 @@ SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe_t *a) {
     return a->n[0] & 1;
 }
 
-SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
     int i;
 #ifdef VERIFY
     a->magnitude = 0;
@@ -269,7 +269,7 @@ SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe_t *a) {
     }
 }
 
-static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -288,7 +288,7 @@ static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b
     return 0;
 }
 
-static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
     int i;
     r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
     for (i=0; i<32; i++) {
@@ -311,7 +311,7 @@ static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a) {
 }
 
 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
     int i;
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
@@ -329,7 +329,7 @@ static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a) {
     }
 }
 
-SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m) {
+SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= m);
     secp256k1_fe_verify(a);
@@ -346,7 +346,7 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp25
 #endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
     r->n[0] *= a;
     r->n[1] *= a;
     r->n[2] *= a;
@@ -359,7 +359,7 @@ SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a) {
 #endif
 }
 
-SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     secp256k1_fe_verify(a);
 #endif
@@ -375,7 +375,7 @@ SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1
 #endif
 }
 
-static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b) {
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= 8);
     VERIFY_CHECK(b->magnitude <= 8);
@@ -391,7 +391,7 @@ static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const s
 #endif
 }
 
-static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->magnitude <= 8);
     secp256k1_fe_verify(a);
@@ -404,7 +404,7 @@ static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
 #endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe_t *r, const secp256k1_fe_t *a, int flag) {
+static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
     uint64_t mask0, mask1;
     mask0 = flag + ~((uint64_t)0);
     mask1 = ~mask0;
@@ -414,12 +414,14 @@ static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe_t *r, const secp256k
     r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
     r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
 #ifdef VERIFY
-    r->magnitude = (r->magnitude & mask0) | (a->magnitude & mask1);
-    r->normalized = (r->normalized & mask0) | (a->normalized & mask1);
+    if (a->magnitude > r->magnitude) {
+        r->magnitude = a->magnitude;
+    }
+    r->normalized &= a->normalized;
 #endif
 }
 
-static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r, const secp256k1_fe_storage_t *a, int flag) {
+static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
     uint64_t mask0, mask1;
     mask0 = flag + ~((uint64_t)0);
     mask1 = ~mask0;
@@ -429,7 +431,7 @@ static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage_t *r
     r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
 }
 
-static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
 #ifdef VERIFY
     VERIFY_CHECK(a->normalized);
 #endif
@@ -439,7 +441,7 @@ static void secp256k1_fe_to_storage(secp256k1_fe_storage_t *r, const secp256k1_f
     r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
 }
 
-static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe_t *r, const secp256k1_fe_storage_t *a) {
+static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
     r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
     r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
     r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
diff --git a/src/secp256k1/src/field_impl.h b/src/secp256k1/src/field_impl.h
index e6ec11e8f2..77f4aae2f9 100644
--- a/src/secp256k1/src/field_impl.h
+++ b/src/secp256k1/src/field_impl.h
@@ -21,15 +21,24 @@
 #error "Please select field implementation"
 #endif
 
-SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
-    secp256k1_fe_t na;
+SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe na;
     secp256k1_fe_negate(&na, a, 1);
     secp256k1_fe_add(&na, b);
     return secp256k1_fe_normalizes_to_zero_var(&na);
 }
 
-static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
-    secp256k1_fe_t x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a) {
+    /** Given that p is congruent to 3 mod 4, we can compute the square root of
+     *  a mod p as the (p+1)/4'th power of a.
+     *
+     *  As (p+1)/4 is an even number, it will have the same result for a and for
+     *  (-a). Only one of these two numbers actually has a square root however,
+     *  so we test at the end by squaring and comparing to the input.
+     *  Also because (p+1)/4 is an even number, the computed square root is
+     *  itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
+     */
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
     int j;
 
     /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
@@ -117,8 +126,8 @@ static int secp256k1_fe_sqrt_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
     return secp256k1_fe_equal_var(&t1, a);
 }
 
-static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
-    secp256k1_fe_t x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
     int j;
 
     /** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in
@@ -207,11 +216,15 @@ static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
     secp256k1_fe_mul(r, a, &t1);
 }
 
-static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
 #if defined(USE_FIELD_INV_BUILTIN)
     secp256k1_fe_inv(r, a);
 #elif defined(USE_FIELD_INV_NUM)
-    secp256k1_num_t n, m;
+    secp256k1_num n, m;
+    static const secp256k1_fe negone = SECP256K1_FE_CONST(
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
+        0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL
+    );
     /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
     static const unsigned char prime[32] = {
         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
@@ -220,21 +233,28 @@ static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
         0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
     };
     unsigned char b[32];
-    secp256k1_fe_t c = *a;
+    int res;
+    secp256k1_fe c = *a;
     secp256k1_fe_normalize_var(&c);
     secp256k1_fe_get_b32(b, &c);
     secp256k1_num_set_bin(&n, b, 32);
     secp256k1_num_set_bin(&m, prime, 32);
     secp256k1_num_mod_inverse(&n, &n, &m);
     secp256k1_num_get_bin(b, 32, &n);
-    VERIFY_CHECK(secp256k1_fe_set_b32(r, b));
+    res = secp256k1_fe_set_b32(r, b);
+    (void)res;
+    VERIFY_CHECK(res);
+    /* Verify the result is the (unique) valid inverse using non-GMP code. */
+    secp256k1_fe_mul(&c, &c, r);
+    secp256k1_fe_add(&c, &negone);
+    CHECK(secp256k1_fe_normalizes_to_zero_var(&c));
 #else
 #error "Please select field inverse implementation"
 #endif
 }
 
-static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t *r, const secp256k1_fe_t *a) {
-    secp256k1_fe_t u;
+static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe u;
     size_t i;
     if (len < 1) {
         return;
@@ -252,7 +272,7 @@ static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t *r, const secp25
     secp256k1_fe_inv_var(&u, &r[--i]);
 
     while (i > 0) {
-        int j = i--;
+        size_t j = i--;
         secp256k1_fe_mul(&r[j], &r[i], &u);
         secp256k1_fe_mul(&u, &u, &a[j]);
     }
diff --git a/src/secp256k1/src/gen_context.c b/src/secp256k1/src/gen_context.c
new file mode 100644
index 0000000000..1835fd491d
--- /dev/null
+++ b/src/secp256k1/src/gen_context.c
@@ -0,0 +1,74 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields           *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#define USE_BASIC_CONFIG 1
+
+#include "basic-config.h"
+#include "include/secp256k1.h"
+#include "field_impl.h"
+#include "scalar_impl.h"
+#include "group_impl.h"
+#include "ecmult_gen_impl.h"
+
+static void default_error_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_error_callback = {
+    default_error_callback_fn,
+    NULL
+};
+
+int main(int argc, char **argv) {
+    secp256k1_ecmult_gen_context ctx;
+    int inner;
+    int outer;
+    FILE* fp;
+
+    (void)argc;
+    (void)argv;
+
+    fp = fopen("src/ecmult_static_context.h","w");
+    if (fp == NULL) {
+        fprintf(stderr, "Could not open src/ecmult_static_context.h for writing!\n");
+        return -1;
+    }
+    
+    fprintf(fp, "#ifndef _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
+    fprintf(fp, "#define _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
+    fprintf(fp, "#include \"group.h\"\n");
+    fprintf(fp, "#define SC SECP256K1_GE_STORAGE_CONST\n");
+    fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_static_context[64][16] = {\n");
+
+    secp256k1_ecmult_gen_context_init(&ctx);
+    secp256k1_ecmult_gen_context_build(&ctx, &default_error_callback);
+    for(outer = 0; outer != 64; outer++) {
+        fprintf(fp,"{\n");
+        for(inner = 0; inner != 16; inner++) {
+            fprintf(fp,"    SC(%uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu)", SECP256K1_GE_STORAGE_CONST_GET((*ctx.prec)[outer][inner]));
+            if (inner != 15) {
+                fprintf(fp,",\n");
+            } else {
+                fprintf(fp,"\n");
+            }
+        }
+        if (outer != 63) {
+            fprintf(fp,"},\n");
+        } else {
+            fprintf(fp,"}\n");
+        }
+    }
+    fprintf(fp,"};\n");
+    secp256k1_ecmult_gen_context_clear(&ctx);
+    
+    fprintf(fp, "#undef SC\n");
+    fprintf(fp, "#endif\n");
+    fclose(fp);
+    
+    return 0;
+}
diff --git a/src/secp256k1/src/group.h b/src/secp256k1/src/group.h
index 0b08b3b991..ebfe1ca70c 100644
--- a/src/secp256k1/src/group.h
+++ b/src/secp256k1/src/group.h
@@ -12,110 +12,130 @@
 
 /** A group element of the secp256k1 curve, in affine coordinates. */
 typedef struct {
-    secp256k1_fe_t x;
-    secp256k1_fe_t y;
+    secp256k1_fe x;
+    secp256k1_fe y;
     int infinity; /* whether this represents the point at infinity */
-} secp256k1_ge_t;
+} secp256k1_ge;
 
 #define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
 #define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
 
 /** A group element of the secp256k1 curve, in jacobian coordinates. */
 typedef struct {
-    secp256k1_fe_t x; /* actual X: x/z^2 */
-    secp256k1_fe_t y; /* actual Y: y/z^3 */
-    secp256k1_fe_t z;
+    secp256k1_fe x; /* actual X: x/z^2 */
+    secp256k1_fe y; /* actual Y: y/z^3 */
+    secp256k1_fe z;
     int infinity; /* whether this represents the point at infinity */
-} secp256k1_gej_t;
+} secp256k1_gej;
 
 #define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
 #define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
 
 typedef struct {
-    secp256k1_fe_storage_t x;
-    secp256k1_fe_storage_t y;
-} secp256k1_ge_storage_t;
+    secp256k1_fe_storage x;
+    secp256k1_fe_storage y;
+} secp256k1_ge_storage;
 
 #define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
 
-/** Set a group element equal to the point at infinity */
-static void secp256k1_ge_set_infinity(secp256k1_ge_t *r);
+#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)
 
 /** Set a group element equal to the point with given X and Y coordinates */
-static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y);
+
+/** Set a group element (affine) equal to the point with the given X coordinate
+ *  and a Y coordinate that is a quadratic residue modulo p. The return value
+ *  is true iff a coordinate with the given X coordinate exists.
+ */
+static int secp256k1_ge_set_xquad_var(secp256k1_ge *r, const secp256k1_fe *x);
 
 /** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
  *  for Y. Return value indicates whether the result is valid. */
-static int secp256k1_ge_set_xo_var(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd);
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd);
 
 /** Check whether a group element is the point at infinity. */
-static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a);
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
 
 /** Check whether a group element is valid (i.e., on the curve). */
-static int secp256k1_ge_is_valid_var(const secp256k1_ge_t *a);
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
 
-static void secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a);
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
 
 /** Set a group element equal to another which is given in jacobian coordinates */
-static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a);
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
 
 /** Set a batch of group elements equal to the inputs given in jacobian coordinates */
-static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t *r, const secp256k1_gej_t *a);
+static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb);
 
+/** Set a batch of group elements equal to the inputs given in jacobian
+ *  coordinates (with known z-ratios). zr must contain the known z-ratios such
+ *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. */
+static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr);
 
-/** Set a group element (jacobian) equal to the point at infinity. */
-static void secp256k1_gej_set_infinity(secp256k1_gej_t *r);
+/** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
+ *  the same global z "denominator". zr must contain the known z-ratios such
+ *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y
+ *  coordinates of the result are stored in r, the common z coordinate is
+ *  stored in globalz. */
+static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr);
 
-/** Set a group element (jacobian) equal to the point with given X and Y coordinates. */
-static void secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
+/** Set a group element (jacobian) equal to the point at infinity. */
+static void secp256k1_gej_set_infinity(secp256k1_gej *r);
 
 /** Set a group element (jacobian) equal to another which is given in affine coordinates. */
-static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a);
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
 
 /** Compare the X coordinate of a group element (jacobian). */
-static int secp256k1_gej_eq_x_var(const secp256k1_fe_t *x, const secp256k1_gej_t *a);
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
 
 /** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
-static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a);
 
 /** Check whether a group element is the point at infinity. */
-static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a);
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a);
 
-/** Set r equal to the double of a. */
-static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0).
+ * a may not be zero. Constant time. */
+static void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
 
-/** Set r equal to the sum of a and b. */
-static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b);
+/** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0). */
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr);
 
 /** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
-static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b);
 
 /** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
     than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
-    guarantee, and b is allowed to be infinity. */
-static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
+    guarantee, and b is allowed to be infinity. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
 
 #ifdef USE_ENDOMORPHISM
 /** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
-static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
 #endif
 
-/** Clear a secp256k1_gej_t to prevent leaking sensitive information. */
-static void secp256k1_gej_clear(secp256k1_gej_t *r);
+/** Clear a secp256k1_gej to prevent leaking sensitive information. */
+static void secp256k1_gej_clear(secp256k1_gej *r);
 
-/** Clear a secp256k1_ge_t to prevent leaking sensitive information. */
-static void secp256k1_ge_clear(secp256k1_ge_t *r);
+/** Clear a secp256k1_ge to prevent leaking sensitive information. */
+static void secp256k1_ge_clear(secp256k1_ge *r);
 
 /** Convert a group element to the storage type. */
-static void secp256k1_ge_to_storage(secp256k1_ge_storage_t *r, const secp256k1_ge_t*);
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a);
 
 /** Convert a group element back from the storage type. */
-static void secp256k1_ge_from_storage(secp256k1_ge_t *r, const secp256k1_ge_storage_t*);
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
 
 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
-static void secp256k1_ge_storage_cmov(secp256k1_ge_storage_t *r, const secp256k1_ge_storage_t *a, int flag);
+static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
 
 /** Rescale a jacobian point by b which must be non-zero. Constant-time. */
-static void secp256k1_gej_rescale(secp256k1_gej_t *r, const secp256k1_fe_t *b);
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
 
 #endif
diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h
index 0f64576fbb..42e2f6e6eb 100644
--- a/src/secp256k1/src/group_impl.h
+++ b/src/secp256k1/src/group_impl.h
@@ -16,35 +16,41 @@
 /** Generator for secp256k1, value 'g' defined in
  *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
  */
-static const secp256k1_ge_t secp256k1_ge_const_g = SECP256K1_GE_CONST(
+static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
     0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
     0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
     0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
     0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
 );
 
-static void secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
-    r->infinity = 1;
+static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
+    secp256k1_fe zi2; 
+    secp256k1_fe zi3;
+    secp256k1_fe_sqr(&zi2, zi);
+    secp256k1_fe_mul(&zi3, &zi2, zi);
+    secp256k1_fe_mul(&r->x, &a->x, &zi2);
+    secp256k1_fe_mul(&r->y, &a->y, &zi3);
+    r->infinity = a->infinity;
 }
 
-static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
     r->infinity = 0;
     r->x = *x;
     r->y = *y;
 }
 
-static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
     return a->infinity;
 }
 
-static void secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a) {
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
     *r = *a;
     secp256k1_fe_normalize_weak(&r->y);
     secp256k1_fe_negate(&r->y, &r->y, 1);
 }
 
-static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
-    secp256k1_fe_t z2, z3;
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
+    secp256k1_fe z2, z3;
     r->infinity = a->infinity;
     secp256k1_fe_inv(&a->z, &a->z);
     secp256k1_fe_sqr(&z2, &a->z);
@@ -56,8 +62,8 @@ static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
     r->y = a->y;
 }
 
-static void secp256k1_ge_set_gej_var(secp256k1_ge_t *r, secp256k1_gej_t *a) {
-    secp256k1_fe_t z2, z3;
+static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
+    secp256k1_fe z2, z3;
     r->infinity = a->infinity;
     if (a->infinity) {
         return;
@@ -72,19 +78,19 @@ static void secp256k1_ge_set_gej_var(secp256k1_ge_t *r, secp256k1_gej_t *a) {
     r->y = a->y;
 }
 
-static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t *r, const secp256k1_gej_t *a) {
-    secp256k1_fe_t *az;
-    secp256k1_fe_t *azi;
+static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb) {
+    secp256k1_fe *az;
+    secp256k1_fe *azi;
     size_t i;
     size_t count = 0;
-    az = (secp256k1_fe_t *)checked_malloc(sizeof(secp256k1_fe_t) * len);
+    az = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * len);
     for (i = 0; i < len; i++) {
         if (!a[i].infinity) {
             az[count++] = a[i].z;
         }
     }
 
-    azi = (secp256k1_fe_t *)checked_malloc(sizeof(secp256k1_fe_t) * count);
+    azi = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * count);
     secp256k1_fe_inv_all_var(count, azi, az);
     free(az);
 
@@ -92,53 +98,86 @@ static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t *r, const se
     for (i = 0; i < len; i++) {
         r[i].infinity = a[i].infinity;
         if (!a[i].infinity) {
-            secp256k1_fe_t zi2, zi3;
-            secp256k1_fe_t *zi = &azi[count++];
-            secp256k1_fe_sqr(&zi2, zi);
-            secp256k1_fe_mul(&zi3, &zi2, zi);
-            secp256k1_fe_mul(&r[i].x, &a[i].x, &zi2);
-            secp256k1_fe_mul(&r[i].y, &a[i].y, &zi3);
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &azi[count++]);
         }
     }
     free(azi);
 }
 
-static void secp256k1_gej_set_infinity(secp256k1_gej_t *r) {
+static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr) {
+    size_t i = len - 1;
+    secp256k1_fe zi;
+
+    if (len > 0) {
+        /* Compute the inverse of the last z coordinate, and use it to compute the last affine output. */
+        secp256k1_fe_inv(&zi, &a[i].z);
+        secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
+
+        /* Work out way backwards, using the z-ratios to scale the x/y values. */
+        while (i > 0) {
+            secp256k1_fe_mul(&zi, &zi, &zr[i]);
+            i--;
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zi);
+        }
+    }
+}
+
+static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr) {
+    size_t i = len - 1;
+    secp256k1_fe zs;
+
+    if (len > 0) {
+        /* The z of the final point gives us the "global Z" for the table. */
+        r[i].x = a[i].x;
+        r[i].y = a[i].y;
+        *globalz = a[i].z;
+        r[i].infinity = 0;
+        zs = zr[i];
+
+        /* Work our way backwards, using the z-ratios to scale the x/y values. */
+        while (i > 0) {
+            if (i != len - 1) {
+                secp256k1_fe_mul(&zs, &zs, &zr[i]);
+            }
+            i--;
+            secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zs);
+        }
+    }
+}
+
+static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
     r->infinity = 1;
     secp256k1_fe_set_int(&r->x, 0);
     secp256k1_fe_set_int(&r->y, 0);
     secp256k1_fe_set_int(&r->z, 0);
 }
 
-static void secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
-    r->infinity = 0;
-    r->x = *x;
-    r->y = *y;
-    secp256k1_fe_set_int(&r->z, 1);
-}
-
-static void secp256k1_gej_clear(secp256k1_gej_t *r) {
+static void secp256k1_gej_clear(secp256k1_gej *r) {
     r->infinity = 0;
     secp256k1_fe_clear(&r->x);
     secp256k1_fe_clear(&r->y);
     secp256k1_fe_clear(&r->z);
 }
 
-static void secp256k1_ge_clear(secp256k1_ge_t *r) {
+static void secp256k1_ge_clear(secp256k1_ge *r) {
     r->infinity = 0;
     secp256k1_fe_clear(&r->x);
     secp256k1_fe_clear(&r->y);
 }
 
-static int secp256k1_ge_set_xo_var(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd) {
-    secp256k1_fe_t x2, x3, c;
+static int secp256k1_ge_set_xquad_var(secp256k1_ge *r, const secp256k1_fe *x) {
+    secp256k1_fe x2, x3, c;
     r->x = *x;
     secp256k1_fe_sqr(&x2, x);
     secp256k1_fe_mul(&x3, x, &x2);
     r->infinity = 0;
     secp256k1_fe_set_int(&c, 7);
     secp256k1_fe_add(&c, &x3);
-    if (!secp256k1_fe_sqrt_var(&r->y, &c)) {
+    return secp256k1_fe_sqrt_var(&r->y, &c);
+}
+
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
+    if (!secp256k1_ge_set_xquad_var(r, x)) {
         return 0;
     }
     secp256k1_fe_normalize_var(&r->y);
@@ -146,24 +185,25 @@ static int secp256k1_ge_set_xo_var(secp256k1_ge_t *r, const secp256k1_fe_t *x, i
         secp256k1_fe_negate(&r->y, &r->y, 1);
     }
     return 1;
+
 }
 
-static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
    r->infinity = a->infinity;
    r->x = a->x;
    r->y = a->y;
    secp256k1_fe_set_int(&r->z, 1);
 }
 
-static int secp256k1_gej_eq_x_var(const secp256k1_fe_t *x, const secp256k1_gej_t *a) {
-    secp256k1_fe_t r, r2;
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
+    secp256k1_fe r, r2;
     VERIFY_CHECK(!a->infinity);
     secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
     r2 = a->x; secp256k1_fe_normalize_weak(&r2);
     return secp256k1_fe_equal_var(&r, &r2);
 }
 
-static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
     r->infinity = a->infinity;
     r->x = a->x;
     r->y = a->y;
@@ -172,12 +212,12 @@ static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
     secp256k1_fe_negate(&r->y, &r->y, 1);
 }
 
-static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
     return a->infinity;
 }
 
-static int secp256k1_gej_is_valid_var(const secp256k1_gej_t *a) {
-    secp256k1_fe_t y2, x3, z2, z6;
+static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
+    secp256k1_fe y2, x3, z2, z6;
     if (a->infinity) {
         return 0;
     }
@@ -196,8 +236,8 @@ static int secp256k1_gej_is_valid_var(const secp256k1_gej_t *a) {
     return secp256k1_fe_equal_var(&y2, &x3);
 }
 
-static int secp256k1_ge_is_valid_var(const secp256k1_ge_t *a) {
-    secp256k1_fe_t y2, x3, c;
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
+    secp256k1_fe y2, x3, c;
     if (a->infinity) {
         return 0;
     }
@@ -210,18 +250,27 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge_t *a) {
     return secp256k1_fe_equal_var(&y2, &x3);
 }
 
-static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
     /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate */
-    secp256k1_fe_t t1,t2,t3,t4;
+    secp256k1_fe t1,t2,t3,t4;
     /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
      *  Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
      *  y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
      */
     r->infinity = a->infinity;
     if (r->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
         return;
     }
 
+    if (rzr != NULL) {
+        *rzr = a->y;
+        secp256k1_fe_normalize_weak(rzr);
+        secp256k1_fe_mul_int(rzr, 2);
+    }
+
     secp256k1_fe_mul(&r->z, &a->z, &a->y);
     secp256k1_fe_mul_int(&r->z, 2);       /* Z' = 2*Y*Z (2) */
     secp256k1_fe_sqr(&t1, &a->x);
@@ -244,17 +293,29 @@ static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *
     secp256k1_fe_add(&r->y, &t2);         /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
 }
 
-static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
+static SECP256K1_INLINE void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
+    VERIFY_CHECK(!secp256k1_gej_is_infinity(a));
+    secp256k1_gej_double_var(r, a, rzr);
+}
+
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) {
     /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
-    secp256k1_fe_t z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+
     if (a->infinity) {
+        VERIFY_CHECK(rzr == NULL);
         *r = *b;
         return;
     }
+
     if (b->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
         *r = *a;
         return;
     }
+
     r->infinity = 0;
     secp256k1_fe_sqr(&z22, &b->z);
     secp256k1_fe_sqr(&z12, &a->z);
@@ -266,8 +327,11 @@ static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a,
     secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
-            secp256k1_gej_double_var(r, a);
+            secp256k1_gej_double_var(r, a, rzr);
         } else {
+            if (rzr != NULL) {
+                secp256k1_fe_set_int(rzr, 0);
+            }
             r->infinity = 1;
         }
         return;
@@ -275,7 +339,11 @@ static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a,
     secp256k1_fe_sqr(&i2, &i);
     secp256k1_fe_sqr(&h2, &h);
     secp256k1_fe_mul(&h3, &h, &h2);
-    secp256k1_fe_mul(&r->z, &a->z, &b->z); secp256k1_fe_mul(&r->z, &r->z, &h);
+    secp256k1_fe_mul(&h, &h, &b->z);
+    if (rzr != NULL) {
+        *rzr = h;
+    }
+    secp256k1_fe_mul(&r->z, &a->z, &h);
     secp256k1_fe_mul(&t, &u1, &h2);
     r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
     secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
@@ -283,21 +351,23 @@ static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a,
     secp256k1_fe_add(&r->y, &h3);
 }
 
-static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
     /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
-    secp256k1_fe_t z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+    secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
     if (a->infinity) {
-        r->infinity = b->infinity;
-        r->x = b->x;
-        r->y = b->y;
-        secp256k1_fe_set_int(&r->z, 1);
+        VERIFY_CHECK(rzr == NULL);
+        secp256k1_gej_set_ge(r, b);
         return;
     }
     if (b->infinity) {
+        if (rzr != NULL) {
+            secp256k1_fe_set_int(rzr, 1);
+        }
         *r = *a;
         return;
     }
     r->infinity = 0;
+
     secp256k1_fe_sqr(&z12, &a->z);
     u1 = a->x; secp256k1_fe_normalize_weak(&u1);
     secp256k1_fe_mul(&u2, &b->x, &z12);
@@ -307,7 +377,69 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *
     secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
-            secp256k1_gej_double_var(r, a);
+            secp256k1_gej_double_var(r, a, rzr);
+        } else {
+            if (rzr != NULL) {
+                secp256k1_fe_set_int(rzr, 0);
+            }
+            r->infinity = 1;
+        }
+        return;
+    }
+    secp256k1_fe_sqr(&i2, &i);
+    secp256k1_fe_sqr(&h2, &h);
+    secp256k1_fe_mul(&h3, &h, &h2);
+    if (rzr != NULL) {
+        *rzr = h;
+    }
+    secp256k1_fe_mul(&r->z, &a->z, &h);
+    secp256k1_fe_mul(&t, &u1, &h2);
+    r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+    secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+    secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+    secp256k1_fe_add(&r->y, &h3);
+}
+
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
+    /* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
+    secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
+
+    if (b->infinity) {
+        *r = *a;
+        return;
+    }
+    if (a->infinity) {
+        secp256k1_fe bzinv2, bzinv3;
+        r->infinity = b->infinity;
+        secp256k1_fe_sqr(&bzinv2, bzinv);
+        secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv);
+        secp256k1_fe_mul(&r->x, &b->x, &bzinv2);
+        secp256k1_fe_mul(&r->y, &b->y, &bzinv3);
+        secp256k1_fe_set_int(&r->z, 1);
+        return;
+    }
+    r->infinity = 0;
+
+    /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
+     *  secp256k1's isomorphism we can multiply the Z coordinates on both sides
+     *  by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1).
+     *  This means that (rx,ry,rz) can be calculated as
+     *  (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz.
+     *  The variable az below holds the modified Z coordinate for a, which is used
+     *  for the computation of rx and ry, but not for rz.
+     */
+    secp256k1_fe_mul(&az, &a->z, bzinv);
+
+    secp256k1_fe_sqr(&z12, &az);
+    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    secp256k1_fe_mul(&u2, &b->x, &z12);
+    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
+    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+    if (secp256k1_fe_normalizes_to_zero_var(&h)) {
+        if (secp256k1_fe_normalizes_to_zero_var(&i)) {
+            secp256k1_gej_double_var(r, a, NULL);
         } else {
             r->infinity = 1;
         }
@@ -324,11 +456,13 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *
     secp256k1_fe_add(&r->y, &h3);
 }
 
-static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
-    /* Operations: 7 mul, 5 sqr, 5 normalize, 17 mul_int/add/negate/cmov */
-    static const secp256k1_fe_t fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
-    secp256k1_fe_t zz, u1, u2, s1, s2, z, t, m, n, q, rr;
-    int infinity;
+
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
+    /* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */
+    static const secp256k1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
+    secp256k1_fe m_alt, rr_alt;
+    int infinity, degenerate;
     VERIFY_CHECK(!b->infinity);
     VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
 
@@ -352,53 +486,102 @@ static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, c
      *    Y3 = 4*(R*(3*Q-2*R^2)-M^4)
      *    Z3 = 2*M*Z
      *  (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
+     *
+     *  This formula has the benefit of being the same for both addition
+     *  of distinct points and doubling. However, it breaks down in the
+     *  case that either point is infinity, or that y1 = -y2. We handle
+     *  these cases in the following ways:
+     *
+     *    - If b is infinity we simply bail by means of a VERIFY_CHECK.
+     *
+     *    - If a is infinity, we detect this, and at the end of the
+     *      computation replace the result (which will be meaningless,
+     *      but we compute to be constant-time) with b.x : b.y : 1.
+     *
+     *    - If a = -b, we have y1 = -y2, which is a degenerate case.
+     *      But here the answer is infinity, so we simply set the
+     *      infinity flag of the result, overriding the computed values
+     *      without even needing to cmov.
+     *
+     *    - If y1 = -y2 but x1 != x2, which does occur thanks to certain
+     *      properties of our curve (specifically, 1 has nontrivial cube
+     *      roots in our field, and the curve equation has no x coefficient)
+     *      then the answer is not infinity but also not given by the above
+     *      equation. In this case, we cmov in place an alternate expression
+     *      for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these
+     *      expressions for lambda are defined, they are equal, and can be
+     *      obtained from each other by multiplication by (y1 + y2)/(y1 + y2)
+     *      then substitution of x^3 + 7 for y^2 (using the curve equation).
+     *      For all pairs of nonzero points (a, b) at least one is defined,
+     *      so this covers everything.
      */
 
     secp256k1_fe_sqr(&zz, &a->z);                       /* z = Z1^2 */
     u1 = a->x; secp256k1_fe_normalize_weak(&u1);        /* u1 = U1 = X1*Z2^2 (1) */
     secp256k1_fe_mul(&u2, &b->x, &zz);                  /* u2 = U2 = X2*Z1^2 (1) */
     s1 = a->y; secp256k1_fe_normalize_weak(&s1);        /* s1 = S1 = Y1*Z2^3 (1) */
-    secp256k1_fe_mul(&s2, &b->y, &zz);                  /* s2 = Y2*Z2^2 (1) */
+    secp256k1_fe_mul(&s2, &b->y, &zz);                  /* s2 = Y2*Z1^2 (1) */
     secp256k1_fe_mul(&s2, &s2, &a->z);                  /* s2 = S2 = Y2*Z1^3 (1) */
-    z = a->z;                                           /* z = Z = Z1*Z2 (8) */
     t = u1; secp256k1_fe_add(&t, &u2);                  /* t = T = U1+U2 (2) */
     m = s1; secp256k1_fe_add(&m, &s2);                  /* m = M = S1+S2 (2) */
-    secp256k1_fe_sqr(&n, &m);                           /* n = M^2 (1) */
-    secp256k1_fe_mul(&q, &n, &t);                       /* q = Q = T*M^2 (1) */
-    secp256k1_fe_sqr(&n, &n);                           /* n = M^4 (1) */
     secp256k1_fe_sqr(&rr, &t);                          /* rr = T^2 (1) */
-    secp256k1_fe_mul(&t, &u1, &u2); secp256k1_fe_negate(&t, &t, 1); /* t = -U1*U2 (2) */
-    secp256k1_fe_add(&rr, &t);                                      /* rr = R = T^2-U1*U2 (3) */
-    secp256k1_fe_sqr(&t, &rr);                                      /* t = R^2 (1) */
-    secp256k1_fe_mul(&r->z, &m, &z);                                /* r->z = M*Z (1) */
+    secp256k1_fe_negate(&m_alt, &u2, 1);                /* Malt = -X2*Z1^2 */
+    secp256k1_fe_mul(&tt, &u1, &m_alt);                 /* tt = -U1*U2 (2) */
+    secp256k1_fe_add(&rr, &tt);                         /* rr = R = T^2-U1*U2 (3) */
+    /** If lambda = R/M = 0/0 we have a problem (except in the "trivial"
+     *  case that Z = z1z2 = 0, and this is special-cased later on). */
+    degenerate = secp256k1_fe_normalizes_to_zero(&m) &
+                 secp256k1_fe_normalizes_to_zero(&rr);
+    /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2.
+     * This means either x1 == beta*x2 or beta*x1 == x2, where beta is
+     * a nontrivial cube root of one. In either case, an alternate
+     * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
+     * so we set R/M equal to this. */
+    rr_alt = s1;
+    secp256k1_fe_mul_int(&rr_alt, 2);       /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
+    secp256k1_fe_add(&m_alt, &u1);          /* Malt = X1*Z2^2 - X2*Z1^2 */
+
+    secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);
+    secp256k1_fe_cmov(&m_alt, &m, !degenerate);
+    /* Now Ralt / Malt = lambda and is guaranteed not to be 0/0.
+     * From here on out Ralt and Malt represent the numerator
+     * and denominator of lambda; R and M represent the explicit
+     * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
+    secp256k1_fe_sqr(&n, &m_alt);                       /* n = Malt^2 (1) */
+    secp256k1_fe_mul(&q, &n, &t);                       /* q = Q = T*Malt^2 (1) */
+    /* These two lines use the observation that either M == Malt or M == 0,
+     * so M^3 * Malt is either Malt^4 (which is computed by squaring), or
+     * zero (which is "computed" by cmov). So the cost is one squaring
+     * versus two multiplications. */
+    secp256k1_fe_sqr(&n, &n);
+    secp256k1_fe_cmov(&n, &m, degenerate);              /* n = M^3 * Malt (2) */
+    secp256k1_fe_sqr(&t, &rr_alt);                      /* t = Ralt^2 (1) */
+    secp256k1_fe_mul(&r->z, &a->z, &m_alt);             /* r->z = Malt*Z (1) */
     infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity);
-    secp256k1_fe_mul_int(&r->z, 2 * (1 - a->infinity)); /* r->z = Z3 = 2*M*Z (2) */
-    r->x = t;                                           /* r->x = R^2 (1) */
+    secp256k1_fe_mul_int(&r->z, 2);                     /* r->z = Z3 = 2*Malt*Z (2) */
     secp256k1_fe_negate(&q, &q, 1);                     /* q = -Q (2) */
-    secp256k1_fe_add(&r->x, &q);                        /* r->x = R^2-Q (3) */
-    secp256k1_fe_normalize(&r->x);
-    secp256k1_fe_mul_int(&q, 3);                        /* q = -3*Q (6) */
-    secp256k1_fe_mul_int(&t, 2);                        /* t = 2*R^2 (2) */
-    secp256k1_fe_add(&t, &q);                           /* t = 2*R^2-3*Q (8) */
-    secp256k1_fe_mul(&t, &t, &rr);                      /* t = R*(2*R^2-3*Q) (1) */
-    secp256k1_fe_add(&t, &n);                           /* t = R*(2*R^2-3*Q)+M^4 (2) */
-    secp256k1_fe_negate(&r->y, &t, 2);                  /* r->y = R*(3*Q-2*R^2)-M^4 (3) */
+    secp256k1_fe_add(&t, &q);                           /* t = Ralt^2-Q (3) */
+    secp256k1_fe_normalize_weak(&t);
+    r->x = t;                                           /* r->x = Ralt^2-Q (1) */
+    secp256k1_fe_mul_int(&t, 2);                        /* t = 2*x3 (2) */
+    secp256k1_fe_add(&t, &q);                           /* t = 2*x3 - Q: (4) */
+    secp256k1_fe_mul(&t, &t, &rr_alt);                  /* t = Ralt*(2*x3 - Q) (1) */
+    secp256k1_fe_add(&t, &n);                           /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */
+    secp256k1_fe_negate(&r->y, &t, 3);                  /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */
     secp256k1_fe_normalize_weak(&r->y);
-    secp256k1_fe_mul_int(&r->x, 4 * (1 - a->infinity)); /* r->x = X3 = 4*(R^2-Q) */
-    secp256k1_fe_mul_int(&r->y, 4 * (1 - a->infinity)); /* r->y = Y3 = 4*R*(3*Q-2*R^2)-4*M^4 (4) */
+    secp256k1_fe_mul_int(&r->x, 4);                     /* r->x = X3 = 4*(Ralt^2-Q) */
+    secp256k1_fe_mul_int(&r->y, 4);                     /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */
 
-    /** In case a->infinity == 1, the above code results in r->x, r->y, and r->z all equal to 0.
-     *  Replace r with b->x, b->y, 1 in that case.
-     */
+    /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
     secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
     secp256k1_fe_cmov(&r->y, &b->y, a->infinity);
     secp256k1_fe_cmov(&r->z, &fe_1, a->infinity);
     r->infinity = infinity;
 }
 
-static void secp256k1_gej_rescale(secp256k1_gej_t *r, const secp256k1_fe_t *s) {
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
     /* Operations: 4 mul, 1 sqr */
-    secp256k1_fe_t zz;
+    secp256k1_fe zz;
     VERIFY_CHECK(!secp256k1_fe_is_zero(s));
     secp256k1_fe_sqr(&zz, s);
     secp256k1_fe_mul(&r->x, &r->x, &zz);                /* r->x *= s^2 */
@@ -407,8 +590,8 @@ static void secp256k1_gej_rescale(secp256k1_gej_t *r, const secp256k1_fe_t *s) {
     secp256k1_fe_mul(&r->z, &r->z, s);                  /* r->z *= s   */
 }
 
-static void secp256k1_ge_to_storage(secp256k1_ge_storage_t *r, const secp256k1_ge_t *a) {
-    secp256k1_fe_t x, y;
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) {
+    secp256k1_fe x, y;
     VERIFY_CHECK(!a->infinity);
     x = a->x;
     secp256k1_fe_normalize(&x);
@@ -418,20 +601,20 @@ static void secp256k1_ge_to_storage(secp256k1_ge_storage_t *r, const secp256k1_g
     secp256k1_fe_to_storage(&r->y, &y);
 }
 
-static void secp256k1_ge_from_storage(secp256k1_ge_t *r, const secp256k1_ge_storage_t *a) {
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) {
     secp256k1_fe_from_storage(&r->x, &a->x);
     secp256k1_fe_from_storage(&r->y, &a->y);
     r->infinity = 0;
 }
 
-static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage_t *r, const secp256k1_ge_storage_t *a, int flag) {
+static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
     secp256k1_fe_storage_cmov(&r->x, &a->x, flag);
     secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
 }
 
 #ifdef USE_ENDOMORPHISM
-static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
-    static const secp256k1_fe_t beta = SECP256K1_FE_CONST(
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
+    static const secp256k1_fe beta = SECP256K1_FE_CONST(
         0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
         0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
     );
diff --git a/src/secp256k1/src/hash.h b/src/secp256k1/src/hash.h
index 843423d7f7..0ff01e63fa 100644
--- a/src/secp256k1/src/hash.h
+++ b/src/secp256k1/src/hash.h
@@ -34,7 +34,7 @@ typedef struct {
     int retry;
 } secp256k1_rfc6979_hmac_sha256_t;
 
-static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen, const unsigned char *msg, size_t msglen, const unsigned char *rnd, size_t rndlen);
+static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen);
 static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256_t *rng, unsigned char *out, size_t outlen);
 static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256_t *rng);
 
diff --git a/src/secp256k1/src/hash_impl.h b/src/secp256k1/src/hash_impl.h
index 9828827bcd..ae55df6d8a 100644
--- a/src/secp256k1/src/hash_impl.h
+++ b/src/secp256k1/src/hash_impl.h
@@ -202,7 +202,7 @@ static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256_t *hash, unsign
 }
 
 
-static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen, const unsigned char *msg, size_t msglen, const unsigned char *rnd, size_t rndlen) {
+static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256_t *rng, const unsigned char *key, size_t keylen) {
     secp256k1_hmac_sha256_t hmac;
     static const unsigned char zero[1] = {0x00};
     static const unsigned char one[1] = {0x01};
@@ -215,11 +215,6 @@ static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha2
     secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
     secp256k1_hmac_sha256_write(&hmac, zero, 1);
     secp256k1_hmac_sha256_write(&hmac, key, keylen);
-    secp256k1_hmac_sha256_write(&hmac, msg, msglen);
-    if (rnd && rndlen) {
-        /* RFC6979 3.6 "Additional data". */
-        secp256k1_hmac_sha256_write(&hmac, rnd, rndlen);
-    }
     secp256k1_hmac_sha256_finalize(&hmac, rng->k);
     secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
     secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
@@ -230,11 +225,6 @@ static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha2
     secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
     secp256k1_hmac_sha256_write(&hmac, one, 1);
     secp256k1_hmac_sha256_write(&hmac, key, keylen);
-    secp256k1_hmac_sha256_write(&hmac, msg, msglen);
-    if (rnd && rndlen) {
-        /* RFC6979 3.6 "Additional data". */
-        secp256k1_hmac_sha256_write(&hmac, rnd, rndlen);
-    }
     secp256k1_hmac_sha256_finalize(&hmac, rng->k);
     secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32);
     secp256k1_hmac_sha256_write(&hmac, rng->v, 32);
diff --git a/src/secp256k1/src/modules/ecdh/Makefile.am.include b/src/secp256k1/src/modules/ecdh/Makefile.am.include
new file mode 100644
index 0000000000..670b9c1152
--- /dev/null
+++ b/src/secp256k1/src/modules/ecdh/Makefile.am.include
@@ -0,0 +1,8 @@
+include_HEADERS += include/secp256k1_ecdh.h
+noinst_HEADERS += src/modules/ecdh/main_impl.h
+noinst_HEADERS += src/modules/ecdh/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_ecdh
+bench_ecdh_SOURCES = src/bench_ecdh.c
+bench_ecdh_LDADD = libsecp256k1.la $(SECP_LIBS)
+endif
diff --git a/src/secp256k1/src/modules/ecdh/main_impl.h b/src/secp256k1/src/modules/ecdh/main_impl.h
new file mode 100644
index 0000000000..c23e4f82f7
--- /dev/null
+++ b/src/secp256k1/src/modules/ecdh/main_impl.h
@@ -0,0 +1,54 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_ECDH_MAIN_
+#define _SECP256K1_MODULE_ECDH_MAIN_
+
+#include "include/secp256k1_ecdh.h"
+#include "ecmult_const_impl.h"
+
+int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *result, const secp256k1_pubkey *point, const unsigned char *scalar) {
+    int ret = 0;
+    int overflow = 0;
+    secp256k1_gej res;
+    secp256k1_ge pt;
+    secp256k1_scalar s;
+    ARG_CHECK(result != NULL);
+    ARG_CHECK(point != NULL);
+    ARG_CHECK(scalar != NULL);
+    (void)ctx;
+
+    secp256k1_pubkey_load(ctx, &pt, point);
+    secp256k1_scalar_set_b32(&s, scalar, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&s)) {
+        ret = 0;
+    } else {
+        unsigned char x[32];
+        unsigned char y[1];
+        secp256k1_sha256_t sha;
+
+        secp256k1_ecmult_const(&res, &pt, &s);
+        secp256k1_ge_set_gej(&pt, &res);
+        /* Compute a hash of the point in compressed form
+         * Note we cannot use secp256k1_eckey_pubkey_serialize here since it does not
+         * expect its output to be secret and has a timing sidechannel. */
+        secp256k1_fe_normalize(&pt.x);
+        secp256k1_fe_normalize(&pt.y);
+        secp256k1_fe_get_b32(x, &pt.x);
+        y[0] = 0x02 | secp256k1_fe_is_odd(&pt.y);
+
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(&sha, y, sizeof(y));
+        secp256k1_sha256_write(&sha, x, sizeof(x));
+        secp256k1_sha256_finalize(&sha, result);
+        ret = 1;
+    }
+
+    secp256k1_scalar_clear(&s);
+    return ret;
+}
+
+#endif
diff --git a/src/secp256k1/src/modules/ecdh/tests_impl.h b/src/secp256k1/src/modules/ecdh/tests_impl.h
new file mode 100644
index 0000000000..7badc9033f
--- /dev/null
+++ b/src/secp256k1/src/modules/ecdh/tests_impl.h
@@ -0,0 +1,75 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_ECDH_TESTS_
+#define _SECP256K1_MODULE_ECDH_TESTS_
+
+void test_ecdh_generator_basepoint(void) {
+    unsigned char s_one[32] = { 0 };
+    secp256k1_pubkey point[2];
+    int i;
+
+    s_one[31] = 1;
+    /* Check against pubkey creation when the basepoint is the generator */
+    for (i = 0; i < 100; ++i) {
+        secp256k1_sha256_t sha;
+        unsigned char s_b32[32];
+        unsigned char output_ecdh[32];
+        unsigned char output_ser[32];
+        unsigned char point_ser[33];
+        size_t point_ser_len = sizeof(point_ser);
+        secp256k1_scalar s;
+
+        random_scalar_order(&s);
+        secp256k1_scalar_get_b32(s_b32, &s);
+
+        /* compute using ECDH function */
+        CHECK(secp256k1_ec_pubkey_create(ctx, &point[0], s_one) == 1);
+        CHECK(secp256k1_ecdh(ctx, output_ecdh, &point[0], s_b32) == 1);
+        /* compute "explicitly" */
+        CHECK(secp256k1_ec_pubkey_create(ctx, &point[1], s_b32) == 1);
+        CHECK(secp256k1_ec_pubkey_serialize(ctx, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1);
+        CHECK(point_ser_len == sizeof(point_ser));
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(&sha, point_ser, point_ser_len);
+        secp256k1_sha256_finalize(&sha, output_ser);
+        /* compare */
+        CHECK(memcmp(output_ecdh, output_ser, sizeof(output_ser)) == 0);
+    }
+}
+
+void test_bad_scalar(void) {
+    unsigned char s_zero[32] = { 0 };
+    unsigned char s_overflow[32] = {
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+        0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+        0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
+    };
+    unsigned char s_rand[32] = { 0 };
+    unsigned char output[32];
+    secp256k1_scalar rand;
+    secp256k1_pubkey point;
+
+    /* Create random point */
+    random_scalar_order(&rand);
+    secp256k1_scalar_get_b32(s_rand, &rand);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &point, s_rand) == 1);
+
+    /* Try to multiply it by bad values */
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_zero) == 0);
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow) == 0);
+    /* ...and a good one */
+    s_overflow[31] -= 1;
+    CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow) == 1);
+}
+
+void run_ecdh_tests(void) {
+    test_ecdh_generator_basepoint();
+    test_bad_scalar();
+}
+
+#endif
diff --git a/src/secp256k1/src/modules/recovery/Makefile.am.include b/src/secp256k1/src/modules/recovery/Makefile.am.include
new file mode 100644
index 0000000000..5de3ea33ea
--- /dev/null
+++ b/src/secp256k1/src/modules/recovery/Makefile.am.include
@@ -0,0 +1,8 @@
+include_HEADERS += include/secp256k1_recovery.h
+noinst_HEADERS += src/modules/recovery/main_impl.h
+noinst_HEADERS += src/modules/recovery/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_recover
+bench_recover_SOURCES = src/bench_recover.c
+bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS)
+endif
diff --git a/src/secp256k1/src/modules/recovery/main_impl.h b/src/secp256k1/src/modules/recovery/main_impl.h
new file mode 100644
index 0000000000..ec42f4bb6c
--- /dev/null
+++ b/src/secp256k1/src/modules/recovery/main_impl.h
@@ -0,0 +1,193 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_RECOVERY_MAIN_
+#define _SECP256K1_MODULE_RECOVERY_MAIN_
+
+#include "include/secp256k1_recovery.h"
+
+static void secp256k1_ecdsa_recoverable_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, int* recid, const secp256k1_ecdsa_recoverable_signature* sig) {
+    (void)ctx;
+    if (sizeof(secp256k1_scalar) == 32) {
+        /* When the secp256k1_scalar type is exactly 32 byte, use its
+         * representation inside secp256k1_ecdsa_signature, as conversion is very fast.
+         * Note that secp256k1_ecdsa_signature_save must use the same representation. */
+        memcpy(r, &sig->data[0], 32);
+        memcpy(s, &sig->data[32], 32);
+    } else {
+        secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
+        secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
+    }
+    *recid = sig->data[64];
+}
+
+static void secp256k1_ecdsa_recoverable_signature_save(secp256k1_ecdsa_recoverable_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s, int recid) {
+    if (sizeof(secp256k1_scalar) == 32) {
+        memcpy(&sig->data[0], r, 32);
+        memcpy(&sig->data[32], s, 32);
+    } else {
+        secp256k1_scalar_get_b32(&sig->data[0], r);
+        secp256k1_scalar_get_b32(&sig->data[32], s);
+    }
+    sig->data[64] = recid;
+}
+
+int secp256k1_ecdsa_recoverable_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature* sig, const unsigned char *input64, int recid) {
+    secp256k1_scalar r, s;
+    int ret = 1;
+    int overflow = 0;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input64 != NULL);
+    ARG_CHECK(recid >= 0 && recid <= 3);
+
+    secp256k1_scalar_set_b32(&r, &input64[0], &overflow);
+    ret &= !overflow;
+    secp256k1_scalar_set_b32(&s, &input64[32], &overflow);
+    ret &= !overflow;
+    if (ret) {
+        secp256k1_ecdsa_recoverable_signature_save(sig, &r, &s, recid);
+    } else {
+        memset(sig, 0, sizeof(*sig));
+    }
+    return ret;
+}
+
+int secp256k1_ecdsa_recoverable_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, int *recid, const secp256k1_ecdsa_recoverable_signature* sig) {
+    secp256k1_scalar r, s;
+
+    (void)ctx;
+    ARG_CHECK(output64 != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(recid != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, recid, sig);
+    secp256k1_scalar_get_b32(&output64[0], &r);
+    secp256k1_scalar_get_b32(&output64[32], &s);
+    return 1;
+}
+
+int secp256k1_ecdsa_recoverable_signature_convert(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const secp256k1_ecdsa_recoverable_signature* sigin) {
+    secp256k1_scalar r, s;
+    int recid;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(sigin != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, sigin);
+    secp256k1_ecdsa_signature_save(sig, &r, &s);
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) {
+    unsigned char brx[32];
+    secp256k1_fe fx;
+    secp256k1_ge x;
+    secp256k1_gej xj;
+    secp256k1_scalar rn, u1, u2;
+    secp256k1_gej qj;
+    int r;
+
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
+        return 0;
+    }
+
+    secp256k1_scalar_get_b32(brx, sigr);
+    r = secp256k1_fe_set_b32(&fx, brx);
+    (void)r;
+    VERIFY_CHECK(r); /* brx comes from a scalar, so is less than the order; certainly less than p */
+    if (recid & 2) {
+        if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
+            return 0;
+        }
+        secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
+    }
+    if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&xj, &x);
+    secp256k1_scalar_inverse_var(&rn, sigr);
+    secp256k1_scalar_mul(&u1, &rn, message);
+    secp256k1_scalar_negate(&u1, &u1);
+    secp256k1_scalar_mul(&u2, &rn, sigs);
+    secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1);
+    secp256k1_ge_set_gej_var(pubkey, &qj);
+    return !secp256k1_gej_is_infinity(&qj);
+}
+
+int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar r, s;
+    secp256k1_scalar sec, non, msg;
+    int recid;
+    int ret = 0;
+    int overflow = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(seckey != NULL);
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
+    /* Fail if the secret key is invalid. */
+    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned int count = 0;
+        secp256k1_scalar_set_b32(&msg, msg32, NULL);
+        while (1) {
+            unsigned char nonce32[32];
+            ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
+            if (!ret) {
+                break;
+            }
+            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
+            memset(nonce32, 0, 32);
+            if (!secp256k1_scalar_is_zero(&non) && !overflow) {
+                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, &recid)) {
+                    break;
+                }
+            }
+            count++;
+        }
+        secp256k1_scalar_clear(&msg);
+        secp256k1_scalar_clear(&non);
+        secp256k1_scalar_clear(&sec);
+    }
+    if (ret) {
+        secp256k1_ecdsa_recoverable_signature_save(signature, &r, &s, recid);
+    } else {
+        memset(signature, 0, sizeof(*signature));
+    }
+    return ret;
+}
+
+int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32) {
+    secp256k1_ge q;
+    secp256k1_scalar r, s;
+    secp256k1_scalar m;
+    int recid;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, signature);
+    ARG_CHECK(recid >= 0 && recid < 4);
+    secp256k1_scalar_set_b32(&m, msg32, NULL);
+    if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &r, &s, &q, &m, recid)) {
+        secp256k1_pubkey_save(pubkey, &q);
+        return 1;
+    } else {
+        memset(pubkey, 0, sizeof(*pubkey));
+        return 0;
+    }
+}
+
+#endif
diff --git a/src/secp256k1/src/modules/recovery/tests_impl.h b/src/secp256k1/src/modules/recovery/tests_impl.h
new file mode 100644
index 0000000000..8932d5f0af
--- /dev/null
+++ b/src/secp256k1/src/modules/recovery/tests_impl.h
@@ -0,0 +1,250 @@
+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_RECOVERY_TESTS_
+#define _SECP256K1_MODULE_RECOVERY_TESTS_
+
+void test_ecdsa_recovery_end_to_end(void) {
+    unsigned char extra[32] = {0x00};
+    unsigned char privkey[32];
+    unsigned char message[32];
+    secp256k1_ecdsa_signature signature[5];
+    secp256k1_ecdsa_recoverable_signature rsignature[5];
+    unsigned char sig[74];
+    secp256k1_pubkey pubkey;
+    secp256k1_pubkey recpubkey;
+    int recid = 0;
+
+    /* Generate a random key and message. */
+    {
+        secp256k1_scalar msg, key;
+        random_scalar_order_test(&msg);
+        random_scalar_order_test(&key);
+        secp256k1_scalar_get_b32(privkey, &key);
+        secp256k1_scalar_get_b32(message, &msg);
+    }
+
+    /* Construct and verify corresponding public key. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Serialize/parse compact and verify/recover. */
+    extra[0] = 0;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[0], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[4], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[1], message, privkey, NULL, extra) == 1);
+    extra[31] = 1;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[2], message, privkey, NULL, extra) == 1);
+    extra[31] = 0;
+    extra[0] = 1;
+    CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[3], message, privkey, NULL, extra) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(memcmp(&signature[4], &signature[0], 64) == 0);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
+    memset(&rsignature[4], 0, sizeof(rsignature[4]));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
+    /* Parse compact (with recovery id) and recover. */
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 1);
+    CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
+    /* Serialize/destroy/parse signature and verify again. */
+    CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
+    sig[secp256k1_rand_bits(6)] += 1 + secp256k1_rand_int(255);
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
+    CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 0);
+    /* Recover again */
+    CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 0 ||
+          memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
+}
+
+/* Tests several edge cases. */
+void test_ecdsa_recovery_edge_cases(void) {
+    const unsigned char msg32[32] = {
+        'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
+        'a', ' ', 'v', 'e', 'r', 'y', ' ', 's',
+        'e', 'c', 'r', 'e', 't', ' ', 'm', 'e',
+        's', 's', 'a', 'g', 'e', '.', '.', '.'
+    };
+    const unsigned char sig64[64] = {
+        /* Generated by signing the above message with nonce 'This is the nonce we will use...'
+         * and secret key 0 (which is not valid), resulting in recid 0. */
+        0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8,
+        0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96,
+        0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63,
+        0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32,
+        0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E,
+        0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD,
+        0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86,
+        0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57
+    };
+    secp256k1_pubkey pubkey;
+    /* signature (r,s) = (4,4), which can be recovered with all 4 recids. */
+    const unsigned char sigb64[64] = {
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+    };
+    secp256k1_pubkey pubkeyb;
+    secp256k1_ecdsa_recoverable_signature rsig;
+    secp256k1_ecdsa_signature sig;
+    int recid;
+
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 0));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 1));
+    CHECK(secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 2));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+    CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 3));
+    CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32));
+
+    for (recid = 0; recid < 4; recid++) {
+        int i;
+        int recid2;
+        /* (4,4) encoded in DER. */
+        unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04};
+        unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01};
+        unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00};
+        unsigned char sigbderalt1[39] = {
+            0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+        };
+        unsigned char sigbderalt2[39] = {
+            0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        };
+        unsigned char sigbderalt3[40] = {
+            0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+        };
+        unsigned char sigbderalt4[40] = {
+            0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+        };
+        /* (order + r,4) encoded in DER. */
+        unsigned char sigbderlong[40] = {
+            0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC,
+            0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E,
+            0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04
+        };
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1);
+        for (recid2 = 0; recid2 < 4; recid2++) {
+            secp256k1_pubkey pubkey2b;
+            CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid2) == 1);
+            CHECK(secp256k1_ecdsa_recover(ctx, &pubkey2b, &rsig, msg32) == 1);
+            /* Verifying with (order + r,4) should always fail. */
+            CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderlong, sizeof(sigbderlong)) == 1);
+            CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        }
+        /* DER parsing tests. */
+        /* Zero length r/s. */
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zr, sizeof(sigcder_zr)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zs, sizeof(sigcder_zs)) == 0);
+        /* Leading zeros. */
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt1, sizeof(sigbderalt1)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt2, sizeof(sigbderalt2)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 0);
+        sigbderalt3[4] = 1;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        sigbderalt4[7] = 1;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        /* Damage signature. */
+        sigbder[7]++;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+        sigbder[7]--;
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, 6) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder) - 1) == 0);
+        for(i = 0; i < 8; i++) {
+            int c;
+            unsigned char orig = sigbder[i];
+            /*Try every single-byte change.*/
+            for (c = 0; c < 256; c++) {
+                if (c == orig ) {
+                    continue;
+                }
+                sigbder[i] = c;
+                CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 0 || secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0);
+            }
+            sigbder[i] = orig;
+        }
+    }
+
+    /* Test r/s equal to zero */
+    {
+        /* (1,1) encoded in DER. */
+        unsigned char sigcder[8] = {0x30, 0x06, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01};
+        unsigned char sigc64[64] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        };
+        secp256k1_pubkey pubkeyc;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyc, &rsig, msg32) == 1);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 1);
+        sigcder[4] = 0;
+        sigc64[31] = 0;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0);
+        sigcder[4] = 1;
+        sigcder[7] = 0;
+        sigc64[31] = 1;
+        sigc64[63] = 0;
+        CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1);
+        CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0);
+    }
+}
+
+void run_recovery_tests(void) {
+    int i;
+    for (i = 0; i < 64*count; i++) {
+        test_ecdsa_recovery_end_to_end();
+    }
+    test_ecdsa_recovery_edge_cases();
+}
+
+#endif
diff --git a/src/secp256k1/src/modules/schnorr/Makefile.am.include b/src/secp256k1/src/modules/schnorr/Makefile.am.include
new file mode 100644
index 0000000000..b3bfa7d5cc
--- /dev/null
+++ b/src/secp256k1/src/modules/schnorr/Makefile.am.include
@@ -0,0 +1,10 @@
+include_HEADERS += include/secp256k1_schnorr.h
+noinst_HEADERS += src/modules/schnorr/main_impl.h
+noinst_HEADERS += src/modules/schnorr/schnorr.h
+noinst_HEADERS += src/modules/schnorr/schnorr_impl.h
+noinst_HEADERS += src/modules/schnorr/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_schnorr_verify
+bench_schnorr_verify_SOURCES = src/bench_schnorr_verify.c
+bench_schnorr_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
+endif
diff --git a/src/secp256k1/src/modules/schnorr/main_impl.h b/src/secp256k1/src/modules/schnorr/main_impl.h
new file mode 100644
index 0000000000..fa176a1767
--- /dev/null
+++ b/src/secp256k1/src/modules/schnorr/main_impl.h
@@ -0,0 +1,164 @@
+/**********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODULE_SCHNORR_MAIN
+#define SECP256K1_MODULE_SCHNORR_MAIN
+
+#include "include/secp256k1_schnorr.h"
+#include "modules/schnorr/schnorr_impl.h"
+
+static void secp256k1_schnorr_msghash_sha256(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32) {
+    secp256k1_sha256_t sha;
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(&sha, r32, 32);
+    secp256k1_sha256_write(&sha, msg32, 32);
+    secp256k1_sha256_finalize(&sha, h32);
+}
+
+static const unsigned char secp256k1_schnorr_algo16[17] = "Schnorr+SHA256  ";
+
+int secp256k1_schnorr_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar sec, non;
+    int ret = 0;
+    int overflow = 0;
+    unsigned int count = 0;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(seckey != NULL);
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    secp256k1_scalar_set_b32(&sec, seckey, NULL);
+    while (1) {
+        unsigned char nonce32[32];
+        ret = noncefp(nonce32, msg32, seckey, secp256k1_schnorr_algo16, (void*)noncedata, count);
+        if (!ret) {
+            break;
+        }
+        secp256k1_scalar_set_b32(&non, nonce32, &overflow);
+        memset(nonce32, 0, 32);
+        if (!secp256k1_scalar_is_zero(&non) && !overflow) {
+            if (secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64, &sec, &non, NULL, secp256k1_schnorr_msghash_sha256, msg32)) {
+                break;
+            }
+        }
+        count++;
+    }
+    if (!ret) {
+        memset(sig64, 0, 64);
+    }
+    secp256k1_scalar_clear(&non);
+    secp256k1_scalar_clear(&sec);
+    return ret;
+}
+
+int secp256k1_schnorr_verify(const secp256k1_context* ctx, const unsigned char *sig64, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
+    secp256k1_ge q;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_pubkey_load(ctx, &q, pubkey);
+    return secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64, &q, secp256k1_schnorr_msghash_sha256, msg32);
+}
+
+int secp256k1_schnorr_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *sig64, const unsigned char *msg32) {
+    secp256k1_ge q;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    if (secp256k1_schnorr_sig_recover(&ctx->ecmult_ctx, sig64, &q, secp256k1_schnorr_msghash_sha256, msg32)) {
+        secp256k1_pubkey_save(pubkey, &q);
+        return 1;
+    } else {
+        memset(pubkey, 0, sizeof(*pubkey));
+        return 0;
+    }
+}
+
+int secp256k1_schnorr_generate_nonce_pair(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, unsigned char *privnonce32, const unsigned char *sec32, const unsigned char *msg32, secp256k1_nonce_function noncefp, const void* noncedata) {
+    int count = 0;
+    int ret = 1;
+    secp256k1_gej Qj;
+    secp256k1_ge Q;
+    secp256k1_scalar sec;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sec32 != NULL);
+    ARG_CHECK(pubnonce != NULL);
+    ARG_CHECK(privnonce32 != NULL);
+
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_default;
+    }
+
+    do {
+        int overflow;
+        ret = noncefp(privnonce32, sec32, msg32, secp256k1_schnorr_algo16, (void*)noncedata, count++);
+        if (!ret) {
+            break;
+        }
+        secp256k1_scalar_set_b32(&sec, privnonce32, &overflow);
+        if (overflow || secp256k1_scalar_is_zero(&sec)) {
+            continue;
+        }
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sec);
+        secp256k1_ge_set_gej(&Q, &Qj);
+
+        secp256k1_pubkey_save(pubnonce, &Q);
+        break;
+    } while(1);
+
+    secp256k1_scalar_clear(&sec);
+    if (!ret) {
+        memset(pubnonce, 0, sizeof(*pubnonce));
+    }
+    return ret;
+}
+
+int secp256k1_schnorr_partial_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const unsigned char *sec32, const secp256k1_pubkey *pubnonce_others, const unsigned char *secnonce32) {
+    int overflow = 0;
+    secp256k1_scalar sec, non;
+    secp256k1_ge pubnon;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(sec32 != NULL);
+    ARG_CHECK(secnonce32 != NULL);
+    ARG_CHECK(pubnonce_others != NULL);
+
+    secp256k1_scalar_set_b32(&sec, sec32, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&sec)) {
+        return -1;
+    }
+    secp256k1_scalar_set_b32(&non, secnonce32, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&non)) {
+        return -1;
+    }
+    secp256k1_pubkey_load(ctx, &pubnon, pubnonce_others);
+    return secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64, &sec, &non, &pubnon, secp256k1_schnorr_msghash_sha256, msg32);
+}
+
+int secp256k1_schnorr_partial_combine(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char * const *sig64sin, size_t n) {
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(n >= 1);
+    ARG_CHECK(sig64sin != NULL);
+    return secp256k1_schnorr_sig_combine(sig64, n, sig64sin);
+}
+
+#endif
diff --git a/src/secp256k1/src/modules/schnorr/schnorr.h b/src/secp256k1/src/modules/schnorr/schnorr.h
new file mode 100644
index 0000000000..de18147bd5
--- /dev/null
+++ b/src/secp256k1/src/modules/schnorr/schnorr.h
@@ -0,0 +1,20 @@
+/***********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                               *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php. *
+ ***********************************************************************/
+
+#ifndef _SECP256K1_MODULE_SCHNORR_H_
+#define _SECP256K1_MODULE_SCHNORR_H_
+
+#include "scalar.h"
+#include "group.h"
+
+typedef void (*secp256k1_schnorr_msghash)(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32);
+
+static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
+static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
+static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
+static int secp256k1_schnorr_sig_combine(unsigned char *sig64, size_t n, const unsigned char * const *sig64ins);
+
+#endif
diff --git a/src/secp256k1/src/modules/schnorr/schnorr_impl.h b/src/secp256k1/src/modules/schnorr/schnorr_impl.h
new file mode 100644
index 0000000000..e13ab6db7c
--- /dev/null
+++ b/src/secp256k1/src/modules/schnorr/schnorr_impl.h
@@ -0,0 +1,207 @@
+/***********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                               *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php. *
+ ***********************************************************************/
+
+#ifndef _SECP256K1_SCHNORR_IMPL_H_
+#define _SECP256K1_SCHNORR_IMPL_H_
+
+#include <string.h>
+
+#include "schnorr.h"
+#include "num.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+
+/**
+ * Custom Schnorr-based signature scheme. They support multiparty signing, public key
+ * recovery and batch validation.
+ *
+ * Rationale for verifying R's y coordinate:
+ * In order to support batch validation and public key recovery, the full R point must
+ * be known to verifiers, rather than just its x coordinate. In order to not risk
+ * being more strict in batch validation than normal validation, validators must be
+ * required to reject signatures with incorrect y coordinate. This is only possible
+ * by including a (relatively slow) field inverse, or a field square root. However,
+ * batch validation offers potentially much higher benefits than this cost.
+ *
+ * Rationale for having an implicit y coordinate oddness:
+ * If we commit to having the full R point known to verifiers, there are two mechanism.
+ * Either include its oddness in the signature, or give it an implicit fixed value.
+ * As the R y coordinate can be flipped by a simple negation of the nonce, we choose the
+ * latter, as it comes with nearly zero impact on signing or validation performance, and
+ * saves a byte in the signature.
+ *
+ * Signing:
+ *   Inputs: 32-byte message m, 32-byte scalar key x (!=0), 32-byte scalar nonce k (!=0)
+ *
+ *   Compute point R = k * G. Reject nonce if R's y coordinate is odd (or negate nonce).
+ *   Compute 32-byte r, the serialization of R's x coordinate.
+ *   Compute scalar h = Hash(r || m). Reject nonce if h == 0 or h >= order.
+ *   Compute scalar s = k - h * x.
+ *   The signature is (r, s).
+ *
+ *
+ * Verification:
+ *   Inputs: 32-byte message m, public key point Q, signature: (32-byte r, scalar s)
+ *
+ *   Signature is invalid if s >= order.
+ *   Signature is invalid if r >= p.
+ *   Compute scalar h = Hash(r || m). Signature is invalid if h == 0 or h >= order.
+ *   Option 1 (faster for single verification):
+ *     Compute point R = h * Q + s * G. Signature is invalid if R is infinity or R's y coordinate is odd.
+ *     Signature is valid if the serialization of R's x coordinate equals r.
+ *   Option 2 (allows batch validation and pubkey recovery):
+ *     Decompress x coordinate r into point R, with odd y coordinate. Fail if R is not on the curve.
+ *     Signature is valid if R + h * Q + s * G == 0.
+ */
+
+static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
+    secp256k1_gej Rj;
+    secp256k1_ge Ra;
+    unsigned char h32[32];
+    secp256k1_scalar h, s;
+    int overflow;
+    secp256k1_scalar n;
+
+    if (secp256k1_scalar_is_zero(key) || secp256k1_scalar_is_zero(nonce)) {
+        return 0;
+    }
+    n = *nonce;
+
+    secp256k1_ecmult_gen(ctx, &Rj, &n);
+    if (pubnonce != NULL) {
+        secp256k1_gej_add_ge(&Rj, &Rj, pubnonce);
+    }
+    secp256k1_ge_set_gej(&Ra, &Rj);
+    secp256k1_fe_normalize(&Ra.y);
+    if (secp256k1_fe_is_odd(&Ra.y)) {
+        /* R's y coordinate is odd, which is not allowed (see rationale above).
+           Force it to be even by negating the nonce. Note that this even works
+           for multiparty signing, as the R point is known to all participants,
+           which can all decide to flip the sign in unison, resulting in the
+           overall R point to be negated too. */
+        secp256k1_scalar_negate(&n, &n);
+    }
+    secp256k1_fe_normalize(&Ra.x);
+    secp256k1_fe_get_b32(sig64, &Ra.x);
+    hash(h32, sig64, msg32);
+    overflow = 0;
+    secp256k1_scalar_set_b32(&h, h32, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&h)) {
+        secp256k1_scalar_clear(&n);
+        return 0;
+    }
+    secp256k1_scalar_mul(&s, &h, key);
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_scalar_add(&s, &s, &n);
+    secp256k1_scalar_clear(&n);
+    secp256k1_scalar_get_b32(sig64 + 32, &s);
+    return 1;
+}
+
+static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
+    secp256k1_gej Qj, Rj;
+    secp256k1_ge Ra;
+    secp256k1_fe Rx;
+    secp256k1_scalar h, s;
+    unsigned char hh[32];
+    int overflow;
+
+    if (secp256k1_ge_is_infinity(pubkey)) {
+        return 0;
+    }
+    hash(hh, sig64, msg32);
+    overflow = 0;
+    secp256k1_scalar_set_b32(&h, hh, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&h)) {
+        return 0;
+    }
+    overflow = 0;
+    secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
+    if (overflow) {
+        return 0;
+    }
+    if (!secp256k1_fe_set_b32(&Rx, sig64)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&Qj, pubkey);
+    secp256k1_ecmult(ctx, &Rj, &Qj, &h, &s);
+    if (secp256k1_gej_is_infinity(&Rj)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej_var(&Ra, &Rj);
+    secp256k1_fe_normalize_var(&Ra.y);
+    if (secp256k1_fe_is_odd(&Ra.y)) {
+        return 0;
+    }
+    return secp256k1_fe_equal_var(&Rx, &Ra.x);
+}
+
+static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
+    secp256k1_gej Qj, Rj;
+    secp256k1_ge Ra;
+    secp256k1_fe Rx;
+    secp256k1_scalar h, s;
+    unsigned char hh[32];
+    int overflow;
+
+    hash(hh, sig64, msg32);
+    overflow = 0;
+    secp256k1_scalar_set_b32(&h, hh, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&h)) {
+        return 0;
+    }
+    overflow = 0;
+    secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
+    if (overflow) {
+        return 0;
+    }
+    if (!secp256k1_fe_set_b32(&Rx, sig64)) {
+        return 0;
+    }
+    if (!secp256k1_ge_set_xo_var(&Ra, &Rx, 0)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&Rj, &Ra);
+    secp256k1_scalar_inverse_var(&h, &h);
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_scalar_mul(&s, &s, &h);
+    secp256k1_ecmult(ctx, &Qj, &Rj, &h, &s);
+    if (secp256k1_gej_is_infinity(&Qj)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(pubkey, &Qj);
+    return 1;
+}
+
+static int secp256k1_schnorr_sig_combine(unsigned char *sig64, size_t n, const unsigned char * const *sig64ins) {
+    secp256k1_scalar s = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    size_t i;
+    for (i = 0; i < n; i++) {
+        secp256k1_scalar si;
+        int overflow;
+        secp256k1_scalar_set_b32(&si, sig64ins[i] + 32, &overflow);
+        if (overflow) {
+            return -1;
+        }
+        if (i) {
+            if (memcmp(sig64ins[i - 1], sig64ins[i], 32) != 0) {
+                return -1;
+            }
+        }
+        secp256k1_scalar_add(&s, &s, &si);
+    }
+    if (secp256k1_scalar_is_zero(&s)) {
+        return 0;
+    }
+    memcpy(sig64, sig64ins[0], 32);
+    secp256k1_scalar_get_b32(sig64 + 32, &s);
+    secp256k1_scalar_clear(&s);
+    return 1;
+}
+
+#endif
diff --git a/src/secp256k1/src/modules/schnorr/tests_impl.h b/src/secp256k1/src/modules/schnorr/tests_impl.h
new file mode 100644
index 0000000000..5bd14a03e3
--- /dev/null
+++ b/src/secp256k1/src/modules/schnorr/tests_impl.h
@@ -0,0 +1,175 @@
+/**********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODULE_SCHNORR_TESTS
+#define SECP256K1_MODULE_SCHNORR_TESTS
+
+#include "include/secp256k1_schnorr.h"
+
+void test_schnorr_end_to_end(void) {
+    unsigned char privkey[32];
+    unsigned char message[32];
+    unsigned char schnorr_signature[64];
+    secp256k1_pubkey pubkey, recpubkey;
+
+    /* Generate a random key and message. */
+    {
+        secp256k1_scalar key;
+        random_scalar_order_test(&key);
+        secp256k1_scalar_get_b32(privkey, &key);
+        secp256k1_rand256_test(message);
+    }
+
+    /* Construct and verify corresponding public key. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Schnorr sign. */
+    CHECK(secp256k1_schnorr_sign(ctx, schnorr_signature, message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_schnorr_verify(ctx, schnorr_signature, message, &pubkey) == 1);
+    CHECK(secp256k1_schnorr_recover(ctx, &recpubkey, schnorr_signature, message) == 1);
+    CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
+    /* Destroy signature and verify again. */
+    schnorr_signature[secp256k1_rand_bits(6)] += 1 + secp256k1_rand_int(255);
+    CHECK(secp256k1_schnorr_verify(ctx, schnorr_signature, message, &pubkey) == 0);
+    CHECK(secp256k1_schnorr_recover(ctx, &recpubkey, schnorr_signature, message) != 1 ||
+          memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
+}
+
+/** Horribly broken hash function. Do not use for anything but tests. */
+void test_schnorr_hash(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32) {
+    int i;
+    for (i = 0; i < 32; i++) {
+        h32[i] = r32[i] ^ msg32[i];
+    }
+}
+
+void test_schnorr_sign_verify(void) {
+    unsigned char msg32[32];
+    unsigned char sig64[3][64];
+    secp256k1_gej pubkeyj[3];
+    secp256k1_ge pubkey[3];
+    secp256k1_scalar nonce[3], key[3];
+    int i = 0;
+    int k;
+
+    secp256k1_rand256_test(msg32);
+
+    for (k = 0; k < 3; k++) {
+        random_scalar_order_test(&key[k]);
+
+        do {
+            random_scalar_order_test(&nonce[k]);
+            if (secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64[k], &key[k], &nonce[k], NULL, &test_schnorr_hash, msg32)) {
+                break;
+            }
+        } while(1);
+
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubkeyj[k], &key[k]);
+        secp256k1_ge_set_gej_var(&pubkey[k], &pubkeyj[k]);
+        CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64[k], &pubkey[k], &test_schnorr_hash, msg32));
+
+        for (i = 0; i < 4; i++) {
+            int pos = secp256k1_rand_bits(6);
+            int mod = 1 + secp256k1_rand_int(255);
+            sig64[k][pos] ^= mod;
+            CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64[k], &pubkey[k], &test_schnorr_hash, msg32) == 0);
+            sig64[k][pos] ^= mod;
+        }
+    }
+}
+
+void test_schnorr_threshold(void) {
+    unsigned char msg[32];
+    unsigned char sec[5][32];
+    secp256k1_pubkey pub[5];
+    unsigned char nonce[5][32];
+    secp256k1_pubkey pubnonce[5];
+    unsigned char sig[5][64];
+    const unsigned char* sigs[5];
+    unsigned char allsig[64];
+    const secp256k1_pubkey* pubs[5];
+    secp256k1_pubkey allpub;
+    int n, i;
+    int damage;
+    int ret = 0;
+
+    damage = secp256k1_rand_bits(1) ? (1 + secp256k1_rand_int(4)) : 0;
+    secp256k1_rand256_test(msg);
+    n = 2 + secp256k1_rand_int(4);
+    for (i = 0; i < n; i++) {
+        do {
+            secp256k1_rand256_test(sec[i]);
+        } while (!secp256k1_ec_seckey_verify(ctx, sec[i]));
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pub[i], sec[i]));
+        CHECK(secp256k1_schnorr_generate_nonce_pair(ctx, &pubnonce[i], nonce[i], msg, sec[i], NULL, NULL));
+        pubs[i] = &pub[i];
+    }
+    if (damage == 1) {
+        nonce[secp256k1_rand_int(n)][secp256k1_rand_int(32)] ^= 1 + secp256k1_rand_int(255);
+    } else if (damage == 2) {
+        sec[secp256k1_rand_int(n)][secp256k1_rand_int(32)] ^= 1 + secp256k1_rand_int(255);
+    }
+    for (i = 0; i < n; i++) {
+        secp256k1_pubkey allpubnonce;
+        const secp256k1_pubkey *pubnonces[4];
+        int j;
+        for (j = 0; j < i; j++) {
+            pubnonces[j] = &pubnonce[j];
+        }
+        for (j = i + 1; j < n; j++) {
+            pubnonces[j - 1] = &pubnonce[j];
+        }
+        CHECK(secp256k1_ec_pubkey_combine(ctx, &allpubnonce, pubnonces, n - 1));
+        ret |= (secp256k1_schnorr_partial_sign(ctx, sig[i], msg, sec[i], &allpubnonce, nonce[i]) != 1) * 1;
+        sigs[i] = sig[i];
+    }
+    if (damage == 3) {
+        sig[secp256k1_rand_int(n)][secp256k1_rand_bits(6)] ^= 1 + secp256k1_rand_int(255);
+    }
+    ret |= (secp256k1_ec_pubkey_combine(ctx, &allpub, pubs, n) != 1) * 2;
+    if ((ret & 1) == 0) {
+        ret |= (secp256k1_schnorr_partial_combine(ctx, allsig, sigs, n) != 1) * 4;
+    }
+    if (damage == 4) {
+        allsig[secp256k1_rand_int(32)] ^= 1 + secp256k1_rand_int(255);
+    }
+    if ((ret & 7) == 0) {
+        ret |= (secp256k1_schnorr_verify(ctx, allsig, msg, &allpub) != 1) * 8;
+    }
+    CHECK((ret == 0) == (damage == 0));
+}
+
+void test_schnorr_recovery(void) {
+    unsigned char msg32[32];
+    unsigned char sig64[64];
+    secp256k1_ge Q;
+
+    secp256k1_rand256_test(msg32);
+    secp256k1_rand256_test(sig64);
+    secp256k1_rand256_test(sig64 + 32);
+    if (secp256k1_schnorr_sig_recover(&ctx->ecmult_ctx, sig64, &Q, &test_schnorr_hash, msg32) == 1) {
+        CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64, &Q, &test_schnorr_hash, msg32) == 1);
+    }
+}
+
+void run_schnorr_tests(void) {
+    int i;
+    for (i = 0; i < 32*count; i++) {
+        test_schnorr_end_to_end();
+    }
+    for (i = 0; i < 32 * count; i++) {
+         test_schnorr_sign_verify();
+    }
+    for (i = 0; i < 16 * count; i++) {
+         test_schnorr_recovery();
+    }
+    for (i = 0; i < 10 * count; i++) {
+         test_schnorr_threshold();
+    }
+}
+
+#endif
diff --git a/src/secp256k1/src/num.h b/src/secp256k1/src/num.h
index 339b6bb6ec..ebfa71eb44 100644
--- a/src/secp256k1/src/num.h
+++ b/src/secp256k1/src/num.h
@@ -20,48 +20,48 @@
 #endif
 
 /** Copy a number. */
-static void secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a);
+static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a);
 
 /** Convert a number's absolute value to a binary big-endian string.
  *  There must be enough place. */
-static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a);
+static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a);
 
 /** Set a number to the value of a binary big-endian string. */
-static void secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen);
+static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen);
 
 /** Compute a modular inverse. The input must be less than the modulus. */
-static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m);
+static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m);
 
 /** Compare the absolute value of two numbers. */
-static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b);
+static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b);
 
 /** Test whether two number are equal (including sign). */
-static int secp256k1_num_eq(const secp256k1_num_t *a, const secp256k1_num_t *b);
+static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b);
 
 /** Add two (signed) numbers. */
-static void secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
+static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
 
 /** Subtract two (signed) numbers. */
-static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
+static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
 
 /** Multiply two (signed) numbers. */
-static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b);
+static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b);
 
 /** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1,
     even if r was negative. */
-static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m);
+static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m);
 
 /** Right-shift the passed number by bits bits. */
-static void secp256k1_num_shift(secp256k1_num_t *r, int bits);
+static void secp256k1_num_shift(secp256k1_num *r, int bits);
 
 /** Check whether a number is zero. */
-static int secp256k1_num_is_zero(const secp256k1_num_t *a);
+static int secp256k1_num_is_zero(const secp256k1_num *a);
 
 /** Check whether a number is strictly negative. */
-static int secp256k1_num_is_neg(const secp256k1_num_t *a);
+static int secp256k1_num_is_neg(const secp256k1_num *a);
 
 /** Change a number's sign. */
-static void secp256k1_num_negate(secp256k1_num_t *r);
+static void secp256k1_num_negate(secp256k1_num *r);
 
 #endif
 
diff --git a/src/secp256k1/src/num_gmp.h b/src/secp256k1/src/num_gmp.h
index baa1f2bf2e..7dd813088a 100644
--- a/src/secp256k1/src/num_gmp.h
+++ b/src/secp256k1/src/num_gmp.h
@@ -15,6 +15,6 @@ typedef struct {
     mp_limb_t data[2*NUM_LIMBS];
     int neg;
     int limbs;
-} secp256k1_num_t;
+} secp256k1_num;
 
 #endif
diff --git a/src/secp256k1/src/num_gmp_impl.h b/src/secp256k1/src/num_gmp_impl.h
index dbbc458d5d..7b6a89719a 100644
--- a/src/secp256k1/src/num_gmp_impl.h
+++ b/src/secp256k1/src/num_gmp_impl.h
@@ -15,18 +15,18 @@
 #include "num.h"
 
 #ifdef VERIFY
-static void secp256k1_num_sanity(const secp256k1_num_t *a) {
+static void secp256k1_num_sanity(const secp256k1_num *a) {
     VERIFY_CHECK(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0));
 }
 #else
 #define secp256k1_num_sanity(a) do { } while(0)
 #endif
 
-static void secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a) {
+static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) {
     *r = *a;
 }
 
-static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a) {
+static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a) {
     unsigned char tmp[65];
     int len = 0;
     int shift = 0;
@@ -42,7 +42,7 @@ static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const sec
     memset(tmp, 0, sizeof(tmp));
 }
 
-static void secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen) {
+static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen) {
     int len;
     VERIFY_CHECK(alen > 0);
     VERIFY_CHECK(alen <= 64);
@@ -59,7 +59,7 @@ static void secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, un
     }
 }
 
-static void secp256k1_num_add_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
     r->limbs = a->limbs;
     if (c != 0) {
@@ -68,8 +68,9 @@ static void secp256k1_num_add_abs(secp256k1_num_t *r, const secp256k1_num_t *a,
     }
 }
 
-static void secp256k1_num_sub_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
+    (void)c;
     VERIFY_CHECK(c == 0);
     r->limbs = a->limbs;
     while (r->limbs > 1 && r->data[r->limbs-1]==0) {
@@ -77,7 +78,7 @@ static void secp256k1_num_sub_abs(secp256k1_num_t *r, const secp256k1_num_t *a,
     }
 }
 
-static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m) {
+static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) {
     secp256k1_num_sanity(r);
     secp256k1_num_sanity(m);
 
@@ -97,7 +98,7 @@ static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m) {
     }
 }
 
-static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m) {
+static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m) {
     int i;
     mp_limb_t g[NUM_LIMBS+1];
     mp_limb_t u[NUM_LIMBS+1];
@@ -125,6 +126,7 @@ static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t
     }
     sn = NUM_LIMBS+1;
     gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs);
+    (void)gn;
     VERIFY_CHECK(gn == 1);
     VERIFY_CHECK(g[0] == 1);
     r->neg = a->neg ^ m->neg;
@@ -142,15 +144,15 @@ static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t
     memset(v, 0, sizeof(v));
 }
 
-static int secp256k1_num_is_zero(const secp256k1_num_t *a) {
+static int secp256k1_num_is_zero(const secp256k1_num *a) {
     return (a->limbs == 1 && a->data[0] == 0);
 }
 
-static int secp256k1_num_is_neg(const secp256k1_num_t *a) {
+static int secp256k1_num_is_neg(const secp256k1_num *a) {
     return (a->limbs > 1 || a->data[0] != 0) && a->neg;
 }
 
-static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) {
     if (a->limbs > b->limbs) {
         return 1;
     }
@@ -160,7 +162,7 @@ static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b)
     return mpn_cmp(a->data, b->data, a->limbs);
 }
 
-static int secp256k1_num_eq(const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) {
     if (a->limbs > b->limbs) {
         return 0;
     }
@@ -173,7 +175,7 @@ static int secp256k1_num_eq(const secp256k1_num_t *a, const secp256k1_num_t *b)
     return mpn_cmp(a->data, b->data, a->limbs) == 0;
 }
 
-static void secp256k1_num_subadd(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b, int bneg) {
+static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) {
     if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */
         r->neg = a->neg;
         if (a->limbs >= b->limbs) {
@@ -192,19 +194,19 @@ static void secp256k1_num_subadd(secp256k1_num_t *r, const secp256k1_num_t *a, c
     }
 }
 
-static void secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     secp256k1_num_sanity(a);
     secp256k1_num_sanity(b);
     secp256k1_num_subadd(r, a, b, 0);
 }
 
-static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     secp256k1_num_sanity(a);
     secp256k1_num_sanity(b);
     secp256k1_num_subadd(r, a, b, 1);
 }
 
-static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
+static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
     mp_limb_t tmp[2*NUM_LIMBS+1];
     secp256k1_num_sanity(a);
     secp256k1_num_sanity(b);
@@ -231,13 +233,13 @@ static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, cons
     memset(tmp, 0, sizeof(tmp));
 }
 
-static void secp256k1_num_shift(secp256k1_num_t *r, int bits) {
-    int i;
+static void secp256k1_num_shift(secp256k1_num *r, int bits) {
     if (bits % GMP_NUMB_BITS) {
         /* Shift within limbs. */
         mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
     }
     if (bits >= GMP_NUMB_BITS) {
+        int i;
         /* Shift full limbs. */
         for (i = 0; i < r->limbs; i++) {
             int index = i + (bits / GMP_NUMB_BITS);
@@ -253,7 +255,7 @@ static void secp256k1_num_shift(secp256k1_num_t *r, int bits) {
     }
 }
 
-static void secp256k1_num_negate(secp256k1_num_t *r) {
+static void secp256k1_num_negate(secp256k1_num *r) {
     r->neg ^= 1;
 }
 
diff --git a/src/secp256k1/src/scalar.h b/src/secp256k1/src/scalar.h
index f5d09f8d47..b590ccd6dd 100644
--- a/src/secp256k1/src/scalar.h
+++ b/src/secp256k1/src/scalar.h
@@ -22,72 +22,83 @@
 #endif
 
 /** Clear a scalar to prevent the leak of sensitive data. */
-static void secp256k1_scalar_clear(secp256k1_scalar_t *r);
+static void secp256k1_scalar_clear(secp256k1_scalar *r);
 
 /** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
-static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count);
+static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
 
 /** Access bits from a scalar. Not constant time. */
-static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count);
+static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
 
 /** Set a scalar from a big endian byte array. */
-static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *bin, int *overflow);
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow);
 
 /** Set a scalar to an unsigned integer. */
-static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v);
+static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v);
 
 /** Convert a scalar to a byte array. */
-static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a);
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a);
 
 /** Add two scalars together (modulo the group order). Returns whether it overflowed. */
-static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
 
-/** Add a power of two to a scalar. The result is not allowed to overflow. */
-static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit);
+/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag);
 
 /** Multiply two scalars (modulo the group order). */
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Shift a scalar right by some amount strictly between 0 and 16, returning
+ *  the low bits that were shifted off */
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n);
 
 /** Compute the square of a scalar (modulo the group order). */
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a);
 
 /** Compute the inverse of a scalar (modulo the group order). */
-static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a);
 
 /** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */
-static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a);
 
 /** Compute the complement of a scalar (modulo the group order). */
-static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a);
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a);
 
 /** Check whether a scalar equals zero. */
-static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a);
+static int secp256k1_scalar_is_zero(const secp256k1_scalar *a);
 
 /** Check whether a scalar equals one. */
-static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a);
+static int secp256k1_scalar_is_one(const secp256k1_scalar *a);
+
+/** Check whether a scalar, considered as an nonnegative integer, is even. */
+static int secp256k1_scalar_is_even(const secp256k1_scalar *a);
 
 /** Check whether a scalar is higher than the group order divided by 2. */
-static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a);
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a);
+
+/** Conditionally negate a number, in constant time.
+ * Returns -1 if the number was negated, 1 otherwise */
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag);
 
 #ifndef USE_NUM_NONE
 /** Convert a scalar to a number. */
-static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a);
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a);
 
 /** Get the order of the group as a number. */
-static void secp256k1_scalar_order_get_num(secp256k1_num_t *r);
+static void secp256k1_scalar_order_get_num(secp256k1_num *r);
 #endif
 
 /** Compare two scalars. */
-static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b);
+static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b);
 
 #ifdef USE_ENDOMORPHISM
 /** Find r1 and r2 such that r1+r2*2^128 = a. */
-static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a);
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
 /** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
-static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a);
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
 #endif
 
 /** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
-static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift);
+static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
 
 #endif
diff --git a/src/secp256k1/src/scalar_4x64.h b/src/secp256k1/src/scalar_4x64.h
index 82899aa7b0..cff406038f 100644
--- a/src/secp256k1/src/scalar_4x64.h
+++ b/src/secp256k1/src/scalar_4x64.h
@@ -12,7 +12,7 @@
 /** A scalar modulo the group order of the secp256k1 curve. */
 typedef struct {
     uint64_t d[4];
-} secp256k1_scalar_t;
+} secp256k1_scalar;
 
 #define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
 
diff --git a/src/secp256k1/src/scalar_4x64_impl.h b/src/secp256k1/src/scalar_4x64_impl.h
index ff365292f8..aa2703dd23 100644
--- a/src/secp256k1/src/scalar_4x64_impl.h
+++ b/src/secp256k1/src/scalar_4x64_impl.h
@@ -24,26 +24,26 @@
 #define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL)
 #define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL)
 
-SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
     r->d[0] = 0;
     r->d[1] = 0;
     r->d[2] = 0;
     r->d[3] = 0;
 }
 
-SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v) {
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
     r->d[0] = v;
     r->d[1] = 0;
     r->d[2] = 0;
     r->d[3] = 0;
 }
 
-SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6);
     return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1);
 }
 
-SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     VERIFY_CHECK(count < 32);
     VERIFY_CHECK(offset + count <= 256);
     if ((offset + count - 1) >> 6 == offset >> 6) {
@@ -54,7 +54,7 @@ SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256
     }
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
     int yes = 0;
     int no = 0;
     no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */
@@ -66,7 +66,7 @@ SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scal
     return yes;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, unsigned int overflow) {
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) {
     uint128_t t;
     VERIFY_CHECK(overflow <= 1);
     t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0;
@@ -80,7 +80,7 @@ SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, unsig
     return overflow;
 }
 
-static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     int overflow;
     uint128_t t = (uint128_t)a->d[0] + b->d[0];
     r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
@@ -96,9 +96,10 @@ static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t
     return overflow;
 }
 
-static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
     uint128_t t;
     VERIFY_CHECK(bit < 256);
+    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 6) > 3 makes this a noop */
     t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F));
     r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64;
     t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F));
@@ -113,7 +114,7 @@ static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
 #endif
 }
 
-static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *b32, int *overflow) {
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
     int over;
     r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56;
     r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56;
@@ -125,18 +126,18 @@ static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char
     }
 }
 
-static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a) {
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
     bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3];
     bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2];
     bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1];
     bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
     return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0;
 }
 
-static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0);
     uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1;
     r->d[0] = t & nonzero; t >>= 64;
@@ -148,11 +149,11 @@ static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scala
     r->d[3] = t & nonzero;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
     return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0;
 }
 
-static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
     int yes = 0;
     int no = 0;
     no |= (a->d[3] < SECP256K1_N_H_3);
@@ -164,6 +165,22 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
     return yes;
 }
 
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    /* If we are flag = 0, mask = 00...00 and this is a no-op;
+     * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+    uint64_t mask = !flag - 1;
+    uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1;
+    uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+    r->d[0] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+    r->d[1] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+    r->d[2] = t & nonzero; t >>= 64;
+    t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+    r->d[3] = t & nonzero;
+    return 2 * (mask == 0) - 1;
+}
+
 /* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
 
 /** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
@@ -250,7 +267,7 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
     VERIFY_CHECK(c2 == 0); \
 }
 
-static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint64_t *l) {
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) {
 #ifdef USE_ASM_X86_64
     /* Reduce 512 bits into 385. */
     uint64_t m0, m1, m2, m3, m4, m5, m6;
@@ -559,7 +576,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint64_t *l
     secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
 }
 
-static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) {
 #ifdef USE_ASM_X86_64
     const uint64_t *pb = b->d;
     __asm__ __volatile__(
@@ -721,12 +738,12 @@ static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar_t *a,
     extract(l[5]);
     muladd_fast(a->d[3], b->d[3]);
     extract_fast(l[6]);
-    VERIFY_CHECK(c1 <= 0);
+    VERIFY_CHECK(c1 == 0);
     l[7] = c0;
 #endif
 }
 
-static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) {
 #ifdef USE_ASM_X86_64
     __asm__ __volatile__(
     /* Preload */
@@ -871,19 +888,32 @@ static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar_t *a)
 #undef extract
 #undef extract_fast
 
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     uint64_t l[8];
     secp256k1_scalar_mul_512(l, a, b);
     secp256k1_scalar_reduce_512(r, l);
 }
 
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = r->d[0] & ((1 << n) - 1);
+    r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n));
+    r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n));
+    r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n));
+    r->d[3] = (r->d[3] >> n);
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint64_t l[8];
     secp256k1_scalar_sqr_512(l, a);
     secp256k1_scalar_reduce_512(r, l);
 }
 
-static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
     r1->d[0] = a->d[0];
     r1->d[1] = a->d[1];
     r1->d[2] = 0;
@@ -893,12 +923,13 @@ static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_
     r2->d[2] = 0;
     r2->d[3] = 0;
 }
+#endif
 
-SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
     return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
 }
 
-SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
     uint64_t l[8];
     unsigned int shiftlimbs;
     unsigned int shiftlow;
@@ -912,9 +943,7 @@ SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *
     r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
     r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
     r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0;
-    if ((l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1) {
-        secp256k1_scalar_add_bit(r, 0);
-    }
+    secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1);
 }
 
 #endif
diff --git a/src/secp256k1/src/scalar_8x32.h b/src/secp256k1/src/scalar_8x32.h
index f17017e24e..1319664f65 100644
--- a/src/secp256k1/src/scalar_8x32.h
+++ b/src/secp256k1/src/scalar_8x32.h
@@ -12,7 +12,7 @@
 /** A scalar modulo the group order of the secp256k1 curve. */
 typedef struct {
     uint32_t d[8];
-} secp256k1_scalar_t;
+} secp256k1_scalar;
 
 #define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
 
diff --git a/src/secp256k1/src/scalar_8x32_impl.h b/src/secp256k1/src/scalar_8x32_impl.h
index 22b31d4112..aae4f35c08 100644
--- a/src/secp256k1/src/scalar_8x32_impl.h
+++ b/src/secp256k1/src/scalar_8x32_impl.h
@@ -34,7 +34,7 @@
 #define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
 #define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
 
-SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
     r->d[0] = 0;
     r->d[1] = 0;
     r->d[2] = 0;
@@ -45,7 +45,7 @@ SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar_t *r) {
     r->d[7] = 0;
 }
 
-SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, unsigned int v) {
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
     r->d[0] = v;
     r->d[1] = 0;
     r->d[2] = 0;
@@ -56,12 +56,12 @@ SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar_t *r, uns
     r->d[7] = 0;
 }
 
-SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
     return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
 }
 
-SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar_t *a, unsigned int offset, unsigned int count) {
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
     VERIFY_CHECK(count < 32);
     VERIFY_CHECK(offset + count <= 256);
     if ((offset + count - 1) >> 5 == offset >> 5) {
@@ -72,7 +72,7 @@ SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256
     }
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
     int yes = 0;
     int no = 0;
     no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
@@ -90,7 +90,7 @@ SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scal
     return yes;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, uint32_t overflow) {
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
     uint64_t t;
     VERIFY_CHECK(overflow <= 1);
     t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
@@ -112,7 +112,7 @@ SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar_t *r, uint3
     return overflow;
 }
 
-static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     int overflow;
     uint64_t t = (uint64_t)a->d[0] + b->d[0];
     r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
@@ -136,9 +136,10 @@ static int secp256k1_scalar_add(secp256k1_scalar_t *r, const secp256k1_scalar_t
     return overflow;
 }
 
-static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
     uint64_t t;
     VERIFY_CHECK(bit < 256);
+    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 5) > 7 makes this a noop */
     t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
     r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
     t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
@@ -161,7 +162,7 @@ static void secp256k1_scalar_add_bit(secp256k1_scalar_t *r, unsigned int bit) {
 #endif
 }
 
-static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char *b32, int *overflow) {
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
     int over;
     r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
     r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
@@ -177,7 +178,7 @@ static void secp256k1_scalar_set_b32(secp256k1_scalar_t *r, const unsigned char
     }
 }
 
-static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_t* a) {
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
     bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
     bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
     bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
@@ -188,11 +189,11 @@ static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar_
     bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
     return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
 }
 
-static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
     uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
     r->d[0] = t & nonzero; t >>= 32;
@@ -212,11 +213,11 @@ static void secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scala
     r->d[7] = t & nonzero;
 }
 
-SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar_t *a) {
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
     return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
 }
 
-static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
     int yes = 0;
     int no = 0;
     no |= (a->d[7] < SECP256K1_N_H_7);
@@ -234,6 +235,31 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
     return yes;
 }
 
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    /* If we are flag = 0, mask = 00...00 and this is a no-op;
+     * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+    uint32_t mask = !flag - 1;
+    uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
+    uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+    r->d[0] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+    r->d[1] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+    r->d[2] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+    r->d[3] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
+    r->d[4] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
+    r->d[5] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
+    r->d[6] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
+    r->d[7] = t & nonzero;
+    return 2 * (mask == 0) - 1;
+}
+
+
 /* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
 
 /** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
@@ -320,7 +346,7 @@ static int secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
     VERIFY_CHECK(c2 == 0); \
 }
 
-static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint32_t *l) {
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
     uint64_t c;
     uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
     uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
@@ -462,7 +488,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar_t *r, const uint32_t *l
     secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
 }
 
-static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     /* 96 bit accumulator. */
     uint32_t c0 = 0, c1 = 0, c2 = 0;
 
@@ -550,7 +576,7 @@ static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar_t *a, c
     l[15] = c0;
 }
 
-static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) {
     /* 96 bit accumulator. */
     uint32_t c0 = 0, c1 = 0, c2 = 0;
 
@@ -618,20 +644,36 @@ static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar_t *a) {
 #undef extract
 #undef extract_fast
 
-static void secp256k1_scalar_mul(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
     uint32_t l[16];
     secp256k1_scalar_mul_512(l, a, b);
     secp256k1_scalar_reduce_512(r, l);
 }
 
-static void secp256k1_scalar_sqr(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = r->d[0] & ((1 << n) - 1);
+    r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n));
+    r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n));
+    r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n));
+    r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n));
+    r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n));
+    r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n));
+    r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n));
+    r->d[7] = (r->d[7] >> n);
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
     uint32_t l[16];
     secp256k1_scalar_sqr_512(l, a);
     secp256k1_scalar_reduce_512(r, l);
 }
 
 #ifdef USE_ENDOMORPHISM
-static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
     r1->d[0] = a->d[0];
     r1->d[1] = a->d[1];
     r1->d[2] = a->d[2];
@@ -651,11 +693,11 @@ static void secp256k1_scalar_split_128(secp256k1_scalar_t *r1, secp256k1_scalar_
 }
 #endif
 
-SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar_t *a, const secp256k1_scalar_t *b) {
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
     return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
 }
 
-SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *a, const secp256k1_scalar_t *b, unsigned int shift) {
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
     uint32_t l[16];
     unsigned int shiftlimbs;
     unsigned int shiftlow;
@@ -673,9 +715,7 @@ SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar_t *
     r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
     r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
     r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow)  : 0;
-    if ((l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1) {
-        secp256k1_scalar_add_bit(r, 0);
-    }
+    secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
 }
 
 #endif
diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h
index 33824983e4..88ea97de86 100644
--- a/src/secp256k1/src/scalar_impl.h
+++ b/src/secp256k1/src/scalar_impl.h
@@ -25,14 +25,14 @@
 #endif
 
 #ifndef USE_NUM_NONE
-static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a) {
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) {
     unsigned char c[32];
     secp256k1_scalar_get_b32(c, a);
     secp256k1_num_set_bin(r, c, 32);
 }
 
 /** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
-static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) {
+static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
     static const unsigned char order[32] = {
         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
@@ -43,11 +43,11 @@ static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) {
 }
 #endif
 
-static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) {
-    secp256k1_scalar_t *t;
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
+    secp256k1_scalar *t;
     int i;
     /* First compute x ^ (2^N - 1) for some values of N. */
-    secp256k1_scalar_t x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
+    secp256k1_scalar x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
 
     secp256k1_scalar_sqr(&x2,  x);
     secp256k1_scalar_mul(&x2, &x2,  x);
@@ -234,18 +234,27 @@ static void secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scal
     secp256k1_scalar_mul(r, t, &x6); /* 111111 */
 }
 
-static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_scalar_t *x) {
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    /* d[0] is present and is the lowest word for all representations */
+    return !(a->d[0] & 1);
+}
+
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
 #if defined(USE_SCALAR_INV_BUILTIN)
     secp256k1_scalar_inverse(r, x);
 #elif defined(USE_SCALAR_INV_NUM)
     unsigned char b[32];
-    secp256k1_num_t n, m;
-    secp256k1_scalar_get_b32(b, x);
+    secp256k1_num n, m;
+    secp256k1_scalar t = *x;
+    secp256k1_scalar_get_b32(b, &t);
     secp256k1_num_set_bin(&n, b, 32);
     secp256k1_scalar_order_get_num(&m);
     secp256k1_num_mod_inverse(&n, &n, &m);
     secp256k1_num_get_bin(b, 32, &n);
     secp256k1_scalar_set_b32(r, b, NULL);
+    /* Verify that the inverse was computed correctly, without GMP code. */
+    secp256k1_scalar_mul(&t, &t, r);
+    CHECK(secp256k1_scalar_is_one(&t));
 #else
 #error "Please select scalar inverse implementation"
 #endif
@@ -290,30 +299,31 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_
  * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
  */
 
-static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
-    secp256k1_scalar_t c1, c2;
-    static const secp256k1_scalar_t minus_lambda = SECP256K1_SCALAR_CONST(
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    secp256k1_scalar c1, c2;
+    static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST(
         0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
         0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
     );
-    static const secp256k1_scalar_t minus_b1 = SECP256K1_SCALAR_CONST(
+    static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST(
         0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
         0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
     );
-    static const secp256k1_scalar_t minus_b2 = SECP256K1_SCALAR_CONST(
+    static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST(
         0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
         0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
     );
-    static const secp256k1_scalar_t g1 = SECP256K1_SCALAR_CONST(
+    static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST(
         0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
         0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
     );
-    static const secp256k1_scalar_t g2 = SECP256K1_SCALAR_CONST(
+    static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST(
         0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
         0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
     );
     VERIFY_CHECK(r1 != a);
     VERIFY_CHECK(r2 != a);
+    /* these _var calls are constant time since the shift amount is constant */
     secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
     secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
     secp256k1_scalar_mul(&c1, &c1, &minus_b1);
diff --git a/src/secp256k1/src/secp256k1.c b/src/secp256k1/src/secp256k1.c
index d6192dc4ed..62d192baeb 100644
--- a/src/secp256k1/src/secp256k1.c
+++ b/src/secp256k1/src/secp256k1.c
@@ -14,150 +14,348 @@
 #include "scalar_impl.h"
 #include "group_impl.h"
 #include "ecmult_impl.h"
+#include "ecmult_const_impl.h"
 #include "ecmult_gen_impl.h"
 #include "ecdsa_impl.h"
 #include "eckey_impl.h"
 #include "hash_impl.h"
 
+#define ARG_CHECK(cond) do { \
+    if (EXPECT(!(cond), 0)) { \
+        secp256k1_callback_call(&ctx->illegal_callback, #cond); \
+        return 0; \
+    } \
+} while(0)
+
+static void default_illegal_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_illegal_callback = {
+    default_illegal_callback_fn,
+    NULL
+};
+
+static void default_error_callback_fn(const char* str, void* data) {
+    (void)data;
+    fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str);
+    abort();
+}
+
+static const secp256k1_callback default_error_callback = {
+    default_error_callback_fn,
+    NULL
+};
+
+
 struct secp256k1_context_struct {
-    secp256k1_ecmult_context_t ecmult_ctx;
-    secp256k1_ecmult_gen_context_t ecmult_gen_ctx;
+    secp256k1_ecmult_context ecmult_ctx;
+    secp256k1_ecmult_gen_context ecmult_gen_ctx;
+    secp256k1_callback illegal_callback;
+    secp256k1_callback error_callback;
 };
 
-secp256k1_context_t* secp256k1_context_create(int flags) {
-    secp256k1_context_t* ret = (secp256k1_context_t*)checked_malloc(sizeof(secp256k1_context_t));
+secp256k1_context* secp256k1_context_create(unsigned int flags) {
+    secp256k1_context* ret = (secp256k1_context*)checked_malloc(&default_error_callback, sizeof(secp256k1_context));
+    ret->illegal_callback = default_illegal_callback;
+    ret->error_callback = default_error_callback;
+
+    if (EXPECT((flags & SECP256K1_FLAGS_TYPE_MASK) != SECP256K1_FLAGS_TYPE_CONTEXT, 0)) {
+            secp256k1_callback_call(&ret->illegal_callback,
+                                    "Invalid flags");
+            free(ret);
+            return NULL;
+    }
 
     secp256k1_ecmult_context_init(&ret->ecmult_ctx);
     secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx);
 
-    if (flags & SECP256K1_CONTEXT_SIGN) {
-        secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx);
+    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) {
+        secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &ret->error_callback);
     }
-    if (flags & SECP256K1_CONTEXT_VERIFY) {
-        secp256k1_ecmult_context_build(&ret->ecmult_ctx);
+    if (flags & SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) {
+        secp256k1_ecmult_context_build(&ret->ecmult_ctx, &ret->error_callback);
     }
 
     return ret;
 }
 
-secp256k1_context_t* secp256k1_context_clone(const secp256k1_context_t* ctx) {
-    secp256k1_context_t* ret = (secp256k1_context_t*)checked_malloc(sizeof(secp256k1_context_t));
-    secp256k1_ecmult_context_clone(&ret->ecmult_ctx, &ctx->ecmult_ctx);
-    secp256k1_ecmult_gen_context_clone(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx);
+secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) {
+    secp256k1_context* ret = (secp256k1_context*)checked_malloc(&ctx->error_callback, sizeof(secp256k1_context));
+    ret->illegal_callback = ctx->illegal_callback;
+    ret->error_callback = ctx->error_callback;
+    secp256k1_ecmult_context_clone(&ret->ecmult_ctx, &ctx->ecmult_ctx, &ctx->error_callback);
+    secp256k1_ecmult_gen_context_clone(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx, &ctx->error_callback);
     return ret;
 }
 
-void secp256k1_context_destroy(secp256k1_context_t* ctx) {
-    secp256k1_ecmult_context_clear(&ctx->ecmult_ctx);
-    secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx);
+void secp256k1_context_destroy(secp256k1_context* ctx) {
+    if (ctx != NULL) {
+        secp256k1_ecmult_context_clear(&ctx->ecmult_ctx);
+        secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx);
 
-    free(ctx);
+        free(ctx);
+    }
 }
 
-int secp256k1_ecdsa_verify(const secp256k1_context_t* ctx, const unsigned char *msg32, const unsigned char *sig, int siglen, const unsigned char *pubkey, int pubkeylen) {
-    secp256k1_ge_t q;
-    secp256k1_ecdsa_sig_t s;
-    secp256k1_scalar_t m;
-    int ret = -3;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
-    DEBUG_CHECK(msg32 != NULL);
-    DEBUG_CHECK(sig != NULL);
-    DEBUG_CHECK(pubkey != NULL);
+void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
+    if (fun == NULL) {
+        fun = default_illegal_callback_fn;
+    }
+    ctx->illegal_callback.fn = fun;
+    ctx->illegal_callback.data = data;
+}
 
-    secp256k1_scalar_set_b32(&m, msg32, NULL);
+void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) {
+    if (fun == NULL) {
+        fun = default_error_callback_fn;
+    }
+    ctx->error_callback.fn = fun;
+    ctx->error_callback.data = data;
+}
 
-    if (secp256k1_eckey_pubkey_parse(&q, pubkey, pubkeylen)) {
-        if (secp256k1_ecdsa_sig_parse(&s, sig, siglen)) {
-            if (secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &s, &q, &m)) {
-                /* success is 1, all other values are fail */
-                ret = 1;
-            } else {
-                ret = 0;
-            }
-        } else {
-            ret = -2;
-        }
+static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge, const secp256k1_pubkey* pubkey) {
+    if (sizeof(secp256k1_ge_storage) == 64) {
+        /* When the secp256k1_ge_storage type is exactly 64 byte, use its
+         * representation inside secp256k1_pubkey, as conversion is very fast.
+         * Note that secp256k1_pubkey_save must use the same representation. */
+        secp256k1_ge_storage s;
+        memcpy(&s, &pubkey->data[0], 64);
+        secp256k1_ge_from_storage(ge, &s);
+    } else {
+        /* Otherwise, fall back to 32-byte big endian for X and Y. */
+        secp256k1_fe x, y;
+        secp256k1_fe_set_b32(&x, pubkey->data);
+        secp256k1_fe_set_b32(&y, pubkey->data + 32);
+        secp256k1_ge_set_xy(ge, &x, &y);
+    }
+    ARG_CHECK(!secp256k1_fe_is_zero(&ge->x));
+    return 1;
+}
+
+static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) {
+    if (sizeof(secp256k1_ge_storage) == 64) {
+        secp256k1_ge_storage s;
+        secp256k1_ge_to_storage(&s, ge);
+        memcpy(&pubkey->data[0], &s, 64);
     } else {
-        ret = -1;
+        VERIFY_CHECK(!secp256k1_ge_is_infinity(ge));
+        secp256k1_fe_normalize_var(&ge->x);
+        secp256k1_fe_normalize_var(&ge->y);
+        secp256k1_fe_get_b32(pubkey->data, &ge->x);
+        secp256k1_fe_get_b32(pubkey->data + 32, &ge->y);
     }
+}
+
+int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pubkey, const unsigned char *input, size_t inputlen) {
+    secp256k1_ge Q;
+
+    (void)ctx;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+    memset(pubkey, 0, sizeof(*pubkey));
+    ARG_CHECK(input != NULL);
+    if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) {
+        return 0;
+    }
+    secp256k1_pubkey_save(pubkey, &Q);
+    secp256k1_ge_clear(&Q);
+    return 1;
+}
+
+int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_pubkey* pubkey, unsigned int flags) {
+    secp256k1_ge Q;
+    size_t len;
+    int ret = 0;
 
+    (void)ctx;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(outputlen != NULL);
+    ARG_CHECK(*outputlen >= ((flags & SECP256K1_FLAGS_BIT_COMPRESSION) ? 33 : 65));
+    len = *outputlen;
+    *outputlen = 0;
+    ARG_CHECK(output != NULL);
+    memset(output, 0, len);
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_COMPRESSION);
+    if (secp256k1_pubkey_load(ctx, &Q, pubkey)) {
+        ret = secp256k1_eckey_pubkey_serialize(&Q, output, &len, flags & SECP256K1_FLAGS_BIT_COMPRESSION);
+        if (ret) {
+            *outputlen = len;
+        }
+    }
     return ret;
 }
 
-static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) {
-   secp256k1_rfc6979_hmac_sha256_t rng;
-   unsigned int i;
-   secp256k1_rfc6979_hmac_sha256_initialize(&rng, key32, 32, msg32, 32, (const unsigned char*)data, data != NULL ? 32 : 0);
-   for (i = 0; i <= counter; i++) {
-       secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
-   }
-   secp256k1_rfc6979_hmac_sha256_finalize(&rng);
-   return 1;
+static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) {
+    (void)ctx;
+    if (sizeof(secp256k1_scalar) == 32) {
+        /* When the secp256k1_scalar type is exactly 32 byte, use its
+         * representation inside secp256k1_ecdsa_signature, as conversion is very fast.
+         * Note that secp256k1_ecdsa_signature_save must use the same representation. */
+        memcpy(r, &sig->data[0], 32);
+        memcpy(s, &sig->data[32], 32);
+    } else {
+        secp256k1_scalar_set_b32(r, &sig->data[0], NULL);
+        secp256k1_scalar_set_b32(s, &sig->data[32], NULL);
+    }
 }
 
-const secp256k1_nonce_function_t secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
-const secp256k1_nonce_function_t secp256k1_nonce_function_default = nonce_function_rfc6979;
+static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s) {
+    if (sizeof(secp256k1_scalar) == 32) {
+        memcpy(&sig->data[0], r, 32);
+        memcpy(&sig->data[32], s, 32);
+    } else {
+        secp256k1_scalar_get_b32(&sig->data[0], r);
+        secp256k1_scalar_get_b32(&sig->data[32], s);
+    }
+}
 
-int secp256k1_ecdsa_sign(const secp256k1_context_t* ctx, const unsigned char *msg32, unsigned char *signature, int *signaturelen, const unsigned char *seckey, secp256k1_nonce_function_t noncefp, const void* noncedata) {
-    secp256k1_ecdsa_sig_t sig;
-    secp256k1_scalar_t sec, non, msg;
-    int ret = 0;
+int secp256k1_ecdsa_signature_parse_der(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) {
+    secp256k1_scalar r, s;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input != NULL);
+
+    if (secp256k1_ecdsa_sig_parse(&r, &s, input, inputlen)) {
+        secp256k1_ecdsa_signature_save(sig, &r, &s);
+        return 1;
+    } else {
+        memset(sig, 0, sizeof(*sig));
+        return 0;
+    }
+}
+
+int secp256k1_ecdsa_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input64) {
+    secp256k1_scalar r, s;
+    int ret = 1;
     int overflow = 0;
-    unsigned int count = 0;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
-    DEBUG_CHECK(msg32 != NULL);
-    DEBUG_CHECK(signature != NULL);
-    DEBUG_CHECK(signaturelen != NULL);
-    DEBUG_CHECK(seckey != NULL);
-    if (noncefp == NULL) {
-        noncefp = secp256k1_nonce_function_default;
+
+    (void)ctx;
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(input64 != NULL);
+
+    secp256k1_scalar_set_b32(&r, &input64[0], &overflow);
+    ret &= !overflow;
+    secp256k1_scalar_set_b32(&s, &input64[32], &overflow);
+    ret &= !overflow;
+    if (ret) {
+        secp256k1_ecdsa_signature_save(sig, &r, &s);
+    } else {
+        memset(sig, 0, sizeof(*sig));
     }
+    return ret;
+}
 
-    secp256k1_scalar_set_b32(&sec, seckey, &overflow);
-    /* Fail if the secret key is invalid. */
-    if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
-        secp256k1_scalar_set_b32(&msg, msg32, NULL);
-        while (1) {
-            unsigned char nonce32[32];
-            ret = noncefp(nonce32, msg32, seckey, count, noncedata);
-            if (!ret) {
-                break;
-            }
-            secp256k1_scalar_set_b32(&non, nonce32, &overflow);
-            memset(nonce32, 0, 32);
-            if (!secp256k1_scalar_is_zero(&non) && !overflow) {
-                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &sig, &sec, &msg, &non, NULL)) {
-                    break;
-                }
-            }
-            count++;
-        }
+int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_ecdsa_signature* sig) {
+    secp256k1_scalar r, s;
+
+    (void)ctx;
+    ARG_CHECK(output != NULL);
+    ARG_CHECK(outputlen != NULL);
+    ARG_CHECK(sig != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    return secp256k1_ecdsa_sig_serialize(output, outputlen, &r, &s);
+}
+
+int secp256k1_ecdsa_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, const secp256k1_ecdsa_signature* sig) {
+    secp256k1_scalar r, s;
+
+    (void)ctx;
+    ARG_CHECK(output64 != NULL);
+    ARG_CHECK(sig != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    secp256k1_scalar_get_b32(&output64[0], &r);
+    secp256k1_scalar_get_b32(&output64[32], &s);
+    return 1;
+}
+
+int secp256k1_ecdsa_signature_normalize(const secp256k1_context* ctx, secp256k1_ecdsa_signature *sigout, const secp256k1_ecdsa_signature *sigin) {
+    secp256k1_scalar r, s;
+    int ret = 0;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sigin != NULL);
+
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sigin);
+    ret = secp256k1_scalar_is_high(&s);
+    if (sigout != NULL) {
         if (ret) {
-            ret = secp256k1_ecdsa_sig_serialize(signature, signaturelen, &sig);
+            secp256k1_scalar_negate(&s, &s);
         }
-        secp256k1_scalar_clear(&msg);
-        secp256k1_scalar_clear(&non);
-        secp256k1_scalar_clear(&sec);
-    }
-    if (!ret) {
-        *signaturelen = 0;
+        secp256k1_ecdsa_signature_save(sigout, &r, &s);
     }
+
     return ret;
 }
 
-int secp256k1_ecdsa_sign_compact(const secp256k1_context_t* ctx, const unsigned char *msg32, unsigned char *sig64, const unsigned char *seckey, secp256k1_nonce_function_t noncefp, const void* noncedata, int *recid) {
-    secp256k1_ecdsa_sig_t sig;
-    secp256k1_scalar_t sec, non, msg;
+int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
+    secp256k1_ge q;
+    secp256k1_scalar r, s;
+    secp256k1_scalar m;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    secp256k1_scalar_set_b32(&m, msg32, NULL);
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    return (!secp256k1_scalar_is_high(&s) &&
+            secp256k1_pubkey_load(ctx, &q, pubkey) &&
+            secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &r, &s, &q, &m));
+}
+
+static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+   unsigned char keydata[112];
+   int keylen = 64;
+   secp256k1_rfc6979_hmac_sha256_t rng;
+   unsigned int i;
+   /* We feed a byte array to the PRNG as input, consisting of:
+    * - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d.
+    * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data.
+    * - optionally 16 extra bytes with the algorithm name.
+    * Because the arguments have distinct fixed lengths it is not possible for
+    *  different argument mixtures to emulate each other and result in the same
+    *  nonces.
+    */
+   memcpy(keydata, key32, 32);
+   memcpy(keydata + 32, msg32, 32);
+   if (data != NULL) {
+       memcpy(keydata + 64, data, 32);
+       keylen = 96;
+   }
+   if (algo16 != NULL) {
+       memcpy(keydata + keylen, algo16, 16);
+       keylen += 16;
+   }
+   secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, keylen);
+   memset(keydata, 0, sizeof(keydata));
+   for (i = 0; i <= counter; i++) {
+       secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32);
+   }
+   secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+   return 1;
+}
+
+const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979;
+const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979;
+
+int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
+    secp256k1_scalar r, s;
+    secp256k1_scalar sec, non, msg;
     int ret = 0;
     int overflow = 0;
-    unsigned int count = 0;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
-    DEBUG_CHECK(msg32 != NULL);
-    DEBUG_CHECK(sig64 != NULL);
-    DEBUG_CHECK(seckey != NULL);
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(signature != NULL);
+    ARG_CHECK(seckey != NULL);
     if (noncefp == NULL) {
         noncefp = secp256k1_nonce_function_default;
     }
@@ -165,139 +363,87 @@ int secp256k1_ecdsa_sign_compact(const secp256k1_context_t* ctx, const unsigned
     secp256k1_scalar_set_b32(&sec, seckey, &overflow);
     /* Fail if the secret key is invalid. */
     if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned int count = 0;
         secp256k1_scalar_set_b32(&msg, msg32, NULL);
         while (1) {
             unsigned char nonce32[32];
-            ret = noncefp(nonce32, msg32, seckey, count, noncedata);
+            ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
             if (!ret) {
                 break;
             }
             secp256k1_scalar_set_b32(&non, nonce32, &overflow);
             memset(nonce32, 0, 32);
-            if (!secp256k1_scalar_is_zero(&non) && !overflow) {
-                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &sig, &sec, &msg, &non, recid)) {
+            if (!overflow && !secp256k1_scalar_is_zero(&non)) {
+                if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL)) {
                     break;
                 }
             }
             count++;
         }
-        if (ret) {
-            secp256k1_scalar_get_b32(sig64, &sig.r);
-            secp256k1_scalar_get_b32(sig64 + 32, &sig.s);
-        }
         secp256k1_scalar_clear(&msg);
         secp256k1_scalar_clear(&non);
         secp256k1_scalar_clear(&sec);
     }
-    if (!ret) {
-        memset(sig64, 0, 64);
-    }
-    return ret;
-}
-
-int secp256k1_ecdsa_recover_compact(const secp256k1_context_t* ctx, const unsigned char *msg32, const unsigned char *sig64, unsigned char *pubkey, int *pubkeylen, int compressed, int recid) {
-    secp256k1_ge_t q;
-    secp256k1_ecdsa_sig_t sig;
-    secp256k1_scalar_t m;
-    int ret = 0;
-    int overflow = 0;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
-    DEBUG_CHECK(msg32 != NULL);
-    DEBUG_CHECK(sig64 != NULL);
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(pubkeylen != NULL);
-    DEBUG_CHECK(recid >= 0 && recid <= 3);
-
-    secp256k1_scalar_set_b32(&sig.r, sig64, &overflow);
-    if (!overflow) {
-        secp256k1_scalar_set_b32(&sig.s, sig64 + 32, &overflow);
-        if (!overflow) {
-            secp256k1_scalar_set_b32(&m, msg32, NULL);
-
-            if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &sig, &q, &m, recid)) {
-                ret = secp256k1_eckey_pubkey_serialize(&q, pubkey, pubkeylen, compressed);
-            }
-        }
+    if (ret) {
+        secp256k1_ecdsa_signature_save(signature, &r, &s);
+    } else {
+        memset(signature, 0, sizeof(*signature));
     }
     return ret;
 }
 
-int secp256k1_ec_seckey_verify(const secp256k1_context_t* ctx, const unsigned char *seckey) {
-    secp256k1_scalar_t sec;
+int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char *seckey) {
+    secp256k1_scalar sec;
     int ret;
     int overflow;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(seckey != NULL);
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
     (void)ctx;
 
     secp256k1_scalar_set_b32(&sec, seckey, &overflow);
-    ret = !secp256k1_scalar_is_zero(&sec) && !overflow;
+    ret = !overflow && !secp256k1_scalar_is_zero(&sec);
     secp256k1_scalar_clear(&sec);
     return ret;
 }
 
-int secp256k1_ec_pubkey_verify(const secp256k1_context_t* ctx, const unsigned char *pubkey, int pubkeylen) {
-    secp256k1_ge_t q;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(pubkey != NULL);
-    (void)ctx;
-
-    return secp256k1_eckey_pubkey_parse(&q, pubkey, pubkeylen);
-}
-
-int secp256k1_ec_pubkey_create(const secp256k1_context_t* ctx, unsigned char *pubkey, int *pubkeylen, const unsigned char *seckey, int compressed) {
-    secp256k1_gej_t pj;
-    secp256k1_ge_t p;
-    secp256k1_scalar_t sec;
+int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *seckey) {
+    secp256k1_gej pj;
+    secp256k1_ge p;
+    secp256k1_scalar sec;
     int overflow;
     int ret = 0;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(pubkeylen != NULL);
-    DEBUG_CHECK(seckey != NULL);
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+    memset(pubkey, 0, sizeof(*pubkey));
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(seckey != NULL);
 
     secp256k1_scalar_set_b32(&sec, seckey, &overflow);
-    if (!overflow) {
+    ret = (!overflow) & (!secp256k1_scalar_is_zero(&sec));
+    if (ret) {
         secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pj, &sec);
-        secp256k1_scalar_clear(&sec);
         secp256k1_ge_set_gej(&p, &pj);
-        ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, pubkeylen, compressed);
-    }
-    if (!ret) {
-        *pubkeylen = 0;
-    }
-    return ret;
-}
-
-int secp256k1_ec_pubkey_decompress(const secp256k1_context_t* ctx, unsigned char *pubkey, int *pubkeylen) {
-    secp256k1_ge_t p;
-    int ret = 0;
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(pubkeylen != NULL);
-    (void)ctx;
-
-    if (secp256k1_eckey_pubkey_parse(&p, pubkey, *pubkeylen)) {
-        ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, pubkeylen, 0);
+        secp256k1_pubkey_save(pubkey, &p);
     }
+    secp256k1_scalar_clear(&sec);
     return ret;
 }
 
-int secp256k1_ec_privkey_tweak_add(const secp256k1_context_t* ctx, unsigned char *seckey, const unsigned char *tweak) {
-    secp256k1_scalar_t term;
-    secp256k1_scalar_t sec;
+int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
+    secp256k1_scalar term;
+    secp256k1_scalar sec;
     int ret = 0;
     int overflow = 0;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(seckey != NULL);
-    DEBUG_CHECK(tweak != NULL);
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(tweak != NULL);
     (void)ctx;
 
     secp256k1_scalar_set_b32(&term, tweak, &overflow);
     secp256k1_scalar_set_b32(&sec, seckey, NULL);
 
-    ret = secp256k1_eckey_privkey_tweak_add(&sec, &term) && !overflow;
+    ret = !overflow && secp256k1_eckey_privkey_tweak_add(&sec, &term);
+    memset(seckey, 0, 32);
     if (ret) {
         secp256k1_scalar_get_b32(seckey, &sec);
     }
@@ -307,45 +453,44 @@ int secp256k1_ec_privkey_tweak_add(const secp256k1_context_t* ctx, unsigned char
     return ret;
 }
 
-int secp256k1_ec_pubkey_tweak_add(const secp256k1_context_t* ctx, unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
-    secp256k1_ge_t p;
-    secp256k1_scalar_t term;
+int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
+    secp256k1_ge p;
+    secp256k1_scalar term;
     int ret = 0;
     int overflow = 0;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(tweak != NULL);
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(tweak != NULL);
 
     secp256k1_scalar_set_b32(&term, tweak, &overflow);
-    if (!overflow) {
-        ret = secp256k1_eckey_pubkey_parse(&p, pubkey, pubkeylen);
-        if (ret) {
-            ret = secp256k1_eckey_pubkey_tweak_add(&ctx->ecmult_ctx, &p, &term);
-        }
-        if (ret) {
-            int oldlen = pubkeylen;
-            ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
-            VERIFY_CHECK(pubkeylen == oldlen);
+    ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey);
+    memset(pubkey, 0, sizeof(*pubkey));
+    if (ret) {
+        if (secp256k1_eckey_pubkey_tweak_add(&ctx->ecmult_ctx, &p, &term)) {
+            secp256k1_pubkey_save(pubkey, &p);
+        } else {
+            ret = 0;
         }
     }
 
     return ret;
 }
 
-int secp256k1_ec_privkey_tweak_mul(const secp256k1_context_t* ctx, unsigned char *seckey, const unsigned char *tweak) {
-    secp256k1_scalar_t factor;
-    secp256k1_scalar_t sec;
+int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) {
+    secp256k1_scalar factor;
+    secp256k1_scalar sec;
     int ret = 0;
     int overflow = 0;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(seckey != NULL);
-    DEBUG_CHECK(tweak != NULL);
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(seckey != NULL);
+    ARG_CHECK(tweak != NULL);
     (void)ctx;
 
     secp256k1_scalar_set_b32(&factor, tweak, &overflow);
     secp256k1_scalar_set_b32(&sec, seckey, NULL);
-    ret = secp256k1_eckey_privkey_tweak_mul(&sec, &factor) && !overflow;
+    ret = !overflow && secp256k1_eckey_privkey_tweak_mul(&sec, &factor);
+    memset(seckey, 0, 32);
     if (ret) {
         secp256k1_scalar_get_b32(seckey, &sec);
     }
@@ -355,65 +500,69 @@ int secp256k1_ec_privkey_tweak_mul(const secp256k1_context_t* ctx, unsigned char
     return ret;
 }
 
-int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context_t* ctx, unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
-    secp256k1_ge_t p;
-    secp256k1_scalar_t factor;
+int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) {
+    secp256k1_ge p;
+    secp256k1_scalar factor;
     int ret = 0;
     int overflow = 0;
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
-    DEBUG_CHECK(pubkey != NULL);
-    DEBUG_CHECK(tweak != NULL);
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(tweak != NULL);
 
     secp256k1_scalar_set_b32(&factor, tweak, &overflow);
-    if (!overflow) {
-        ret = secp256k1_eckey_pubkey_parse(&p, pubkey, pubkeylen);
-        if (ret) {
-            ret = secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor);
-        }
-        if (ret) {
-            int oldlen = pubkeylen;
-            ret = secp256k1_eckey_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
-            VERIFY_CHECK(pubkeylen == oldlen);
+    ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey);
+    memset(pubkey, 0, sizeof(*pubkey));
+    if (ret) {
+        if (secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor)) {
+            secp256k1_pubkey_save(pubkey, &p);
+        } else {
+            ret = 0;
         }
     }
 
     return ret;
 }
 
-int secp256k1_ec_privkey_export(const secp256k1_context_t* ctx, const unsigned char *seckey, unsigned char *privkey, int *privkeylen, int compressed) {
-    secp256k1_scalar_t key;
-    int ret = 0;
-    DEBUG_CHECK(seckey != NULL);
-    DEBUG_CHECK(privkey != NULL);
-    DEBUG_CHECK(privkeylen != NULL);
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
-
-    secp256k1_scalar_set_b32(&key, seckey, NULL);
-    ret = secp256k1_eckey_privkey_serialize(&ctx->ecmult_gen_ctx, privkey, privkeylen, &key, compressed);
-    secp256k1_scalar_clear(&key);
-    return ret;
+int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *seed32) {
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
+    return 1;
 }
 
-int secp256k1_ec_privkey_import(const secp256k1_context_t* ctx, unsigned char *seckey, const unsigned char *privkey, int privkeylen) {
-    secp256k1_scalar_t key;
-    int ret = 0;
-    DEBUG_CHECK(seckey != NULL);
-    DEBUG_CHECK(privkey != NULL);
-    (void)ctx;
+int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, const secp256k1_pubkey * const *pubnonces, size_t n) {
+    size_t i;
+    secp256k1_gej Qj;
+    secp256k1_ge Q;
 
-    ret = secp256k1_eckey_privkey_parse(&key, privkey, privkeylen);
-    if (ret) {
-        secp256k1_scalar_get_b32(seckey, &key);
-    }
-    secp256k1_scalar_clear(&key);
-    return ret;
-}
+    ARG_CHECK(pubnonce != NULL);
+    memset(pubnonce, 0, sizeof(*pubnonce));
+    ARG_CHECK(n >= 1);
+    ARG_CHECK(pubnonces != NULL);
 
-int secp256k1_context_randomize(secp256k1_context_t* ctx, const unsigned char *seed32) {
-    DEBUG_CHECK(ctx != NULL);
-    DEBUG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
-    secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
+    secp256k1_gej_set_infinity(&Qj);
+
+    for (i = 0; i < n; i++) {
+        secp256k1_pubkey_load(ctx, &Q, pubnonces[i]);
+        secp256k1_gej_add_ge(&Qj, &Qj, &Q);
+    }
+    if (secp256k1_gej_is_infinity(&Qj)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(&Q, &Qj);
+    secp256k1_pubkey_save(pubnonce, &Q);
     return 1;
 }
+
+#ifdef ENABLE_MODULE_ECDH
+# include "modules/ecdh/main_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORR
+# include "modules/schnorr/main_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+# include "modules/recovery/main_impl.h"
+#endif
diff --git a/src/secp256k1/src/testrand.h b/src/secp256k1/src/testrand.h
index 041bb92c47..f8efa93c7c 100644
--- a/src/secp256k1/src/testrand.h
+++ b/src/secp256k1/src/testrand.h
@@ -16,13 +16,23 @@
 /** Seed the pseudorandom number generator for testing. */
 SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16);
 
-/** Generate a pseudorandom 32-bit number. */
+/** Generate a pseudorandom number in the range [0..2**32-1]. */
 static uint32_t secp256k1_rand32(void);
 
+/** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or
+ *  more. */
+static uint32_t secp256k1_rand_bits(int bits);
+
+/** Generate a pseudorandom number in the range [0..range-1]. */
+static uint32_t secp256k1_rand_int(uint32_t range);
+
 /** Generate a pseudorandom 32-byte array. */
 static void secp256k1_rand256(unsigned char *b32);
 
 /** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */
 static void secp256k1_rand256_test(unsigned char *b32);
 
+/** Generate pseudorandom bytes with long sequences of zero and one bits. */
+static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len);
+
 #endif
diff --git a/src/secp256k1/src/testrand_impl.h b/src/secp256k1/src/testrand_impl.h
index 21c69f1c51..15c7b9f12d 100644
--- a/src/secp256k1/src/testrand_impl.h
+++ b/src/secp256k1/src/testrand_impl.h
@@ -1,5 +1,5 @@
 /**********************************************************************
- * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Copyright (c) 2013-2015 Pieter Wuille                              *
  * Distributed under the MIT software license, see the accompanying   *
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
@@ -16,9 +16,11 @@
 static secp256k1_rfc6979_hmac_sha256_t secp256k1_test_rng;
 static uint32_t secp256k1_test_rng_precomputed[8];
 static int secp256k1_test_rng_precomputed_used = 8;
+static uint64_t secp256k1_test_rng_integer;
+static int secp256k1_test_rng_integer_bits_left = 0;
 
 SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) {
-    secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, (const unsigned char*)"TestRNG", 7, seed16, 16, NULL, 0);
+    secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16);
 }
 
 SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {
@@ -29,32 +31,80 @@ SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {
     return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++];
 }
 
+static uint32_t secp256k1_rand_bits(int bits) {
+    uint32_t ret;
+    if (secp256k1_test_rng_integer_bits_left < bits) {
+        secp256k1_test_rng_integer |= (((uint64_t)secp256k1_rand32()) << secp256k1_test_rng_integer_bits_left);
+        secp256k1_test_rng_integer_bits_left += 32;
+    }
+    ret = secp256k1_test_rng_integer;
+    secp256k1_test_rng_integer >>= bits;
+    secp256k1_test_rng_integer_bits_left -= bits;
+    ret &= ((~((uint32_t)0)) >> (32 - bits));
+    return ret;
+}
+
+static uint32_t secp256k1_rand_int(uint32_t range) {
+    /* We want a uniform integer between 0 and range-1, inclusive.
+     * B is the smallest number such that range <= 2**B.
+     * two mechanisms implemented here:
+     * - generate B bits numbers until one below range is found, and return it
+     * - find the largest multiple M of range that is <= 2**(B+A), generate B+A
+     *   bits numbers until one below M is found, and return it modulo range
+     * The second mechanism consumes A more bits of entropy in every iteration,
+     * but may need fewer iterations due to M being closer to 2**(B+A) then
+     * range is to 2**B. The array below (indexed by B) contains a 0 when the
+     * first mechanism is to be used, and the number A otherwise.
+     */
+    static const int addbits[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0};
+    uint32_t trange, mult;
+    int bits = 0;
+    if (range <= 1) {
+        return 0;
+    }
+    trange = range - 1;
+    while (trange > 0) {
+        trange >>= 1;
+        bits++;
+    }
+    if (addbits[bits]) {
+        bits = bits + addbits[bits];
+        mult = ((~((uint32_t)0)) >> (32 - bits)) / range;
+        trange = range * mult;
+    } else {
+        trange = range;
+        mult = 1;
+    }
+    while(1) {
+        uint32_t x = secp256k1_rand_bits(bits);
+        if (x < trange) {
+            return (mult == 1) ? x : (x % range);
+        }
+    }
+}
+
 static void secp256k1_rand256(unsigned char *b32) {
     secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32);
 }
 
-static void secp256k1_rand256_test(unsigned char *b32) {
-    int bits=0;
-    uint64_t ent = 0;
-    int entleft = 0;
-    memset(b32, 0, 32);
-    while (bits < 256) {
+static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len) {
+    size_t bits = 0;
+    memset(bytes, 0, len);
+    while (bits < len * 8) {
         int now;
         uint32_t val;
-        if (entleft < 12) {
-            ent |= ((uint64_t)secp256k1_rand32()) << entleft;
-            entleft += 32;
-        }
-        now = 1 + ((ent % 64)*((ent >> 6) % 32)+16)/31;
-        val = 1 & (ent >> 11);
-        ent >>= 12;
-        entleft -= 12;
-        while (now > 0 && bits < 256) {
-            b32[bits / 8] |= val << (bits % 8);
+        now = 1 + (secp256k1_rand_bits(6) * secp256k1_rand_bits(5) + 16) / 31;
+        val = secp256k1_rand_bits(1);
+        while (now > 0 && bits < len * 8) {
+            bytes[bits / 8] |= val << (bits % 8);
             now--;
             bits++;
         }
     }
 }
 
+static void secp256k1_rand256_test(unsigned char *b32) {
+    secp256k1_rand_bytes_test(b32, 32);
+}
+
 #endif
diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
index d0e05057f2..687a5f2fdd 100644
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/src/tests.c
@@ -14,6 +14,7 @@
 #include <time.h>
 
 #include "secp256k1.c"
+#include "include/secp256k1.h"
 #include "testrand_impl.h"
 
 #ifdef ENABLE_OPENSSL_TESTS
@@ -23,10 +24,40 @@
 #include "openssl/obj_mac.h"
 #endif
 
+#include "contrib/lax_der_parsing.c"
+#include "contrib/lax_der_privatekey_parsing.c"
+
+#if !defined(VG_CHECK)
+# if defined(VALGRIND)
+#  include <valgrind/memcheck.h>
+#  define VG_UNDEF(x,y) VALGRIND_MAKE_MEM_UNDEFINED((x),(y))
+#  define VG_CHECK(x,y) VALGRIND_CHECK_MEM_IS_DEFINED((x),(y))
+# else
+#  define VG_UNDEF(x,y)
+#  define VG_CHECK(x,y)
+# endif
+#endif
+
 static int count = 64;
-static secp256k1_context_t *ctx = NULL;
+static secp256k1_context *ctx = NULL;
+
+static void counting_illegal_callback_fn(const char* str, void* data) {
+    /* Dummy callback function that just counts. */
+    int32_t *p;
+    (void)str;
+    p = data;
+    (*p)++;
+}
 
-void random_field_element_test(secp256k1_fe_t *fe) {
+static void uncounting_illegal_callback_fn(const char* str, void* data) {
+    /* Dummy callback function that just counts (backwards). */
+    int32_t *p;
+    (void)str;
+    p = data;
+    (*p)--;
+}
+
+void random_field_element_test(secp256k1_fe *fe) {
     do {
         unsigned char b32[32];
         secp256k1_rand256_test(b32);
@@ -36,9 +67,9 @@ void random_field_element_test(secp256k1_fe_t *fe) {
     } while(1);
 }
 
-void random_field_element_magnitude(secp256k1_fe_t *fe) {
-    secp256k1_fe_t zero;
-    int n = secp256k1_rand32() % 9;
+void random_field_element_magnitude(secp256k1_fe *fe) {
+    secp256k1_fe zero;
+    int n = secp256k1_rand_int(9);
     secp256k1_fe_normalize(fe);
     if (n == 0) {
         return;
@@ -47,23 +78,22 @@ void random_field_element_magnitude(secp256k1_fe_t *fe) {
     secp256k1_fe_negate(&zero, &zero, 0);
     secp256k1_fe_mul_int(&zero, n - 1);
     secp256k1_fe_add(fe, &zero);
-#ifdef VERIFY
-    CHECK(fe->magnitude == n);
-#endif
+    VERIFY_CHECK(fe->magnitude == n);
 }
 
-void random_group_element_test(secp256k1_ge_t *ge) {
-    secp256k1_fe_t fe;
+void random_group_element_test(secp256k1_ge *ge) {
+    secp256k1_fe fe;
     do {
         random_field_element_test(&fe);
-        if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand32() & 1)) {
+        if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) {
+            secp256k1_fe_normalize(&ge->y);
             break;
         }
     } while(1);
 }
 
-void random_group_element_jacobian_test(secp256k1_gej_t *gej, const secp256k1_ge_t *ge) {
-    secp256k1_fe_t z2, z3;
+void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) {
+    secp256k1_fe z2, z3;
     do {
         random_field_element_test(&gej->z);
         if (!secp256k1_fe_is_zero(&gej->z)) {
@@ -77,7 +107,7 @@ void random_group_element_jacobian_test(secp256k1_gej_t *gej, const secp256k1_ge
     gej->infinity = ge->infinity;
 }
 
-void random_scalar_order_test(secp256k1_scalar_t *num) {
+void random_scalar_order_test(secp256k1_scalar *num) {
     do {
         unsigned char b32[32];
         int overflow = 0;
@@ -90,7 +120,7 @@ void random_scalar_order_test(secp256k1_scalar_t *num) {
     } while(1);
 }
 
-void random_scalar_order(secp256k1_scalar_t *num) {
+void random_scalar_order(secp256k1_scalar *num) {
     do {
         unsigned char b32[32];
         int overflow = 0;
@@ -104,19 +134,31 @@ void random_scalar_order(secp256k1_scalar_t *num) {
 }
 
 void run_context_tests(void) {
-    secp256k1_context_t *none = secp256k1_context_create(0);
-    secp256k1_context_t *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
-    secp256k1_context_t *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
-    secp256k1_context_t *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
-
-    secp256k1_gej_t pubj;
-    secp256k1_ge_t pub;
-    secp256k1_scalar_t msg, key, nonce;
-    secp256k1_ecdsa_sig_t sig;
+    secp256k1_pubkey pubkey;
+    secp256k1_ecdsa_signature sig;
+    unsigned char ctmp[32];
+    int32_t ecount;
+    int32_t ecount2;
+    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+    secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    secp256k1_gej pubj;
+    secp256k1_ge pub;
+    secp256k1_scalar msg, key, nonce;
+    secp256k1_scalar sigr, sigs;
+
+    ecount = 0;
+    ecount2 = 10;
+    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2);
+    secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, NULL);
+    CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
 
     /*** clone and destroy all of them to make sure cloning was complete ***/
     {
-        secp256k1_context_t *ctx_tmp;
+        secp256k1_context *ctx_tmp;
 
         ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_destroy(ctx_tmp);
         ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_destroy(ctx_tmp);
@@ -124,30 +166,74 @@ void run_context_tests(void) {
         ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_destroy(ctx_tmp);
     }
 
+    /* Verify that the error callback makes it across the clone. */
+    CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
+    /* And that it resets back to default. */
+    secp256k1_context_set_error_callback(sign, NULL, NULL);
+    CHECK(vrfy->error_callback.fn == sign->error_callback.fn);
+
     /*** attempt to use them ***/
     random_scalar_order_test(&msg);
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key);
     secp256k1_ge_set_gej(&pub, &pubj);
 
+    /* Verify context-type checking illegal-argument errors. */
+    memset(ctmp, 1, 32);
+    CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0);
+    CHECK(ecount == 1);
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0);
+    CHECK(ecount == 2);
+    VG_UNDEF(&sig, sizeof(sig));
+    CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1);
+    VG_CHECK(&sig, sizeof(sig));
+    CHECK(ecount2 == 10);
+    CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0);
+    CHECK(ecount2 == 11);
+    CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0);
+    CHECK(ecount2 == 12);
+    CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0);
+    CHECK(ecount2 == 13);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_context_randomize(vrfy, ctmp) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_context_randomize(sign, NULL) == 1);
+    CHECK(ecount2 == 13);
+    secp256k1_context_set_illegal_callback(vrfy, NULL, NULL);
+    secp256k1_context_set_illegal_callback(sign, NULL, NULL);
+
+    /* This shouldn't leak memory, due to already-set tests. */
+    secp256k1_ecmult_gen_context_build(&sign->ecmult_gen_ctx, NULL);
+    secp256k1_ecmult_context_build(&vrfy->ecmult_ctx, NULL);
+
     /* obtain a working nonce */
     do {
         random_scalar_order_test(&nonce);
-    } while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sig, &key, &msg, &nonce, NULL));
+    } while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
 
     /* try signing */
-    CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sig, &key, &msg, &nonce, NULL));
-    CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sig, &key, &msg, &nonce, NULL));
+    CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
+    CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
 
     /* try verifying */
-    CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sig, &pub, &msg));
-    CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sig, &pub, &msg));
+    CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg));
+    CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg));
 
     /* cleanup */
     secp256k1_context_destroy(none);
     secp256k1_context_destroy(sign);
     secp256k1_context_destroy(vrfy);
     secp256k1_context_destroy(both);
+    /* Defined as no-op. */
+    secp256k1_context_destroy(NULL);
 }
 
 /***** HASH TESTS *****/
@@ -178,7 +264,7 @@ void run_sha256_tests(void) {
         secp256k1_sha256_finalize(&hasher, out);
         CHECK(memcmp(out, outputs[i], 32) == 0);
         if (strlen(inputs[i]) > 0) {
-            int split = secp256k1_rand32() % strlen(inputs[i]);
+            int split = secp256k1_rand_int(strlen(inputs[i]));
             secp256k1_sha256_initialize(&hasher);
             secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
             secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
@@ -222,7 +308,7 @@ void run_hmac_sha256_tests(void) {
         secp256k1_hmac_sha256_finalize(&hasher, out);
         CHECK(memcmp(out, outputs[i], 32) == 0);
         if (strlen(inputs[i]) > 0) {
-            int split = secp256k1_rand32() % strlen(inputs[i]);
+            int split = secp256k1_rand_int(strlen(inputs[i]));
             secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
             secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
             secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
@@ -233,16 +319,14 @@ void run_hmac_sha256_tests(void) {
 }
 
 void run_rfc6979_hmac_sha256_tests(void) {
-    static const unsigned char key1[32] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00};
-    static const unsigned char msg1[32] = {0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a};
+    static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0};
     static const unsigned char out1[3][32] = {
         {0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb},
         {0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a},
         {0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e}
     };
 
-    static const unsigned char key2[32] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff};
-    static const unsigned char msg2[32] = {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55};
+    static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55};
     static const unsigned char out2[3][32] = {
         {0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95},
         {0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9},
@@ -251,24 +335,23 @@ void run_rfc6979_hmac_sha256_tests(void) {
 
     secp256k1_rfc6979_hmac_sha256_t rng;
     unsigned char out[32];
-    unsigned char zero[1] = {0};
     int i;
 
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 32, msg1, 32, NULL, 1);
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
         CHECK(memcmp(out, out1[i], 32) == 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 32, msg1, 32, zero, 1);
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
         CHECK(memcmp(out, out1[i], 32) != 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
-    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 32, msg2, 32, zero, 0);
+    secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
         CHECK(memcmp(out, out2[i], 32) == 0);
@@ -276,30 +359,102 @@ void run_rfc6979_hmac_sha256_tests(void) {
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 }
 
+/***** RANDOM TESTS *****/
+
+void test_rand_bits(int rand32, int bits) {
+    /* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to
+     * get a false negative chance below once in a billion */
+    static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316};
+    /* We try multiplying the results with various odd numbers, which shouldn't
+     * influence the uniform distribution modulo a power of 2. */
+    static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011};
+    /* We only select up to 6 bits from the output to analyse */
+    unsigned int usebits = bits > 6 ? 6 : bits;
+    unsigned int maxshift = bits - usebits;
+    /* For each of the maxshift+1 usebits-bit sequences inside a bits-bit
+       number, track all observed outcomes, one per bit in a uint64_t. */
+    uint64_t x[6][27] = {{0}};
+    unsigned int i, shift, m;
+    /* Multiply the output of all rand calls with the odd number m, which
+       should not change the uniformity of its distribution. */
+    for (i = 0; i < rounds[usebits]; i++) {
+        uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits));
+        CHECK((((uint64_t)r) >> bits) == 0);
+        for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
+            uint32_t rm = r * mults[m];
+            for (shift = 0; shift <= maxshift; shift++) {
+                x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1)));
+            }
+        }
+    }
+    for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
+        for (shift = 0; shift <= maxshift; shift++) {
+            /* Test that the lower usebits bits of x[shift] are 1 */
+            CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0);
+        }
+    }
+}
+
+/* Subrange must be a whole divisor of range, and at most 64 */
+void test_rand_int(uint32_t range, uint32_t subrange) {
+    /* (1-1/subrange)^rounds < 1/10^9 */
+    int rounds = (subrange * 2073) / 100;
+    int i;
+    uint64_t x = 0;
+    CHECK((range % subrange) == 0);
+    for (i = 0; i < rounds; i++) {
+        uint32_t r = secp256k1_rand_int(range);
+        CHECK(r < range);
+        r = r % subrange;
+        x |= (((uint64_t)1) << r);
+    }
+    /* Test that the lower subrange bits of x are 1. */
+    CHECK(((~x) << (64 - subrange)) == 0);
+}
+
+void run_rand_bits(void) {
+    size_t b;
+    test_rand_bits(1, 32);
+    for (b = 1; b <= 32; b++) {
+        test_rand_bits(0, b);
+    }
+}
+
+void run_rand_int(void) {
+    static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432};
+    static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64};
+    unsigned int m, s;
+    for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) {
+        for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) {
+            test_rand_int(ms[m] * ss[s], ss[s]);
+        }
+    }
+}
+
 /***** NUM TESTS *****/
 
 #ifndef USE_NUM_NONE
-void random_num_negate(secp256k1_num_t *num) {
-    if (secp256k1_rand32() & 1) {
+void random_num_negate(secp256k1_num *num) {
+    if (secp256k1_rand_bits(1)) {
         secp256k1_num_negate(num);
     }
 }
 
-void random_num_order_test(secp256k1_num_t *num) {
-    secp256k1_scalar_t sc;
+void random_num_order_test(secp256k1_num *num) {
+    secp256k1_scalar sc;
     random_scalar_order_test(&sc);
     secp256k1_scalar_get_num(num, &sc);
 }
 
-void random_num_order(secp256k1_num_t *num) {
-    secp256k1_scalar_t sc;
+void random_num_order(secp256k1_num *num) {
+    secp256k1_scalar sc;
     random_scalar_order(&sc);
     secp256k1_scalar_get_num(num, &sc);
 }
 
 void test_num_negate(void) {
-    secp256k1_num_t n1;
-    secp256k1_num_t n2;
+    secp256k1_num n1;
+    secp256k1_num n2;
     random_num_order_test(&n1); /* n1 = R */
     random_num_negate(&n1);
     secp256k1_num_copy(&n2, &n1); /* n2 = R */
@@ -318,16 +473,15 @@ void test_num_negate(void) {
 }
 
 void test_num_add_sub(void) {
-    secp256k1_num_t n1;
-    secp256k1_num_t n2;
-    secp256k1_num_t n1p2, n2p1, n1m2, n2m1;
-    int r = secp256k1_rand32();
+    secp256k1_num n1;
+    secp256k1_num n2;
+    secp256k1_num n1p2, n2p1, n1m2, n2m1;
     random_num_order_test(&n1); /* n1 = R1 */
-    if (r & 1) {
+    if (secp256k1_rand_bits(1)) {
         random_num_negate(&n1);
     }
     random_num_order_test(&n2); /* n2 = R2 */
-    if (r & 2) {
+    if (secp256k1_rand_bits(1)) {
         random_num_negate(&n2);
     }
     secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */
@@ -358,12 +512,12 @@ void run_num_smalltests(void) {
 /***** SCALAR TESTS *****/
 
 void scalar_test(void) {
-    secp256k1_scalar_t s;
-    secp256k1_scalar_t s1;
-    secp256k1_scalar_t s2;
+    secp256k1_scalar s;
+    secp256k1_scalar s1;
+    secp256k1_scalar s2;
 #ifndef USE_NUM_NONE
-    secp256k1_num_t snum, s1num, s2num;
-    secp256k1_num_t order, half_order;
+    secp256k1_num snum, s1num, s2num;
+    secp256k1_num order, half_order;
 #endif
     unsigned char c[32];
 
@@ -390,10 +544,10 @@ void scalar_test(void) {
     {
         int i;
         /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
-        secp256k1_scalar_t n;
+        secp256k1_scalar n;
         secp256k1_scalar_set_int(&n, 0);
         for (i = 0; i < 256; i += 4) {
-            secp256k1_scalar_t t;
+            secp256k1_scalar t;
             int j;
             secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
             for (j = 0; j < 4; j++) {
@@ -406,13 +560,13 @@ void scalar_test(void) {
 
     {
         /* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
-        secp256k1_scalar_t n;
+        secp256k1_scalar n;
         int i = 0;
         secp256k1_scalar_set_int(&n, 0);
         while (i < 256) {
-            secp256k1_scalar_t t;
+            secp256k1_scalar t;
             int j;
-            int now = (secp256k1_rand32() % 15) + 1;
+            int now = secp256k1_rand_int(15) + 1;
             if (now + i > 256) {
                 now = 256 - i;
             }
@@ -429,9 +583,9 @@ void scalar_test(void) {
 #ifndef USE_NUM_NONE
     {
         /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
-        secp256k1_num_t rnum;
-        secp256k1_num_t r2num;
-        secp256k1_scalar_t r;
+        secp256k1_num rnum;
+        secp256k1_num r2num;
+        secp256k1_scalar r;
         secp256k1_num_add(&rnum, &snum, &s2num);
         secp256k1_num_mod(&rnum, &order);
         secp256k1_scalar_add(&r, &s, &s2);
@@ -440,10 +594,10 @@ void scalar_test(void) {
     }
 
     {
-        /* Test that multipying the scalars is equal to multiplying their numbers modulo the order. */
-        secp256k1_scalar_t r;
-        secp256k1_num_t r2num;
-        secp256k1_num_t rnum;
+        /* Test that multiplying the scalars is equal to multiplying their numbers modulo the order. */
+        secp256k1_scalar r;
+        secp256k1_num r2num;
+        secp256k1_num rnum;
         secp256k1_num_mul(&rnum, &snum, &s2num);
         secp256k1_num_mod(&rnum, &order);
         secp256k1_scalar_mul(&r, &s, &s2);
@@ -457,9 +611,9 @@ void scalar_test(void) {
     }
 
     {
-        secp256k1_scalar_t neg;
-        secp256k1_num_t negnum;
-        secp256k1_num_t negnum2;
+        secp256k1_scalar neg;
+        secp256k1_num negnum;
+        secp256k1_num negnum2;
         /* Check that comparison with zero matches comparison with zero on the number. */
         CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
         /* Check that comparison with the half order is equal to testing for high scalar. */
@@ -484,12 +638,12 @@ void scalar_test(void) {
 
     {
         /* Test secp256k1_scalar_mul_shift_var. */
-        secp256k1_scalar_t r;
-        secp256k1_num_t one;
-        secp256k1_num_t rnum;
-        secp256k1_num_t rnum2;
+        secp256k1_scalar r;
+        secp256k1_num one;
+        secp256k1_num rnum;
+        secp256k1_num rnum2;
         unsigned char cone[1] = {0x01};
-        unsigned int shift = 256 + (secp256k1_rand32() % 257);
+        unsigned int shift = 256 + secp256k1_rand_int(257);
         secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
         secp256k1_num_mul(&rnum, &s1num, &s2num);
         secp256k1_num_shift(&rnum, shift - 1);
@@ -499,15 +653,29 @@ void scalar_test(void) {
         secp256k1_scalar_get_num(&rnum2, &r);
         CHECK(secp256k1_num_eq(&rnum, &rnum2));
     }
+
+    {
+        /* test secp256k1_scalar_shr_int */
+        secp256k1_scalar r;
+        int i;
+        random_scalar_order_test(&r);
+        for (i = 0; i < 100; ++i) {
+            int low;
+            int shift = 1 + secp256k1_rand_int(15);
+            int expected = r.d[0] % (1 << shift);
+            low = secp256k1_scalar_shr_int(&r, shift);
+            CHECK(expected == low);
+        }
+    }
 #endif
 
     {
         /* Test that scalar inverses are equal to the inverse of their number modulo the order. */
         if (!secp256k1_scalar_is_zero(&s)) {
-            secp256k1_scalar_t inv;
+            secp256k1_scalar inv;
 #ifndef USE_NUM_NONE
-            secp256k1_num_t invnum;
-            secp256k1_num_t invnum2;
+            secp256k1_num invnum;
+            secp256k1_num invnum2;
 #endif
             secp256k1_scalar_inverse(&inv, &s);
 #ifndef USE_NUM_NONE
@@ -526,18 +694,18 @@ void scalar_test(void) {
 
     {
         /* Test commutativity of add. */
-        secp256k1_scalar_t r1, r2;
+        secp256k1_scalar r1, r2;
         secp256k1_scalar_add(&r1, &s1, &s2);
         secp256k1_scalar_add(&r2, &s2, &s1);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
     }
 
     {
-        secp256k1_scalar_t r1, r2;
-        secp256k1_scalar_t b;
+        secp256k1_scalar r1, r2;
+        secp256k1_scalar b;
         int i;
         /* Test add_bit. */
-        int bit = secp256k1_rand32() % 256;
+        int bit = secp256k1_rand_bits(8);
         secp256k1_scalar_set_int(&b, 1);
         CHECK(secp256k1_scalar_is_one(&b));
         for (i = 0; i < bit; i++) {
@@ -547,14 +715,17 @@ void scalar_test(void) {
         r2 = s1;
         if (!secp256k1_scalar_add(&r1, &r1, &b)) {
             /* No overflow happened. */
-            secp256k1_scalar_add_bit(&r2, bit);
+            secp256k1_scalar_cadd_bit(&r2, bit, 1);
+            CHECK(secp256k1_scalar_eq(&r1, &r2));
+            /* cadd is a noop when flag is zero */
+            secp256k1_scalar_cadd_bit(&r2, bit, 0);
             CHECK(secp256k1_scalar_eq(&r1, &r2));
         }
     }
 
     {
         /* Test commutativity of mul. */
-        secp256k1_scalar_t r1, r2;
+        secp256k1_scalar r1, r2;
         secp256k1_scalar_mul(&r1, &s1, &s2);
         secp256k1_scalar_mul(&r2, &s2, &s1);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
@@ -562,7 +733,7 @@ void scalar_test(void) {
 
     {
         /* Test associativity of add. */
-        secp256k1_scalar_t r1, r2;
+        secp256k1_scalar r1, r2;
         secp256k1_scalar_add(&r1, &s1, &s2);
         secp256k1_scalar_add(&r1, &r1, &s);
         secp256k1_scalar_add(&r2, &s2, &s);
@@ -572,7 +743,7 @@ void scalar_test(void) {
 
     {
         /* Test associativity of mul. */
-        secp256k1_scalar_t r1, r2;
+        secp256k1_scalar r1, r2;
         secp256k1_scalar_mul(&r1, &s1, &s2);
         secp256k1_scalar_mul(&r1, &r1, &s);
         secp256k1_scalar_mul(&r2, &s2, &s);
@@ -582,7 +753,7 @@ void scalar_test(void) {
 
     {
         /* Test distributitivity of mul over add. */
-        secp256k1_scalar_t r1, r2, t;
+        secp256k1_scalar r1, r2, t;
         secp256k1_scalar_add(&r1, &s1, &s2);
         secp256k1_scalar_mul(&r1, &r1, &s);
         secp256k1_scalar_mul(&r2, &s1, &s);
@@ -593,7 +764,7 @@ void scalar_test(void) {
 
     {
         /* Test square. */
-        secp256k1_scalar_t r1, r2;
+        secp256k1_scalar r1, r2;
         secp256k1_scalar_sqr(&r1, &s1);
         secp256k1_scalar_mul(&r2, &s1, &s1);
         CHECK(secp256k1_scalar_eq(&r1, &r2));
@@ -601,7 +772,7 @@ void scalar_test(void) {
 
     {
         /* Test multiplicative identity. */
-        secp256k1_scalar_t r1, v1;
+        secp256k1_scalar r1, v1;
         secp256k1_scalar_set_int(&v1,1);
         secp256k1_scalar_mul(&r1, &s1, &v1);
         CHECK(secp256k1_scalar_eq(&r1, &s1));
@@ -609,7 +780,7 @@ void scalar_test(void) {
 
     {
         /* Test additive identity. */
-        secp256k1_scalar_t r1, v0;
+        secp256k1_scalar r1, v0;
         secp256k1_scalar_set_int(&v0,0);
         secp256k1_scalar_add(&r1, &s1, &v0);
         CHECK(secp256k1_scalar_eq(&r1, &s1));
@@ -617,7 +788,7 @@ void scalar_test(void) {
 
     {
         /* Test zero product property. */
-        secp256k1_scalar_t r1, v0;
+        secp256k1_scalar r1, v0;
         secp256k1_scalar_set_int(&v0,0);
         secp256k1_scalar_mul(&r1, &s1, &v0);
         CHECK(secp256k1_scalar_eq(&r1, &v0));
@@ -633,7 +804,7 @@ void run_scalar_tests(void) {
 
     {
         /* (-1)+1 should be zero. */
-        secp256k1_scalar_t s, o;
+        secp256k1_scalar s, o;
         secp256k1_scalar_set_int(&s, 1);
         CHECK(secp256k1_scalar_is_one(&s));
         secp256k1_scalar_negate(&o, &s);
@@ -646,8 +817,8 @@ void run_scalar_tests(void) {
 #ifndef USE_NUM_NONE
     {
         /* A scalar with value of the curve order should be 0. */
-        secp256k1_num_t order;
-        secp256k1_scalar_t zero;
+        secp256k1_num order;
+        secp256k1_scalar zero;
         unsigned char bin[32];
         int overflow = 0;
         secp256k1_scalar_order_get_num(&order);
@@ -657,11 +828,589 @@ void run_scalar_tests(void) {
         CHECK(secp256k1_scalar_is_zero(&zero));
     }
 #endif
+
+    {
+        /* Does check_overflow check catch all ones? */
+        static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST(
+            0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
+            0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
+        );
+        CHECK(secp256k1_scalar_check_overflow(&overflowed));
+    }
+
+    {
+        /* Static test vectors.
+         * These were reduced from ~10^12 random vectors based on comparison-decision
+         *  and edge-case coverage on 32-bit and 64-bit implementations.
+         * The responses were generated with Sage 5.9.
+         */
+        secp256k1_scalar x;
+        secp256k1_scalar y;
+        secp256k1_scalar z;
+        secp256k1_scalar zz;
+        secp256k1_scalar one;
+        secp256k1_scalar r1;
+        secp256k1_scalar r2;
+#if defined(USE_SCALAR_INV_NUM)
+        secp256k1_scalar zzv;
+#endif
+        int overflow;
+        unsigned char chal[32][2][32] = {
+            {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff,
+              0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}},
+            {{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+             {0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0,
+              0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}},
+            {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00},
+             {0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f,
+              0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0,
+              0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff,
+              0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00,
+              0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f,
+              0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f,
+              0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00,
+              0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+             {0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+              0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff,
+              0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+              0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00,
+              0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0},
+             {0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff,
+              0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f},
+             {0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
+              0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff,
+              0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff,
+              0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff},
+             {0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}},
+            {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff,
+              0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00,
+              0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f,
+              0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}},
+            {{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00},
+             {0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}},
+            {{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00,
+              0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}},
+            {{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
+              0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00,
+              0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
+             {0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+             {0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80,
+              0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
+              0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}},
+            {{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff,
+              0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00,
+              0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+              0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+              0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0,
+              0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00,
+              0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}},
+            {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+              0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+              0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00,
+              0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00,
+              0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
+             {0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
+            {{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
+              0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}},
+            {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00},
+             {0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
+              0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f,
+              0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}},
+            {{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01,
+              0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
+             {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
+              0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80,
+              0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8,
+              0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
+             {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00,
+              0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f,
+              0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}},
+            {{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00,
+              0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83,
+              0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
+              0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0},
+             {0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00,
+              0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}}
+        };
+        unsigned char res[32][2][32] = {
+            {{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9,
+              0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1,
+              0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6,
+              0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35},
+             {0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d,
+              0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c,
+              0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49,
+              0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}},
+            {{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22,
+              0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c,
+              0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f,
+              0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8},
+             {0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77,
+              0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4,
+              0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59,
+              0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}},
+            {{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef,
+              0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab,
+              0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55,
+              0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c},
+             {0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96,
+              0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f,
+              0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12,
+              0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}},
+            {{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c,
+              0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf,
+              0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9,
+              0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48},
+             {0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42,
+              0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5,
+              0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c,
+              0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}},
+            {{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb,
+              0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74,
+              0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6,
+              0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63},
+             {0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3,
+              0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99,
+              0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58,
+              0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}},
+            {{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b,
+              0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7,
+              0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f,
+              0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0},
+             {0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d,
+              0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d,
+              0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9,
+              0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}},
+            {{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7,
+              0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70,
+              0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06,
+              0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e},
+             {0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9,
+              0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79,
+              0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e,
+              0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}},
+            {{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb,
+              0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5,
+              0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a,
+              0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe},
+             {0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48,
+              0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e,
+              0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc,
+              0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}},
+            {{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b,
+              0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0,
+              0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53,
+              0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8},
+             {0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c,
+              0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01,
+              0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f,
+              0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}},
+            {{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7,
+              0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c,
+              0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92,
+              0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30},
+             {0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62,
+              0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e,
+              0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb,
+              0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}},
+            {{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25,
+              0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d,
+              0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0,
+              0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13},
+             {0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60,
+              0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00,
+              0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4,
+              0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}},
+            {{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31,
+              0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4,
+              0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88,
+              0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa},
+             {0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57,
+              0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38,
+              0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51,
+              0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}},
+            {{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c,
+              0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f,
+              0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2,
+              0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4},
+             {0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01,
+              0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4,
+              0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86,
+              0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}},
+            {{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5,
+              0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51,
+              0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3,
+              0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62},
+             {0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c,
+              0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91,
+              0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c,
+              0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}},
+            {{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e,
+              0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56,
+              0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58,
+              0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4},
+             {0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41,
+              0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7,
+              0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92,
+              0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}},
+            {{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec,
+              0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19,
+              0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3,
+              0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4},
+             {0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87,
+              0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a,
+              0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92,
+              0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}},
+            {{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64,
+              0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3,
+              0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f,
+              0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33},
+             {0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c,
+              0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d,
+              0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea,
+              0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}},
+            {{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7,
+              0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a,
+              0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae,
+              0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe},
+             {0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc,
+              0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39,
+              0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14,
+              0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}},
+            {{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23,
+              0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d,
+              0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2,
+              0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16},
+             {0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c,
+              0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84,
+              0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0,
+              0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}},
+            {{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb,
+              0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94,
+              0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b,
+              0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e},
+             {0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54,
+              0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00,
+              0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb,
+              0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+            {{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+              0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+              0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+              0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92},
+             {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+              0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+              0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+              0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
+            {{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0,
+              0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b,
+              0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94,
+              0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8},
+             {0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26,
+              0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d,
+              0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a,
+              0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}},
+            {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+              0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+              0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd},
+             {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
+              0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
+              0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
+              0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
+            {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+              0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+              0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
+             {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
+            {{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39,
+              0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea,
+              0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf,
+              0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae},
+             {0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b,
+              0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb,
+              0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6,
+              0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}},
+            {{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a,
+              0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f,
+              0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9,
+              0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56},
+             {0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93,
+              0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07,
+              0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71,
+              0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}},
+            {{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87,
+              0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9,
+              0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55,
+              0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73},
+             {0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d,
+              0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86,
+              0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb,
+              0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}},
+            {{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2,
+              0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7,
+              0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41,
+              0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7},
+             {0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06,
+              0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04,
+              0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08,
+              0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}},
+            {{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2,
+              0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b,
+              0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40,
+              0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68},
+             {0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e,
+              0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a,
+              0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b,
+              0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}},
+            {{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67,
+              0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f,
+              0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a,
+              0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51},
+             {0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2,
+              0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38,
+              0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34,
+              0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}}
+        };
+        secp256k1_scalar_set_int(&one, 1);
+        for (i = 0; i < 32; i++) {
+            secp256k1_scalar_set_b32(&x, chal[i][0], &overflow);
+            CHECK(!overflow);
+            secp256k1_scalar_set_b32(&y, chal[i][1], &overflow);
+            CHECK(!overflow);
+            secp256k1_scalar_set_b32(&r1, res[i][0], &overflow);
+            CHECK(!overflow);
+            secp256k1_scalar_set_b32(&r2, res[i][1], &overflow);
+            CHECK(!overflow);
+            secp256k1_scalar_mul(&z, &x, &y);
+            CHECK(!secp256k1_scalar_check_overflow(&z));
+            CHECK(secp256k1_scalar_eq(&r1, &z));
+            if (!secp256k1_scalar_is_zero(&y)) {
+                secp256k1_scalar_inverse(&zz, &y);
+                CHECK(!secp256k1_scalar_check_overflow(&zz));
+#if defined(USE_SCALAR_INV_NUM)
+                secp256k1_scalar_inverse_var(&zzv, &y);
+                CHECK(secp256k1_scalar_eq(&zzv, &zz));
+#endif
+                secp256k1_scalar_mul(&z, &z, &zz);
+                CHECK(!secp256k1_scalar_check_overflow(&z));
+                CHECK(secp256k1_scalar_eq(&x, &z));
+                secp256k1_scalar_mul(&zz, &zz, &y);
+                CHECK(!secp256k1_scalar_check_overflow(&zz));
+                CHECK(secp256k1_scalar_eq(&one, &zz));
+            }
+            secp256k1_scalar_mul(&z, &x, &x);
+            CHECK(!secp256k1_scalar_check_overflow(&z));
+            secp256k1_scalar_sqr(&zz, &x);
+            CHECK(!secp256k1_scalar_check_overflow(&zz));
+            CHECK(secp256k1_scalar_eq(&zz, &z));
+            CHECK(secp256k1_scalar_eq(&r2, &zz));
+        }
+    }
 }
 
 /***** FIELD TESTS *****/
 
-void random_fe(secp256k1_fe_t *x) {
+void random_fe(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
         secp256k1_rand256(bin);
@@ -671,7 +1420,17 @@ void random_fe(secp256k1_fe_t *x) {
     } while(1);
 }
 
-void random_fe_non_zero(secp256k1_fe_t *nz) {
+void random_fe_test(secp256k1_fe *x) {
+    unsigned char bin[32];
+    do {
+        secp256k1_rand256_test(bin);
+        if (secp256k1_fe_set_b32(x, bin)) {
+            return;
+        }
+    } while(1);
+}
+
+void random_fe_non_zero(secp256k1_fe *nz) {
     int tries = 10;
     while (--tries >= 0) {
         random_fe(nz);
@@ -684,25 +1443,25 @@ void random_fe_non_zero(secp256k1_fe_t *nz) {
     CHECK(tries >= 0);
 }
 
-void random_fe_non_square(secp256k1_fe_t *ns) {
-    secp256k1_fe_t r;
+void random_fe_non_square(secp256k1_fe *ns) {
+    secp256k1_fe r;
     random_fe_non_zero(ns);
     if (secp256k1_fe_sqrt_var(&r, ns)) {
         secp256k1_fe_negate(ns, ns, 1);
     }
 }
 
-int check_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b) {
-    secp256k1_fe_t an = *a;
-    secp256k1_fe_t bn = *b;
+int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe an = *a;
+    secp256k1_fe bn = *b;
     secp256k1_fe_normalize_weak(&an);
     secp256k1_fe_normalize_var(&bn);
     return secp256k1_fe_equal_var(&an, &bn);
 }
 
-int check_fe_inverse(const secp256k1_fe_t *a, const secp256k1_fe_t *ai) {
-    secp256k1_fe_t x;
-    secp256k1_fe_t one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+int check_fe_inverse(const secp256k1_fe *a, const secp256k1_fe *ai) {
+    secp256k1_fe x;
+    secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
     secp256k1_fe_mul(&x, a, ai);
     return check_fe_equal(&x, &one);
 }
@@ -714,17 +1473,17 @@ void run_field_convert(void) {
         0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29,
         0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40
     };
-    static const secp256k1_fe_storage_t fes = SECP256K1_FE_STORAGE_CONST(
+    static const secp256k1_fe_storage fes = SECP256K1_FE_STORAGE_CONST(
         0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
         0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
     );
-    static const secp256k1_fe_t fe = SECP256K1_FE_CONST(
+    static const secp256k1_fe fe = SECP256K1_FE_CONST(
         0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
         0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
     );
-    secp256k1_fe_t fe2;
+    secp256k1_fe fe2;
     unsigned char b322[32];
-    secp256k1_fe_storage_t fes2;
+    secp256k1_fe_storage fes2;
     /* Check conversions to fe. */
     CHECK(secp256k1_fe_set_b32(&fe2, b32));
     CHECK(secp256k1_fe_equal_var(&fe, &fe2));
@@ -737,15 +1496,24 @@ void run_field_convert(void) {
     CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0);
 }
 
+int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe t = *b;
+#ifdef VERIFY
+    t.magnitude = a->magnitude;
+    t.normalized = a->normalized;
+#endif
+    return memcmp(a, &t, sizeof(secp256k1_fe));
+}
+
 void run_field_misc(void) {
-    secp256k1_fe_t x;
-    secp256k1_fe_t y;
-    secp256k1_fe_t z;
-    secp256k1_fe_t q;
-    secp256k1_fe_t fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
-    int i;
+    secp256k1_fe x;
+    secp256k1_fe y;
+    secp256k1_fe z;
+    secp256k1_fe q;
+    secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
+    int i, j;
     for (i = 0; i < 5*count; i++) {
-        secp256k1_fe_storage_t xs, ys, zs;
+        secp256k1_fe_storage xs, ys, zs;
         random_fe(&x);
         random_fe_non_zero(&y);
         /* Test the fe equality and comparison operations. */
@@ -756,14 +1524,27 @@ void run_field_misc(void) {
         /* Test fe conditional move; z is not normalized here. */
         q = x;
         secp256k1_fe_cmov(&x, &z, 0);
+        VERIFY_CHECK(!x.normalized && x.magnitude == z.magnitude);
         secp256k1_fe_cmov(&x, &x, 1);
-        CHECK(memcmp(&x, &z, sizeof(x)) != 0);
-        CHECK(memcmp(&x, &q, sizeof(x)) == 0);
+        CHECK(fe_memcmp(&x, &z) != 0);
+        CHECK(fe_memcmp(&x, &q) == 0);
         secp256k1_fe_cmov(&q, &z, 1);
-        CHECK(memcmp(&q, &z, sizeof(q)) == 0);
-        /* Test storage conversion and conditional moves. */
-        secp256k1_fe_normalize(&z);
+        VERIFY_CHECK(!q.normalized && q.magnitude == z.magnitude);
+        CHECK(fe_memcmp(&q, &z) == 0);
+        secp256k1_fe_normalize_var(&x);
+        secp256k1_fe_normalize_var(&z);
         CHECK(!secp256k1_fe_equal_var(&x, &z));
+        secp256k1_fe_normalize_var(&q);
+        secp256k1_fe_cmov(&q, &z, (i&1));
+        VERIFY_CHECK(q.normalized && q.magnitude == 1);
+        for (j = 0; j < 6; j++) {
+            secp256k1_fe_negate(&z, &z, j+1);
+            secp256k1_fe_normalize_var(&q);
+            secp256k1_fe_cmov(&q, &z, (j&1));
+            VERIFY_CHECK(!q.normalized && q.magnitude == (j+2));
+        }
+        secp256k1_fe_normalize_var(&z);
+        /* Test storage conversion and conditional moves. */
         secp256k1_fe_to_storage(&xs, &x);
         secp256k1_fe_to_storage(&ys, &y);
         secp256k1_fe_to_storage(&zs, &z);
@@ -797,7 +1578,7 @@ void run_field_misc(void) {
 }
 
 void run_field_inv(void) {
-    secp256k1_fe_t x, xi, xii;
+    secp256k1_fe x, xi, xii;
     int i;
     for (i = 0; i < 10*count; i++) {
         random_fe_non_zero(&x);
@@ -809,7 +1590,7 @@ void run_field_inv(void) {
 }
 
 void run_field_inv_var(void) {
-    secp256k1_fe_t x, xi, xii;
+    secp256k1_fe x, xi, xii;
     int i;
     for (i = 0; i < 10*count; i++) {
         random_fe_non_zero(&x);
@@ -821,13 +1602,13 @@ void run_field_inv_var(void) {
 }
 
 void run_field_inv_all_var(void) {
-    secp256k1_fe_t x[16], xi[16], xii[16];
+    secp256k1_fe x[16], xi[16], xii[16];
     int i;
     /* Check it's safe to call for 0 elements */
     secp256k1_fe_inv_all_var(0, xi, x);
     for (i = 0; i < count; i++) {
         size_t j;
-        size_t len = (secp256k1_rand32() & 15) + 1;
+        size_t len = secp256k1_rand_int(15) + 1;
         for (j = 0; j < len; j++) {
             random_fe_non_zero(&x[j]);
         }
@@ -843,7 +1624,7 @@ void run_field_inv_all_var(void) {
 }
 
 void run_sqr(void) {
-    secp256k1_fe_t x, s;
+    secp256k1_fe x, s;
 
     {
         int i;
@@ -858,8 +1639,8 @@ void run_sqr(void) {
     }
 }
 
-void test_sqrt(const secp256k1_fe_t *a, const secp256k1_fe_t *k) {
-    secp256k1_fe_t r1, r2;
+void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) {
+    secp256k1_fe r1, r2;
     int v = secp256k1_fe_sqrt_var(&r1, a);
     CHECK((v == 0) == (k == NULL));
 
@@ -873,7 +1654,7 @@ void test_sqrt(const secp256k1_fe_t *a, const secp256k1_fe_t *k) {
 }
 
 void run_sqrt(void) {
-    secp256k1_fe_t ns, x, s, t;
+    secp256k1_fe ns, x, s, t;
     int i;
 
     /* Check sqrt(0) is 0 */
@@ -908,19 +1689,19 @@ void run_sqrt(void) {
 
 /***** GROUP TESTS *****/
 
-void ge_equals_ge(const secp256k1_ge_t *a, const secp256k1_ge_t *b) {
+void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
     CHECK(a->infinity == b->infinity);
     if (a->infinity) {
         return;
     }
     CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
-    CHECK(secp256k1_fe_equal_var(&b->y, &b->y));
+    CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
 }
 
 /* This compares jacobian points including their Z, not just their geometric meaning. */
-int gej_xyz_equals_gej(const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
-    secp256k1_gej_t a2;
-    secp256k1_gej_t b2;
+int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) {
+    secp256k1_gej a2;
+    secp256k1_gej b2;
     int ret = 1;
     ret &= a->infinity == b->infinity;
     if (ret && !a->infinity) {
@@ -939,9 +1720,9 @@ int gej_xyz_equals_gej(const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
     return ret;
 }
 
-void ge_equals_gej(const secp256k1_ge_t *a, const secp256k1_gej_t *b) {
-    secp256k1_fe_t z2s;
-    secp256k1_fe_t u1, u2, s1, s2;
+void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
+    secp256k1_fe z2s;
+    secp256k1_fe u1, u2, s1, s2;
     CHECK(a->infinity == b->infinity);
     if (a->infinity) {
         return;
@@ -958,21 +1739,39 @@ void ge_equals_gej(const secp256k1_ge_t *a, const secp256k1_gej_t *b) {
 
 void test_ge(void) {
     int i, i1;
+#ifdef USE_ENDOMORPHISM
+    int runs = 6;
+#else
     int runs = 4;
+#endif
     /* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4).
      * The second in each pair of identical points uses a random Z coordinate in the Jacobian form.
      * All magnitudes are randomized.
-     * All 17*17 combinations of points are added to eachother, using all applicable methods.
+     * All 17*17 combinations of points are added to each other, using all applicable methods.
+     *
+     * When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
      */
-    secp256k1_ge_t *ge = (secp256k1_ge_t *)malloc(sizeof(secp256k1_ge_t) * (1 + 4 * runs));
-    secp256k1_gej_t *gej = (secp256k1_gej_t *)malloc(sizeof(secp256k1_gej_t) * (1 + 4 * runs));
+    secp256k1_ge *ge = (secp256k1_ge *)malloc(sizeof(secp256k1_ge) * (1 + 4 * runs));
+    secp256k1_gej *gej = (secp256k1_gej *)malloc(sizeof(secp256k1_gej) * (1 + 4 * runs));
+    secp256k1_fe *zinv = (secp256k1_fe *)malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
+    secp256k1_fe zf;
+    secp256k1_fe zfi2, zfi3;
+
     secp256k1_gej_set_infinity(&gej[0]);
     secp256k1_ge_clear(&ge[0]);
     secp256k1_ge_set_gej_var(&ge[0], &gej[0]);
     for (i = 0; i < runs; i++) {
         int j;
-        secp256k1_ge_t g;
+        secp256k1_ge g;
         random_group_element_test(&g);
+#ifdef USE_ENDOMORPHISM
+        if (i >= runs - 2) {
+            secp256k1_ge_mul_lambda(&g, &ge[1]);
+        }
+        if (i >= runs - 1) {
+            secp256k1_ge_mul_lambda(&g, &g);
+        }
+#endif
         ge[1 + 4 * i] = g;
         ge[2 + 4 * i] = g;
         secp256k1_ge_neg(&ge[3 + 4 * i], &g);
@@ -990,18 +1789,65 @@ void test_ge(void) {
         }
     }
 
+    /* Compute z inverses. */
+    {
+        secp256k1_fe *zs = malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
+        for (i = 0; i < 4 * runs + 1; i++) {
+            if (i == 0) {
+                /* The point at infinity does not have a meaningful z inverse. Any should do. */
+                do {
+                    random_field_element_test(&zs[i]);
+                } while(secp256k1_fe_is_zero(&zs[i]));
+            } else {
+                zs[i] = gej[i].z;
+            }
+        }
+        secp256k1_fe_inv_all_var(4 * runs + 1, zinv, zs);
+        free(zs);
+    }
+
+    /* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */
+    do {
+        random_field_element_test(&zf);
+    } while(secp256k1_fe_is_zero(&zf));
+    random_field_element_magnitude(&zf);
+    secp256k1_fe_inv_var(&zfi3, &zf);
+    secp256k1_fe_sqr(&zfi2, &zfi3);
+    secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
+
     for (i1 = 0; i1 < 1 + 4 * runs; i1++) {
         int i2;
         for (i2 = 0; i2 < 1 + 4 * runs; i2++) {
             /* Compute reference result using gej + gej (var). */
-            secp256k1_gej_t refj, resj;
-            secp256k1_ge_t ref;
-            secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2]);
+            secp256k1_gej refj, resj;
+            secp256k1_ge ref;
+            secp256k1_fe zr;
+            secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
+            /* Check Z ratio. */
+            if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) {
+                secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
+                CHECK(secp256k1_fe_equal_var(&zrz, &refj.z));
+            }
             secp256k1_ge_set_gej_var(&ref, &refj);
 
-            /* Test gej + ge (var). */
-            secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2]);
+            /* Test gej + ge with Z ratio result (var). */
+            secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
             ge_equals_gej(&ref, &resj);
+            if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) {
+                secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
+                CHECK(secp256k1_fe_equal_var(&zrz, &resj.z));
+            }
+
+            /* Test gej + ge (var, with additional Z factor). */
+            {
+                secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */
+                secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2);
+                secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3);
+                random_field_element_magnitude(&ge2_zfi.x);
+                random_field_element_magnitude(&ge2_zfi.y);
+                secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
+                ge_equals_gej(&ref, &resj);
+            }
 
             /* Test gej + ge (const). */
             if (i2 != 0) {
@@ -1012,10 +1858,15 @@ void test_ge(void) {
 
             /* Test doubling (var). */
             if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) {
-                /* Normal doubling. */
-                secp256k1_gej_double_var(&resj, &gej[i1]);
+                secp256k1_fe zr2;
+                /* Normal doubling with Z ratio result. */
+                secp256k1_gej_double_var(&resj, &gej[i1], &zr2);
                 ge_equals_gej(&ref, &resj);
-                secp256k1_gej_double_var(&resj, &gej[i2]);
+                /* Check Z ratio. */
+                secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z);
+                CHECK(secp256k1_fe_equal_var(&zr2, &resj.z));
+                /* Normal doubling. */
+                secp256k1_gej_double_var(&resj, &gej[i2], NULL);
                 ge_equals_gej(&ref, &resj);
             }
 
@@ -1040,41 +1891,121 @@ void test_ge(void) {
 
     /* Test adding all points together in random order equals infinity. */
     {
-        secp256k1_gej_t sum = SECP256K1_GEJ_CONST_INFINITY;
-        secp256k1_gej_t *gej_shuffled = (secp256k1_gej_t *)malloc((4 * runs + 1) * sizeof(secp256k1_gej_t));
+        secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY;
+        secp256k1_gej *gej_shuffled = (secp256k1_gej *)malloc((4 * runs + 1) * sizeof(secp256k1_gej));
         for (i = 0; i < 4 * runs + 1; i++) {
             gej_shuffled[i] = gej[i];
         }
         for (i = 0; i < 4 * runs + 1; i++) {
-            int swap = i + secp256k1_rand32() % (4 * runs + 1 - i);
+            int swap = i + secp256k1_rand_int(4 * runs + 1 - i);
             if (swap != i) {
-                secp256k1_gej_t t = gej_shuffled[i];
+                secp256k1_gej t = gej_shuffled[i];
                 gej_shuffled[i] = gej_shuffled[swap];
                 gej_shuffled[swap] = t;
             }
         }
         for (i = 0; i < 4 * runs + 1; i++) {
-            secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i]);
+            secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL);
         }
         CHECK(secp256k1_gej_is_infinity(&sum));
         free(gej_shuffled);
     }
 
-    /* Test batch gej -> ge conversion. */
+    /* Test batch gej -> ge conversion with and without known z ratios. */
     {
-        secp256k1_ge_t *ge_set_all = (secp256k1_ge_t *)malloc((4 * runs + 1) * sizeof(secp256k1_ge_t));
-        secp256k1_ge_set_all_gej_var(4 * runs + 1, ge_set_all, gej);
+        secp256k1_fe *zr = (secp256k1_fe *)malloc((4 * runs + 1) * sizeof(secp256k1_fe));
+        secp256k1_ge *ge_set_table = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
+        secp256k1_ge *ge_set_all = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
         for (i = 0; i < 4 * runs + 1; i++) {
-            secp256k1_fe_t s;
+            /* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */
+            if (i < 4 * runs) {
+                secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z);
+            }
+        }
+        secp256k1_ge_set_table_gej_var(4 * runs + 1, ge_set_table, gej, zr);
+        secp256k1_ge_set_all_gej_var(4 * runs + 1, ge_set_all, gej, &ctx->error_callback);
+        for (i = 0; i < 4 * runs + 1; i++) {
+            secp256k1_fe s;
             random_fe_non_zero(&s);
             secp256k1_gej_rescale(&gej[i], &s);
+            ge_equals_gej(&ge_set_table[i], &gej[i]);
             ge_equals_gej(&ge_set_all[i], &gej[i]);
         }
+        free(ge_set_table);
         free(ge_set_all);
+        free(zr);
     }
 
     free(ge);
     free(gej);
+    free(zinv);
+}
+
+void test_add_neg_y_diff_x(void) {
+    /* The point of this test is to check that we can add two points
+     * whose y-coordinates are negatives of each other but whose x
+     * coordinates differ. If the x-coordinates were the same, these
+     * points would be negatives of each other and their sum is
+     * infinity. This is cool because it "covers up" any degeneracy
+     * in the addition algorithm that would cause the xy coordinates
+     * of the sum to be wrong (since infinity has no xy coordinates).
+     * HOWEVER, if the x-coordinates are different, infinity is the
+     * wrong answer, and such degeneracies are exposed. This is the
+     * root of https://github.com/bitcoin/secp256k1/issues/257 which
+     * this test is a regression test for.
+     *
+     * These points were generated in sage as
+     * # secp256k1 params
+     * F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
+     * C = EllipticCurve ([F (0), F (7)])
+     * G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
+     * N = FiniteField(G.order())
+     *
+     * # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F)
+     * x = polygen(N)
+     * lam  = (1 - x^3).roots()[1][0]
+     *
+     * # random "bad pair"
+     * P = C.random_element()
+     * Q = -int(lam) * P
+     * print "    P: %x %x" % P.xy()
+     * print "    Q: %x %x" % Q.xy()
+     * print "P + Q: %x %x" % (P + Q).xy()
+     */
+    secp256k1_gej aj = SECP256K1_GEJ_CONST(
+        0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30,
+        0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb,
+        0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8,
+        0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d
+    );
+    secp256k1_gej bj = SECP256K1_GEJ_CONST(
+        0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86,
+        0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7,
+        0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57,
+        0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2
+    );
+    secp256k1_gej sumj = SECP256K1_GEJ_CONST(
+        0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027,
+        0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a,
+        0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08,
+        0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe
+    );
+    secp256k1_ge b;
+    secp256k1_gej resj;
+    secp256k1_ge res;
+    secp256k1_ge_set_gej(&b, &bj);
+
+    secp256k1_gej_add_var(&resj, &aj, &bj, NULL);
+    secp256k1_ge_set_gej(&res, &resj);
+    ge_equals_gej(&res, &sumj);
+
+    secp256k1_gej_add_ge(&resj, &aj, &b);
+    secp256k1_ge_set_gej(&res, &resj);
+    ge_equals_gej(&res, &sumj);
+
+    secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL);
+    secp256k1_ge_set_gej(&res, &resj);
+    ge_equals_gej(&res, &sumj);
 }
 
 void run_ge(void) {
@@ -1082,36 +2013,125 @@ void run_ge(void) {
     for (i = 0; i < count * 32; i++) {
         test_ge();
     }
+    test_add_neg_y_diff_x();
+}
+
+void test_ec_combine(void) {
+    secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    secp256k1_pubkey data[6];
+    const secp256k1_pubkey* d[6];
+    secp256k1_pubkey sd;
+    secp256k1_pubkey sd2;
+    secp256k1_gej Qj;
+    secp256k1_ge Q;
+    int i;
+    for (i = 1; i <= 6; i++) {
+        secp256k1_scalar s;
+        random_scalar_order_test(&s);
+        secp256k1_scalar_add(&sum, &sum, &s);
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s);
+        secp256k1_ge_set_gej(&Q, &Qj);
+        secp256k1_pubkey_save(&data[i - 1], &Q);
+        d[i - 1] = &data[i - 1];
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum);
+        secp256k1_ge_set_gej(&Q, &Qj);
+        secp256k1_pubkey_save(&sd, &Q);
+        CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1);
+        CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0);
+    }
+}
+
+void run_ec_combine(void) {
+    int i;
+    for (i = 0; i < count * 8; i++) {
+         test_ec_combine();
+    }
+}
+
+void test_group_decompress(const secp256k1_fe* x) {
+    /* The input itself, normalized. */
+    secp256k1_fe fex = *x;
+    secp256k1_fe tmp;
+    /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */
+    secp256k1_ge ge_quad, ge_even, ge_odd;
+    /* Return values of the above calls. */
+    int res_quad, res_even, res_odd;
+
+    secp256k1_fe_normalize_var(&fex);
+
+    res_quad = secp256k1_ge_set_xquad_var(&ge_quad, &fex);
+    res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0);
+    res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1);
+
+    CHECK(res_quad == res_even);
+    CHECK(res_quad == res_odd);
+
+    if (res_quad) {
+        secp256k1_fe_normalize_var(&ge_quad.x);
+        secp256k1_fe_normalize_var(&ge_odd.x);
+        secp256k1_fe_normalize_var(&ge_even.x);
+        secp256k1_fe_normalize_var(&ge_quad.y);
+        secp256k1_fe_normalize_var(&ge_odd.y);
+        secp256k1_fe_normalize_var(&ge_even.y);
+
+        /* No infinity allowed. */
+        CHECK(!ge_quad.infinity);
+        CHECK(!ge_even.infinity);
+        CHECK(!ge_odd.infinity);
+
+        /* Check that the x coordinates check out. */
+        CHECK(secp256k1_fe_equal_var(&ge_quad.x, x));
+        CHECK(secp256k1_fe_equal_var(&ge_even.x, x));
+        CHECK(secp256k1_fe_equal_var(&ge_odd.x, x));
+
+        /* Check that the Y coordinate result in ge_quad is a square. */
+        CHECK(secp256k1_fe_sqrt_var(&tmp, &ge_quad.y));
+        secp256k1_fe_sqr(&tmp, &tmp);
+        CHECK(secp256k1_fe_equal_var(&tmp, &ge_quad.y));
+
+        /* Check odd/even Y in ge_odd, ge_even. */
+        CHECK(secp256k1_fe_is_odd(&ge_odd.y));
+        CHECK(!secp256k1_fe_is_odd(&ge_even.y));
+    }
+}
+
+void run_group_decompress(void) {
+    int i;
+    for (i = 0; i < count * 4; i++) {
+        secp256k1_fe fe;
+        random_fe_test(&fe);
+        test_group_decompress(&fe);
+    }
 }
 
 /***** ECMULT TESTS *****/
 
 void run_ecmult_chain(void) {
     /* random starting point A (on the curve) */
-    secp256k1_gej_t a = SECP256K1_GEJ_CONST(
+    secp256k1_gej a = SECP256K1_GEJ_CONST(
         0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3,
         0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004,
         0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f,
         0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f
     );
     /* two random initial factors xn and gn */
-    secp256k1_scalar_t xn = SECP256K1_SCALAR_CONST(
+    secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
         0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c,
         0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407
     );
-    secp256k1_scalar_t gn = SECP256K1_SCALAR_CONST(
+    secp256k1_scalar gn = SECP256K1_SCALAR_CONST(
         0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9,
         0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de
     );
     /* two small multipliers to be applied to xn and gn in every iteration: */
-    static const secp256k1_scalar_t xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337);
-    static const secp256k1_scalar_t gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113);
+    static const secp256k1_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337);
+    static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113);
     /* accumulators with the resulting coefficients to A and G */
-    secp256k1_scalar_t ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
-    secp256k1_scalar_t ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
     /* actual points */
-    secp256k1_gej_t x = a;
-    secp256k1_gej_t x2;
+    secp256k1_gej x;
+    secp256k1_gej x2;
     int i;
 
     /* the point being computed */
@@ -1131,7 +2151,7 @@ void run_ecmult_chain(void) {
         /* verify */
         if (i == 19999) {
             /* expected result after 19999 iterations */
-            secp256k1_gej_t rp = SECP256K1_GEJ_CONST(
+            secp256k1_gej rp = SECP256K1_GEJ_CONST(
                 0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE,
                 0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830,
                 0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D,
@@ -1139,30 +2159,32 @@ void run_ecmult_chain(void) {
             );
 
             secp256k1_gej_neg(&rp, &rp);
-            secp256k1_gej_add_var(&rp, &rp, &x);
+            secp256k1_gej_add_var(&rp, &rp, &x, NULL);
             CHECK(secp256k1_gej_is_infinity(&rp));
         }
     }
     /* redo the computation, but directly with the resulting ae and ge coefficients: */
     secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge);
     secp256k1_gej_neg(&x2, &x2);
-    secp256k1_gej_add_var(&x2, &x2, &x);
+    secp256k1_gej_add_var(&x2, &x2, &x, NULL);
     CHECK(secp256k1_gej_is_infinity(&x2));
 }
 
-void test_point_times_order(const secp256k1_gej_t *point) {
+void test_point_times_order(const secp256k1_gej *point) {
     /* X * (point + G) + (order-X) * (pointer + G) = 0 */
-    secp256k1_scalar_t x;
-    secp256k1_scalar_t nx;
-    secp256k1_gej_t res1, res2;
-    secp256k1_ge_t res3;
+    secp256k1_scalar x;
+    secp256k1_scalar nx;
+    secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_gej res1, res2;
+    secp256k1_ge res3;
     unsigned char pub[65];
-    int psize = 65;
+    size_t psize = 65;
     random_scalar_order_test(&x);
     secp256k1_scalar_negate(&nx, &x);
     secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */
     secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
-    secp256k1_gej_add_var(&res1, &res1, &res2);
+    secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
     CHECK(secp256k1_gej_is_infinity(&res1));
     CHECK(secp256k1_gej_is_valid_var(&res1) == 0);
     secp256k1_ge_set_gej(&res3, &res1);
@@ -1171,19 +2193,29 @@ void test_point_times_order(const secp256k1_gej_t *point) {
     CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0);
     psize = 65;
     CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
+    /* check zero/one edge cases */
+    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero);
+    secp256k1_ge_set_gej(&res3, &res1);
+    CHECK(secp256k1_ge_is_infinity(&res3));
+    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero);
+    secp256k1_ge_set_gej(&res3, &res1);
+    ge_equals_gej(&res3, point);
+    secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one);
+    secp256k1_ge_set_gej(&res3, &res1);
+    ge_equals_ge(&res3, &secp256k1_ge_const_g);
 }
 
 void run_point_times_order(void) {
     int i;
-    secp256k1_fe_t x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
-    static const secp256k1_fe_t xr = SECP256K1_FE_CONST(
+    secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
+    static const secp256k1_fe xr = SECP256K1_FE_CONST(
         0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C,
         0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45
     );
     for (i = 0; i < 500; i++) {
-        secp256k1_ge_t p;
+        secp256k1_ge p;
         if (secp256k1_ge_set_xo_var(&p, &x, 1)) {
-            secp256k1_gej_t j;
+            secp256k1_gej j;
             CHECK(secp256k1_ge_is_valid_var(&p));
             secp256k1_gej_set_ge(&j, &p);
             CHECK(secp256k1_gej_is_valid_var(&j));
@@ -1195,15 +2227,118 @@ void run_point_times_order(void) {
     CHECK(secp256k1_fe_equal_var(&x, &xr));
 }
 
-void test_wnaf(const secp256k1_scalar_t *number, int w) {
-    secp256k1_scalar_t x, two, t;
+void ecmult_const_random_mult(void) {
+    /* random starting point A (on the curve) */
+    secp256k1_ge a = SECP256K1_GE_CONST(
+        0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b,
+        0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a,
+        0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c,
+        0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d
+    );
+    /* random initial factor xn */
+    secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
+        0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327,
+        0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b
+    );
+    /* expected xn * A (from sage) */
+    secp256k1_ge expected_b = SECP256K1_GE_CONST(
+        0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd,
+        0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786,
+        0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f,
+        0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
+    );
+    secp256k1_gej b;
+    secp256k1_ecmult_const(&b, &a, &xn);
+
+    CHECK(secp256k1_ge_is_valid_var(&a));
+    ge_equals_gej(&expected_b, &b);
+}
+
+void ecmult_const_commutativity(void) {
+    secp256k1_scalar a;
+    secp256k1_scalar b;
+    secp256k1_gej res1;
+    secp256k1_gej res2;
+    secp256k1_ge mid1;
+    secp256k1_ge mid2;
+    random_scalar_order_test(&a);
+    random_scalar_order_test(&b);
+
+    secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a);
+    secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b);
+    secp256k1_ge_set_gej(&mid1, &res1);
+    secp256k1_ge_set_gej(&mid2, &res2);
+    secp256k1_ecmult_const(&res1, &mid1, &b);
+    secp256k1_ecmult_const(&res2, &mid2, &a);
+    secp256k1_ge_set_gej(&mid1, &res1);
+    secp256k1_ge_set_gej(&mid2, &res2);
+    ge_equals_ge(&mid1, &mid2);
+}
+
+void ecmult_const_mult_zero_one(void) {
+    secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+    secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+    secp256k1_scalar negone;
+    secp256k1_gej res1;
+    secp256k1_ge res2;
+    secp256k1_ge point;
+    secp256k1_scalar_negate(&negone, &one);
+
+    random_group_element_test(&point);
+    secp256k1_ecmult_const(&res1, &point, &zero);
+    secp256k1_ge_set_gej(&res2, &res1);
+    CHECK(secp256k1_ge_is_infinity(&res2));
+    secp256k1_ecmult_const(&res1, &point, &one);
+    secp256k1_ge_set_gej(&res2, &res1);
+    ge_equals_ge(&res2, &point);
+    secp256k1_ecmult_const(&res1, &point, &negone);
+    secp256k1_gej_neg(&res1, &res1);
+    secp256k1_ge_set_gej(&res2, &res1);
+    ge_equals_ge(&res2, &point);
+}
+
+void ecmult_const_chain_multiply(void) {
+    /* Check known result (randomly generated test problem from sage) */
+    const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST(
+        0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d,
+        0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b
+    );
+    const secp256k1_gej expected_point = SECP256K1_GEJ_CONST(
+        0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd,
+        0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f,
+        0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196,
+        0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435
+    );
+    secp256k1_gej point;
+    secp256k1_ge res;
+    int i;
+
+    secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g);
+    for (i = 0; i < 100; ++i) {
+        secp256k1_ge tmp;
+        secp256k1_ge_set_gej(&tmp, &point);
+        secp256k1_ecmult_const(&point, &tmp, &scalar);
+    }
+    secp256k1_ge_set_gej(&res, &point);
+    ge_equals_gej(&res, &expected_point);
+}
+
+void run_ecmult_const_tests(void) {
+    ecmult_const_mult_zero_one();
+    ecmult_const_random_mult();
+    ecmult_const_commutativity();
+    ecmult_const_chain_multiply();
+}
+
+void test_wnaf(const secp256k1_scalar *number, int w) {
+    secp256k1_scalar x, two, t;
     int wnaf[256];
     int zeroes = -1;
     int i;
     int bits;
     secp256k1_scalar_set_int(&x, 0);
     secp256k1_scalar_set_int(&two, 2);
-    bits = secp256k1_ecmult_wnaf(wnaf, number, w);
+    bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w);
     CHECK(bits <= 256);
     for (i = bits-1; i >= 0; i--) {
         int v = wnaf[i];
@@ -1229,20 +2364,95 @@ void test_wnaf(const secp256k1_scalar_t *number, int w) {
     CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */
 }
 
+void test_constant_wnaf_negate(const secp256k1_scalar *number) {
+    secp256k1_scalar neg1 = *number;
+    secp256k1_scalar neg2 = *number;
+    int sign1 = 1;
+    int sign2 = 1;
+
+    if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) {
+        secp256k1_scalar_negate(&neg1, &neg1);
+        sign1 = -1;
+    }
+    sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2));
+    CHECK(sign1 == sign2);
+    CHECK(secp256k1_scalar_eq(&neg1, &neg2));
+}
+
+void test_constant_wnaf(const secp256k1_scalar *number, int w) {
+    secp256k1_scalar x, shift;
+    int wnaf[256] = {0};
+    int i;
+#ifdef USE_ENDOMORPHISM
+    int skew;
+#endif
+    secp256k1_scalar num = *number;
+
+    secp256k1_scalar_set_int(&x, 0);
+    secp256k1_scalar_set_int(&shift, 1 << w);
+    /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
+#ifdef USE_ENDOMORPHISM
+    for (i = 0; i < 16; ++i) {
+        secp256k1_scalar_shr_int(&num, 8);
+    }
+    skew = secp256k1_wnaf_const(wnaf, num, w);
+#else
+    secp256k1_wnaf_const(wnaf, num, w);
+#endif
+
+    for (i = WNAF_SIZE(w); i >= 0; --i) {
+        secp256k1_scalar t;
+        int v = wnaf[i];
+        CHECK(v != 0); /* check nonzero */
+        CHECK(v & 1);  /* check parity */
+        CHECK(v > -(1 << w)); /* check range above */
+        CHECK(v < (1 << w));  /* check range below */
+
+        secp256k1_scalar_mul(&x, &x, &shift);
+        if (v >= 0) {
+            secp256k1_scalar_set_int(&t, v);
+        } else {
+            secp256k1_scalar_set_int(&t, -v);
+            secp256k1_scalar_negate(&t, &t);
+        }
+        secp256k1_scalar_add(&x, &x, &t);
+    }
+#ifdef USE_ENDOMORPHISM
+    /* Skew num because when encoding 128-bit numbers as odd we use an offset */
+    secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
+#endif
+    CHECK(secp256k1_scalar_eq(&x, &num));
+}
+
 void run_wnaf(void) {
     int i;
-    secp256k1_scalar_t n;
+    secp256k1_scalar n = {{0}};
+
+    /* Sanity check: 1 and 2 are the smallest odd and even numbers and should
+     *               have easier-to-diagnose failure modes  */
+    n.d[0] = 1;
+    test_constant_wnaf(&n, 4);
+    n.d[0] = 2;
+    test_constant_wnaf(&n, 4);
+    /* Random tests */
     for (i = 0; i < count; i++) {
         random_scalar_order(&n);
         test_wnaf(&n, 4+(i%10));
+        test_constant_wnaf_negate(&n);
+        test_constant_wnaf(&n, 4 + (i % 10));
     }
+    secp256k1_scalar_set_int(&n, 0);
+    CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1);
+    CHECK(secp256k1_scalar_is_zero(&n));
+    CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1);
+    CHECK(secp256k1_scalar_is_zero(&n));
 }
 
 void test_ecmult_constants(void) {
     /* Test ecmult_gen() for [0..36) and [order-36..0). */
-    secp256k1_scalar_t x;
-    secp256k1_gej_t r;
-    secp256k1_ge_t ng;
+    secp256k1_scalar x;
+    secp256k1_gej r;
+    secp256k1_ge ng;
     int i;
     int j;
     secp256k1_ge_neg(&ng, &secp256k1_ge_const_g);
@@ -1276,14 +2486,14 @@ void run_ecmult_constants(void) {
 }
 
 void test_ecmult_gen_blind(void) {
-    /* Test ecmult_gen() blinding and confirm that the blinding changes, the affline points match, and the z's don't match. */
-    secp256k1_scalar_t key;
-    secp256k1_scalar_t b;
+    /* Test ecmult_gen() blinding and confirm that the blinding changes, the affine points match, and the z's don't match. */
+    secp256k1_scalar key;
+    secp256k1_scalar b;
     unsigned char seed32[32];
-    secp256k1_gej_t pgej;
-    secp256k1_gej_t pgej2;
-    secp256k1_gej_t i;
-    secp256k1_ge_t pge;
+    secp256k1_gej pgej;
+    secp256k1_gej pgej2;
+    secp256k1_gej i;
+    secp256k1_ge pge;
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key);
     secp256k1_rand256(seed32);
@@ -1300,8 +2510,8 @@ void test_ecmult_gen_blind(void) {
 
 void test_ecmult_gen_blind_reset(void) {
     /* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
-    secp256k1_scalar_t b;
-    secp256k1_gej_t initial;
+    secp256k1_scalar b;
+    secp256k1_gej initial;
     secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
     b = ctx->ecmult_gen_ctx.blind;
     initial = ctx->ecmult_gen_ctx.initial;
@@ -1318,35 +2528,702 @@ void run_ecmult_gen_blind(void) {
     }
 }
 
+#ifdef USE_ENDOMORPHISM
+/***** ENDOMORPHISH TESTS *****/
+void test_scalar_split(void) {
+    secp256k1_scalar full;
+    secp256k1_scalar s1, slam;
+    const unsigned char zero[32] = {0};
+    unsigned char tmp[32];
+
+    random_scalar_order_test(&full);
+    secp256k1_scalar_split_lambda(&s1, &slam, &full);
+
+    /* check that both are <= 128 bits in size */
+    if (secp256k1_scalar_is_high(&s1)) {
+        secp256k1_scalar_negate(&s1, &s1);
+    }
+    if (secp256k1_scalar_is_high(&slam)) {
+        secp256k1_scalar_negate(&slam, &slam);
+    }
+
+    secp256k1_scalar_get_b32(tmp, &s1);
+    CHECK(memcmp(zero, tmp, 16) == 0);
+    secp256k1_scalar_get_b32(tmp, &slam);
+    CHECK(memcmp(zero, tmp, 16) == 0);
+}
+
+void run_endomorphism_tests(void) {
+    test_scalar_split();
+}
+#endif
+
+void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) {
+    unsigned char pubkeyc[65];
+    secp256k1_pubkey pubkey;
+    secp256k1_ge ge;
+    size_t pubkeyclen;
+    int32_t ecount;
+    ecount = 0;
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) {
+        /* Smaller sizes are tested exhaustively elsewhere. */
+        int32_t i;
+        memcpy(&pubkeyc[1], input, 64);
+        VG_UNDEF(&pubkeyc[pubkeyclen], 65 - pubkeyclen);
+        for (i = 0; i < 256; i++) {
+            /* Try all type bytes. */
+            int xpass;
+            int ypass;
+            int ysign;
+            pubkeyc[0] = i;
+            /* What sign does this point have? */
+            ysign = (input[63] & 1) + 2;
+            /* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */
+            xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2);
+            /* Do we expect a parse and re-serialize as uncompressed to give a matching y? */
+            ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) &&
+                ((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65));
+            if (xpass || ypass) {
+                /* These cases must parse. */
+                unsigned char pubkeyo[65];
+                size_t outl;
+                memset(&pubkey, 0, sizeof(pubkey));
+                VG_UNDEF(&pubkey, sizeof(pubkey));
+                ecount = 0;
+                CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
+                VG_CHECK(&pubkey, sizeof(pubkey));
+                outl = 65;
+                VG_UNDEF(pubkeyo, 65);
+                CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+                VG_CHECK(pubkeyo, outl);
+                CHECK(outl == 33);
+                CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0);
+                CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
+                if (ypass) {
+                    /* This test isn't always done because we decode with alternative signs, so the y won't match. */
+                    CHECK(pubkeyo[0] == ysign);
+                    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
+                    memset(&pubkey, 0, sizeof(pubkey));
+                    VG_UNDEF(&pubkey, sizeof(pubkey));
+                    secp256k1_pubkey_save(&pubkey, &ge);
+                    VG_CHECK(&pubkey, sizeof(pubkey));
+                    outl = 65;
+                    VG_UNDEF(pubkeyo, 65);
+                    CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
+                    VG_CHECK(pubkeyo, outl);
+                    CHECK(outl == 65);
+                    CHECK(pubkeyo[0] == 4);
+                    CHECK(memcmp(&pubkeyo[1], input, 64) == 0);
+                }
+                CHECK(ecount == 0);
+            } else {
+                /* These cases must fail to parse. */
+                memset(&pubkey, 0xfe, sizeof(pubkey));
+                ecount = 0;
+                VG_UNDEF(&pubkey, sizeof(pubkey));
+                CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0);
+                VG_CHECK(&pubkey, sizeof(pubkey));
+                CHECK(ecount == 0);
+                CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+                CHECK(ecount == 1);
+            }
+        }
+    }
+    secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+}
+
+void run_ec_pubkey_parse_test(void) {
+#define SECP256K1_EC_PARSE_TEST_NVALID (12)
+    const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = {
+        {
+            /* Point with leading and trailing zeros in x and y serialization. */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83,
+            0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00
+        },
+        {
+            /* Point with x equal to a 3rd root of unity.*/
+            0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9,
+            0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee,
+            0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+            0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+        },
+        {
+            /* Point with largest x. (1/2) */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
+            0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e,
+            0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d,
+        },
+        {
+            /* Point with largest x. (2/2) */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
+            0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1,
+            0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2,
+        },
+        {
+            /* Point with smallest x. (1/2) */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+            0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+        },
+        {
+            /* Point with smallest x. (2/2) */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
+            0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
+        },
+        {
+            /* Point with largest y. (1/3) */
+            0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+            0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+        },
+        {
+            /* Point with largest y. (2/3) */
+            0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+            0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+        },
+        {
+            /* Point with largest y. (3/3) */
+            0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+            0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+        },
+        {
+            /* Point with smallest y. (1/3) */
+            0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+            0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        },
+        {
+            /* Point with smallest y. (2/3) */
+            0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+            0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        },
+        {
+            /* Point with smallest y. (3/3) */
+            0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+            0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01
+        }
+    };
+#define SECP256K1_EC_PARSE_TEST_NXVALID (4)
+    const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = {
+        {
+            /* Valid if y overflow ignored (y = 1 mod p). (1/3) */
+            0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
+            0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+        },
+        {
+            /* Valid if y overflow ignored (y = 1 mod p). (2/3) */
+            0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
+            0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+        },
+        {
+            /* Valid if y overflow ignored (y = 1 mod p). (3/3)*/
+            0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
+            0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+        },
+        {
+            /* x on curve, y is from y^2 = x^3 + 8. */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03
+        }
+    };
+#define SECP256K1_EC_PARSE_TEST_NINVALID (7)
+    const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = {
+        {
+            /* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */
+            0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c,
+            0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+        },
+        {
+            /* Valid if x overflow ignored (x = 1 mod p). */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+            0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
+            0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
+        },
+        {
+            /* Valid if x overflow ignored (x = 1 mod p). */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
+            0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
+            0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
+        },
+        {
+            /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+            0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f,
+            0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28,
+        },
+        {
+            /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
+            0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0,
+            0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07,
+        },
+        {
+            /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d,
+            0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc,
+        },
+        {
+            /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2,
+            0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53
+        }
+    };
+    const unsigned char pubkeyc[66] = {
+        /* Serialization of G. */
+        0x04, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B,
+        0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17,
+        0x98, 0x48, 0x3A, 0xDA, 0x77, 0x26, 0xA3, 0xC4, 0x65, 0x5D, 0xA4, 0xFB, 0xFC, 0x0E, 0x11, 0x08,
+        0xA8, 0xFD, 0x17, 0xB4, 0x48, 0xA6, 0x85, 0x54, 0x19, 0x9C, 0x47, 0xD0, 0x8F, 0xFB, 0x10, 0xD4,
+        0xB8, 0x00
+    };
+    unsigned char sout[65];
+    unsigned char shortkey[2];
+    secp256k1_ge ge;
+    secp256k1_pubkey pubkey;
+    size_t len;
+    int32_t i;
+    int32_t ecount;
+    int32_t ecount2;
+    ecount = 0;
+    /* Nothing should be reading this far into pubkeyc. */
+    VG_UNDEF(&pubkeyc[65], 1);
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    /* Zero length claimed, fail, zeroize, no illegal arg error. */
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(shortkey, 2);
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 1);
+    /* Length one claimed, fail, zeroize, no illegal arg error. */
+    for (i = 0; i < 256 ; i++) {
+        memset(&pubkey, 0xfe, sizeof(pubkey));
+        ecount = 0;
+        shortkey[0] = i;
+        VG_UNDEF(&shortkey[1], 1);
+        VG_UNDEF(&pubkey, sizeof(pubkey));
+        CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0);
+        VG_CHECK(&pubkey, sizeof(pubkey));
+        CHECK(ecount == 0);
+        CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+        CHECK(ecount == 1);
+    }
+    /* Length two claimed, fail, zeroize, no illegal arg error. */
+    for (i = 0; i < 65536 ; i++) {
+        memset(&pubkey, 0xfe, sizeof(pubkey));
+        ecount = 0;
+        shortkey[0] = i & 255;
+        shortkey[1] = i >> 8;
+        VG_UNDEF(&pubkey, sizeof(pubkey));
+        CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0);
+        VG_CHECK(&pubkey, sizeof(pubkey));
+        CHECK(ecount == 0);
+        CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+        CHECK(ecount == 1);
+    }
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    /* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 1);
+    /* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */
+    CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, pubkeyc, 65) == 0);
+    CHECK(ecount == 2);
+    /* NULL input string. Illegal arg and zeroize output. */
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 1);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 2);
+    /* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 1);
+    /* 66 bytes claimed, fail, zeroize output, no illegal arg error. */
+    memset(&pubkey, 0xfe, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
+    CHECK(ecount == 1);
+    /* Valid parse. */
+    memset(&pubkey, 0, sizeof(pubkey));
+    ecount = 0;
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(ecount == 0);
+    VG_UNDEF(&ge, sizeof(ge));
+    CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
+    VG_CHECK(&ge.x, sizeof(ge.x));
+    VG_CHECK(&ge.y, sizeof(ge.y));
+    VG_CHECK(&ge.infinity, sizeof(ge.infinity));
+    ge_equals_ge(&secp256k1_ge_const_g, &ge);
+    CHECK(ecount == 0);
+    /* secp256k1_ec_pubkey_serialize illegal args. */
+    ecount = 0;
+    len = 65;
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
+    CHECK(ecount == 1);
+    CHECK(len == 0);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
+    CHECK(ecount == 2);
+    len = 65;
+    VG_UNDEF(sout, 65);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0);
+    VG_CHECK(sout, 65);
+    CHECK(ecount == 3);
+    CHECK(len == 0);
+    len = 65;
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0);
+    CHECK(ecount == 4);
+    CHECK(len == 0);
+    len = 65;
+    VG_UNDEF(sout, 65);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
+    VG_CHECK(sout, 65);
+    CHECK(ecount == 4);
+    CHECK(len == 65);
+    /* Multiple illegal args. Should still set arg error only once. */
+    ecount = 0;
+    ecount2 = 11;
+    CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
+    CHECK(ecount == 1);
+    /* Does the illegal arg callback actually change the behavior? */
+    secp256k1_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2);
+    CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
+    CHECK(ecount == 1);
+    CHECK(ecount2 == 10);
+    secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+    /* Try a bunch of prefabbed points with all possible encodings. */
+    for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) {
+        ec_pubkey_parse_pointtest(valid[i], 1, 1);
+    }
+    for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) {
+        ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0);
+    }
+    for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) {
+        ec_pubkey_parse_pointtest(invalid[i], 0, 0);
+    }
+}
+
+void run_eckey_edge_case_test(void) {
+    const unsigned char orderc[32] = {
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+        0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+        0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
+    };
+    const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00};
+    unsigned char ctmp[33];
+    unsigned char ctmp2[33];
+    secp256k1_pubkey pubkey;
+    secp256k1_pubkey pubkey2;
+    secp256k1_pubkey pubkey_one;
+    secp256k1_pubkey pubkey_negone;
+    const secp256k1_pubkey *pubkeys[3];
+    size_t len;
+    int32_t ecount;
+    /* Group order is too large, reject. */
+    CHECK(secp256k1_ec_seckey_verify(ctx, orderc) == 0);
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* Maximum value is too large, reject. */
+    memset(ctmp, 255, 32);
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+    memset(&pubkey, 1, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* Zero is too small, reject. */
+    memset(ctmp, 0, 32);
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+    memset(&pubkey, 1, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* One must be accepted. */
+    ctmp[31] = 0x01;
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+    memset(&pubkey, 0, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    pubkey_one = pubkey;
+    /* Group order + 1 is too large, reject. */
+    memcpy(ctmp, orderc, 32);
+    ctmp[31] = 0x42;
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
+    memset(&pubkey, 1, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* -1 must be accepted. */
+    ctmp[31] = 0x40;
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+    memset(&pubkey, 0, sizeof(pubkey));
+    VG_UNDEF(&pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
+    VG_CHECK(&pubkey, sizeof(pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    pubkey_negone = pubkey;
+    /* Tweak of zero leaves the value changed. */
+    memset(ctmp2, 0, 32);
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, ctmp2) == 1);
+    CHECK(memcmp(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
+    memcpy(&pubkey2, &pubkey, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    /* Multiply tweak of zero zeroizes the output. */
+    CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, ctmp2) == 0);
+    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    /* Overflowing key tweak zeroizes. */
+    memcpy(ctmp, orderc, 32);
+    ctmp[31] = 0x40;
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, orderc) == 0);
+    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    memcpy(ctmp, orderc, 32);
+    ctmp[31] = 0x40;
+    CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, orderc) == 0);
+    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    memcpy(ctmp, orderc, 32);
+    ctmp[31] = 0x40;
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    /* Private key tweaks results in a key of zero. */
+    ctmp2[31] = 1;
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 0);
+    CHECK(memcmp(zeros, ctmp2, 32) == 0);
+    ctmp2[31] = 1;
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    /* Tweak computation wraps and results in a key of 1. */
+    ctmp2[31] = 2;
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 1);
+    CHECK(memcmp(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
+    ctmp2[31] = 2;
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+    ctmp2[31] = 1;
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1);
+    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    /* Tweak mul * 2 = 1+1. */
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
+    ctmp2[31] = 2;
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1);
+    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    /* Test argument errors. */
+    ecount = 0;
+    secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+    CHECK(ecount == 0);
+    /* Zeroize pubkey on parse error. */
+    memset(&pubkey, 0, 32);
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    memcpy(&pubkey, &pubkey2, sizeof(pubkey));
+    memset(&pubkey2, 0, 32);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0);
+    CHECK(ecount == 2);
+    CHECK(memcmp(&pubkey2, zeros, sizeof(pubkey2)) == 0);
+    /* Plain argument errors. */
+    ecount = 0;
+    CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_ec_seckey_verify(ctx, NULL) == 0);
+    CHECK(ecount == 1);
+    ecount = 0;
+    memset(ctmp2, 0, 32);
+    ctmp2[31] = 4;
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0);
+    CHECK(ecount == 2);
+    ecount = 0;
+    memset(ctmp2, 0, 32);
+    ctmp2[31] = 4;
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0);
+    CHECK(ecount == 2);
+    ecount = 0;
+    memset(ctmp2, 0, 32);
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, NULL, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, NULL) == 0);
+    CHECK(ecount == 2);
+    ecount = 0;
+    memset(ctmp2, 0, 32);
+    ctmp2[31] = 1;
+    CHECK(secp256k1_ec_privkey_tweak_mul(ctx, NULL, ctmp2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, NULL) == 0);
+    CHECK(ecount == 2);
+    ecount = 0;
+    CHECK(secp256k1_ec_pubkey_create(ctx, NULL, ctmp) == 0);
+    CHECK(ecount == 1);
+    memset(&pubkey, 1, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    /* secp256k1_ec_pubkey_combine tests. */
+    ecount = 0;
+    pubkeys[0] = &pubkey_one;
+    VG_UNDEF(&pubkeys[0], sizeof(secp256k1_pubkey *));
+    VG_UNDEF(&pubkeys[1], sizeof(secp256k1_pubkey *));
+    VG_UNDEF(&pubkeys[2], sizeof(secp256k1_pubkey *));
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0);
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(ecount == 2);
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(ecount == 3);
+    pubkeys[0] = &pubkey_negone;
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(ecount == 3);
+    len = 33;
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1);
+    CHECK(memcmp(ctmp, ctmp2, 33) == 0);
+    /* Result is infinity. */
+    pubkeys[0] = &pubkey_one;
+    pubkeys[1] = &pubkey_negone;
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(ecount == 3);
+    /* Passes through infinity but comes out one. */
+    pubkeys[2] = &pubkey_one;
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(ecount == 3);
+    len = 33;
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1);
+    CHECK(memcmp(ctmp, ctmp2, 33) == 0);
+    /* Adds to two. */
+    pubkeys[1] = &pubkey_one;
+    memset(&pubkey, 255, sizeof(secp256k1_pubkey));
+    VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1);
+    VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
+    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(ecount == 3);
+    secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
+}
 
-void random_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *key, const secp256k1_scalar_t *msg, int *recid) {
-    secp256k1_scalar_t nonce;
+void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
+    secp256k1_scalar nonce;
     do {
         random_scalar_order_test(&nonce);
-    } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sig, key, msg, &nonce, recid));
+    } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid));
 }
 
 void test_ecdsa_sign_verify(void) {
-    secp256k1_gej_t pubj;
-    secp256k1_ge_t pub;
-    secp256k1_scalar_t one;
-    secp256k1_scalar_t msg, key;
-    secp256k1_ecdsa_sig_t sig;
+    secp256k1_gej pubj;
+    secp256k1_ge pub;
+    secp256k1_scalar one;
+    secp256k1_scalar msg, key;
+    secp256k1_scalar sigr, sigs;
     int recid;
     int getrec;
     random_scalar_order_test(&msg);
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
     secp256k1_ge_set_gej(&pub, &pubj);
-    getrec = secp256k1_rand32()&1;
-    random_sign(&sig, &key, &msg, getrec?&recid:NULL);
+    getrec = secp256k1_rand_bits(1);
+    random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL);
     if (getrec) {
         CHECK(recid >= 0 && recid < 4);
     }
-    CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sig, &pub, &msg));
+    CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
     secp256k1_scalar_set_int(&one, 1);
     secp256k1_scalar_add(&msg, &msg, &one);
-    CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sig, &pub, &msg));
+    CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
 }
 
 void run_ecdsa_sign_verify(void) {
@@ -1357,22 +3234,23 @@ void run_ecdsa_sign_verify(void) {
 }
 
 /** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */
-static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) {
+static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
     (void)msg32;
     (void)key32;
+    (void)algo16;
     memcpy(nonce32, data, 32);
     return (counter == 0);
 }
 
-static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) {
+static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
    /* Dummy nonce generator that has a fatal error on the first counter value. */
    if (counter == 0) {
        return 0;
    }
-   return nonce_function_rfc6979(nonce32, msg32, key32, counter - 1, data);
+   return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1);
 }
 
-static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, unsigned int counter, const void *data) {
+static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
    /* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */
    if (counter < 3) {
        memset(nonce32, counter==0 ? 0 : 255, 32);
@@ -1394,17 +3272,17 @@ static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char
        }
        return 1;
    }
-   /* Retry rate of 6979 is negligible esp. as we only call this in determinstic tests. */
+   /* Retry rate of 6979 is negligible esp. as we only call this in deterministic tests. */
    /* If someone does fine a case where it retries for secp256k1, we'd like to know. */
    if (counter > 5) {
        return 0;
    }
-   return nonce_function_rfc6979(nonce32, msg32, key32, counter - 5, data);
+   return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 5);
 }
 
-int is_empty_compact_signature(const unsigned char *sig64) {
-    static const unsigned char res[64] = {0};
-    return memcmp(sig64, res, 64) == 0;
+int is_empty_signature(const secp256k1_ecdsa_signature *sig) {
+    static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0};
+    return memcmp(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
 }
 
 void test_ecdsa_end_to_end(void) {
@@ -1412,26 +3290,19 @@ void test_ecdsa_end_to_end(void) {
     unsigned char privkey[32];
     unsigned char message[32];
     unsigned char privkey2[32];
-    unsigned char csignature[64];
-    unsigned char signature[72];
-    unsigned char signature2[72];
-    unsigned char signature3[72];
-    unsigned char signature4[72];
-    unsigned char pubkey[65];
-    unsigned char recpubkey[65];
+    secp256k1_ecdsa_signature signature[6];
+    secp256k1_scalar r, s;
+    unsigned char sig[74];
+    size_t siglen = 74;
+    unsigned char pubkeyc[65];
+    size_t pubkeyclen = 65;
+    secp256k1_pubkey pubkey;
     unsigned char seckey[300];
-    int signaturelen = 72;
-    int signaturelen2 = 72;
-    int signaturelen3 = 72;
-    int signaturelen4 = 72;
-    int recid = 0;
-    int recpubkeylen = 0;
-    int pubkeylen = 65;
-    int seckeylen = 300;
+    size_t seckeylen = 300;
 
     /* Generate a random key and message. */
     {
-        secp256k1_scalar_t msg, key;
+        secp256k1_scalar msg, key;
         random_scalar_order_test(&msg);
         random_scalar_order_test(&key);
         secp256k1_scalar_get_b32(privkey, &key);
@@ -1440,117 +3311,120 @@ void test_ecdsa_end_to_end(void) {
 
     /* Construct and verify corresponding public key. */
     CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
-    CHECK(secp256k1_ec_pubkey_create(ctx, pubkey, &pubkeylen, privkey, (secp256k1_rand32() & 3) != 0) == 1);
-    if (secp256k1_rand32() & 1) {
-        CHECK(secp256k1_ec_pubkey_decompress(ctx, pubkey, &pubkeylen));
-    }
-    CHECK(secp256k1_ec_pubkey_verify(ctx, pubkey, pubkeylen));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
+
+    /* Verify exporting and importing public key. */
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_rand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
+    memset(&pubkey, 0, sizeof(pubkey));
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
 
     /* Verify private key import and export. */
-    CHECK(secp256k1_ec_privkey_export(ctx, privkey, seckey, &seckeylen, secp256k1_rand32() % 2) == 1);
-    CHECK(secp256k1_ec_privkey_import(ctx, privkey2, seckey, seckeylen) == 1);
+    CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1));
+    CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1);
     CHECK(memcmp(privkey, privkey2, 32) == 0);
 
     /* Optionally tweak the keys using addition. */
-    if (secp256k1_rand32() % 3 == 0) {
+    if (secp256k1_rand_int(3) == 0) {
         int ret1;
         int ret2;
         unsigned char rnd[32];
-        unsigned char pubkey2[65];
-        int pubkeylen2 = 65;
+        secp256k1_pubkey pubkey2;
         secp256k1_rand256_test(rnd);
         ret1 = secp256k1_ec_privkey_tweak_add(ctx, privkey, rnd);
-        ret2 = secp256k1_ec_pubkey_tweak_add(ctx, pubkey, pubkeylen, rnd);
+        ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd);
         CHECK(ret1 == ret2);
         if (ret1 == 0) {
             return;
         }
-        CHECK(secp256k1_ec_pubkey_create(ctx, pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1);
-        CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0);
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
+        CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     }
 
     /* Optionally tweak the keys using multiplication. */
-    if (secp256k1_rand32() % 3 == 0) {
+    if (secp256k1_rand_int(3) == 0) {
         int ret1;
         int ret2;
         unsigned char rnd[32];
-        unsigned char pubkey2[65];
-        int pubkeylen2 = 65;
+        secp256k1_pubkey pubkey2;
         secp256k1_rand256_test(rnd);
         ret1 = secp256k1_ec_privkey_tweak_mul(ctx, privkey, rnd);
-        ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, pubkey, pubkeylen, rnd);
+        ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd);
         CHECK(ret1 == ret2);
         if (ret1 == 0) {
             return;
         }
-        CHECK(secp256k1_ec_pubkey_create(ctx, pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1);
-        CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0);
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
+        CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     }
 
     /* Sign. */
-    CHECK(secp256k1_ecdsa_sign(ctx, message, signature, &signaturelen, privkey, NULL, NULL) == 1);
-    CHECK(signaturelen > 0);
-    CHECK(secp256k1_ecdsa_sign(ctx, message, signature2, &signaturelen2, privkey, NULL, extra) == 1);
-    CHECK(signaturelen2 > 0);
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1);
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1);
     extra[31] = 1;
-    CHECK(secp256k1_ecdsa_sign(ctx, message, signature3, &signaturelen3, privkey, NULL, extra) == 1);
-    CHECK(signaturelen3 > 0);
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1);
     extra[31] = 0;
     extra[0] = 1;
-    CHECK(secp256k1_ecdsa_sign(ctx, message, signature4, &signaturelen4, privkey, NULL, extra) == 1);
-    CHECK(signaturelen3 > 0);
-    CHECK((signaturelen != signaturelen2) || (memcmp(signature, signature2, signaturelen) != 0));
-    CHECK((signaturelen != signaturelen3) || (memcmp(signature, signature3, signaturelen) != 0));
-    CHECK((signaturelen3 != signaturelen2) || (memcmp(signature3, signature2, signaturelen3) != 0));
-    CHECK((signaturelen4 != signaturelen3) || (memcmp(signature4, signature3, signaturelen4) != 0));
-    CHECK((signaturelen4 != signaturelen2) || (memcmp(signature4, signature2, signaturelen4) != 0));
-    CHECK((signaturelen4 != signaturelen) || (memcmp(signature4, signature, signaturelen4) != 0));
+    CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1);
+    CHECK(memcmp(&signature[0], &signature[4], sizeof(signature[0])) == 0);
+    CHECK(memcmp(&signature[0], &signature[1], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[0], &signature[2], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[0], &signature[3], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[1], &signature[2], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[1], &signature[3], sizeof(signature[0])) != 0);
+    CHECK(memcmp(&signature[2], &signature[3], sizeof(signature[0])) != 0);
     /* Verify. */
-    CHECK(secp256k1_ecdsa_verify(ctx, message, signature, signaturelen, pubkey, pubkeylen) == 1);
-    CHECK(secp256k1_ecdsa_verify(ctx, message, signature2, signaturelen2, pubkey, pubkeylen) == 1);
-    CHECK(secp256k1_ecdsa_verify(ctx, message, signature3, signaturelen3, pubkey, pubkeylen) == 1);
-    CHECK(secp256k1_ecdsa_verify(ctx, message, signature4, signaturelen4, pubkey, pubkeylen) == 1);
-    /* Destroy signature and verify again. */
-    signature[signaturelen - 1 - secp256k1_rand32() % 20] += 1 + (secp256k1_rand32() % 255);
-    CHECK(secp256k1_ecdsa_verify(ctx, message, signature, signaturelen, pubkey, pubkeylen) != 1);
-
-    /* Compact sign. */
-    CHECK(secp256k1_ecdsa_sign_compact(ctx, message, csignature, privkey, NULL, NULL, &recid) == 1);
-    CHECK(!is_empty_compact_signature(csignature));
-    /* Recover. */
-    CHECK(secp256k1_ecdsa_recover_compact(ctx, message, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) == 1);
-    CHECK(recpubkeylen == pubkeylen);
-    CHECK(memcmp(pubkey, recpubkey, pubkeylen) == 0);
-    /* Destroy signature and verify again. */
-    csignature[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255);
-    CHECK(secp256k1_ecdsa_recover_compact(ctx, message, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) != 1 ||
-          memcmp(pubkey, recpubkey, pubkeylen) != 0);
-    CHECK(recpubkeylen == pubkeylen);
-
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1);
+    /* Test lower-S form, malleate, verify and fail, test again, malleate again */
+    CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[0]));
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, &signature[0]);
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0);
+    CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+    CHECK(secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
+    CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+    CHECK(!secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
+    CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
+    CHECK(memcmp(&signature[5], &signature[0], 64) == 0);
+
+    /* Serialize/parse DER and verify again */
+    CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
+    memset(&signature[0], 0, sizeof(signature[0]));
+    CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1);
+    CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
+    /* Serialize/destroy/parse DER and verify again. */
+    siglen = 74;
+    CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
+    sig[secp256k1_rand_int(siglen)] += 1 + secp256k1_rand_int(255);
+    CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 ||
+          secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0);
 }
 
 void test_random_pubkeys(void) {
-    secp256k1_ge_t elem;
-    secp256k1_ge_t elem2;
+    secp256k1_ge elem;
+    secp256k1_ge elem2;
     unsigned char in[65];
     /* Generate some randomly sized pubkeys. */
-    uint32_t r = secp256k1_rand32();
-    int len = (r & 3) == 0 ? 65 : 33;
-    r>>=2;
-    if ((r & 3) == 0) {
-        len = (r & 252) >> 3;
+    size_t len = secp256k1_rand_bits(2) == 0 ? 65 : 33;
+    if (secp256k1_rand_bits(2) == 0) {
+        len = secp256k1_rand_bits(6);
     }
-    r>>=8;
     if (len == 65) {
-      in[0] = (r & 2) ? 4 : (r & 1? 6 : 7);
+      in[0] = secp256k1_rand_bits(1) ? 4 : (secp256k1_rand_bits(1) ? 6 : 7);
     } else {
-      in[0] = (r & 1) ? 2 : 3;
+      in[0] = secp256k1_rand_bits(1) ? 2 : 3;
     }
-    r>>=2;
-    if ((r & 7) == 0) {
-        in[0] = (r & 2040) >> 3;
+    if (secp256k1_rand_bits(3) == 0) {
+        in[0] = secp256k1_rand_bits(8);
     }
-    r>>=11;
     if (len > 1) {
         secp256k1_rand256(&in[1]);
     }
@@ -1561,7 +3435,7 @@ void test_random_pubkeys(void) {
         unsigned char out[65];
         unsigned char firstb;
         int res;
-        int size = len;
+        size_t size = len;
         firstb = in[0];
         /* If the pubkey can be parsed, it should round-trip... */
         CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33));
@@ -1577,7 +3451,7 @@ void test_random_pubkeys(void) {
         CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size));
         ge_equals_ge(&elem,&elem2);
         /* Check that the X9.62 hybrid type is checked. */
-        in[0] = (r & 1) ? 6 : 7;
+        in[0] = secp256k1_rand_bits(1) ? 6 : 7;
         res = secp256k1_eckey_pubkey_parse(&elem2, in, size);
         if (firstb == 2 || firstb == 3) {
             if (in[0] == firstb + 4) {
@@ -1608,185 +3482,505 @@ void run_ecdsa_end_to_end(void) {
     }
 }
 
+int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) {
+    static const unsigned char zeroes[32] = {0};
+    static const unsigned char max_scalar[32] = {
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
+        0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
+        0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40
+    };
+
+    int ret = 0;
+
+    secp256k1_ecdsa_signature sig_der;
+    unsigned char roundtrip_der[2048];
+    unsigned char compact_der[64];
+    size_t len_der = 2048;
+    int parsed_der = 0, valid_der = 0, roundtrips_der = 0;
+
+    secp256k1_ecdsa_signature sig_der_lax;
+    unsigned char roundtrip_der_lax[2048];
+    unsigned char compact_der_lax[64];
+    size_t len_der_lax = 2048;
+    int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0;
+
+#ifdef ENABLE_OPENSSL_TESTS
+    ECDSA_SIG *sig_openssl;
+    const unsigned char *sigptr;
+    unsigned char roundtrip_openssl[2048];
+    int len_openssl = 2048;
+    int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0;
+#endif
+
+    parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen);
+    if (parsed_der) {
+        ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0;
+        valid_der = (memcmp(compact_der, zeroes, 32) != 0) && (memcmp(compact_der + 32, zeroes, 32) != 0);
+    }
+    if (valid_der) {
+        ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1;
+        roundtrips_der = (len_der == siglen) && memcmp(roundtrip_der, sig, siglen) == 0;
+    }
+
+    parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen);
+    if (parsed_der_lax) {
+        ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10;
+        valid_der_lax = (memcmp(compact_der_lax, zeroes, 32) != 0) && (memcmp(compact_der_lax + 32, zeroes, 32) != 0);
+    }
+    if (valid_der_lax) {
+        ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11;
+        roundtrips_der_lax = (len_der_lax == siglen) && memcmp(roundtrip_der_lax, sig, siglen) == 0;
+    }
+
+    if (certainly_der) {
+        ret |= (!parsed_der) << 2;
+    }
+    if (certainly_not_der) {
+        ret |= (parsed_der) << 17;
+    }
+    if (valid_der) {
+        ret |= (!roundtrips_der) << 3;
+    }
+
+    if (valid_der) {
+        ret |= (!roundtrips_der_lax) << 12;
+        ret |= (len_der != len_der_lax) << 13;
+        ret |= (memcmp(roundtrip_der_lax, roundtrip_der, len_der) != 0) << 14;
+    }
+    ret |= (roundtrips_der != roundtrips_der_lax) << 15;
+    if (parsed_der) {
+        ret |= (!parsed_der_lax) << 16;
+    }
+
+#ifdef ENABLE_OPENSSL_TESTS
+    sig_openssl = ECDSA_SIG_new();
+    sigptr = sig;
+    parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL);
+    if (parsed_openssl) {
+        valid_openssl = !BN_is_negative(sig_openssl->r) && !BN_is_negative(sig_openssl->s) && BN_num_bits(sig_openssl->r) > 0 && BN_num_bits(sig_openssl->r) <= 256 && BN_num_bits(sig_openssl->s) > 0 && BN_num_bits(sig_openssl->s) <= 256;
+        if (valid_openssl) {
+            unsigned char tmp[32] = {0};
+            BN_bn2bin(sig_openssl->r, tmp + 32 - BN_num_bytes(sig_openssl->r));
+            valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
+        }
+        if (valid_openssl) {
+            unsigned char tmp[32] = {0};
+            BN_bn2bin(sig_openssl->s, tmp + 32 - BN_num_bytes(sig_openssl->s));
+            valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
+        }
+    }
+    len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL);
+    if (len_openssl <= 2048) {
+        unsigned char *ptr = roundtrip_openssl;
+        CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl);
+        roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (memcmp(roundtrip_openssl, sig, siglen) == 0);
+    } else {
+        len_openssl = 0;
+    }
+    ECDSA_SIG_free(sig_openssl);
+
+    ret |= (parsed_der && !parsed_openssl) << 4;
+    ret |= (valid_der && !valid_openssl) << 5;
+    ret |= (roundtrips_openssl && !parsed_der) << 6;
+    ret |= (roundtrips_der != roundtrips_openssl) << 7;
+    if (roundtrips_openssl) {
+        ret |= (len_der != (size_t)len_openssl) << 8;
+        ret |= (memcmp(roundtrip_der, roundtrip_openssl, len_der) != 0) << 9;
+    }
+#endif
+    return ret;
+}
+
+static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) {
+    size_t i;
+    for (i = 0; i < ptrlen; i++) {
+        int shift = ptrlen - 1 - i;
+        if (shift >= 4) {
+            ptr[i] = 0;
+        } else {
+            ptr[i] = (val >> shift) & 0xFF;
+        }
+    }
+}
+
+static void damage_array(unsigned char *sig, size_t *len) {
+    int pos;
+    int action = secp256k1_rand_bits(3);
+    if (action < 1) {
+        /* Delete a byte. */
+        pos = secp256k1_rand_int(*len);
+        memmove(sig + pos, sig + pos + 1, *len - pos - 1);
+        (*len)--;
+        return;
+    } else if (action < 2) {
+        /* Insert a byte. */
+        pos = secp256k1_rand_int(1 + *len);
+        memmove(sig + pos + 1, sig + pos, *len - pos);
+        sig[pos] = secp256k1_rand_bits(8);
+        (*len)++;
+        return;
+    } else if (action < 4) {
+        /* Modify a byte. */
+        sig[secp256k1_rand_int(*len)] += 1 + secp256k1_rand_int(255);
+        return;
+    } else { /* action < 8 */
+        /* Modify a bit. */
+        sig[secp256k1_rand_int(*len)] ^= 1 << secp256k1_rand_bits(3);
+        return;
+    }
+}
+
+static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) {
+    int der;
+    int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2];
+    size_t tlen, elen, glen;
+    int indet;
+    int n;
+
+    *len = 0;
+    der = secp256k1_rand_bits(2) == 0;
+    *certainly_der = der;
+    *certainly_not_der = 0;
+    indet = der ? 0 : secp256k1_rand_int(10) == 0;
+
+    for (n = 0; n < 2; n++) {
+        /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
+        nlow[n] = der ? 1 : (secp256k1_rand_bits(3) != 0);
+        /* The length of the number in bytes (the first byte of which will always be nonzero) */
+        nlen[n] = nlow[n] ? secp256k1_rand_int(33) : 32 + secp256k1_rand_int(200) * secp256k1_rand_int(8) / 8;
+        CHECK(nlen[n] <= 232);
+        /* The top bit of the number. */
+        nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_rand_bits(1));
+        /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
+        nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_rand_bits(7) : 1 + secp256k1_rand_int(127));
+        /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
+        nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_rand_int(3) : secp256k1_rand_int(300 - nlen[n]) * secp256k1_rand_int(8) / 8);
+        if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
+            *certainly_not_der = 1;
+        }
+        CHECK(nlen[n] + nzlen[n] <= 300);
+        /* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */
+        nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
+        if (!der) {
+            /* nlenlen[n] max 127 bytes */
+            int add = secp256k1_rand_int(127 - nlenlen[n]) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
+            nlenlen[n] += add;
+            if (add != 0) {
+                *certainly_not_der = 1;
+            }
+        }
+        CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427);
+    }
+
+    /* The total length of the data to go, so far */
+    tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1];
+    CHECK(tlen <= 856);
+
+    /* The length of the garbage inside the tuple. */
+    elen = (der || indet) ? 0 : secp256k1_rand_int(980 - tlen) * secp256k1_rand_int(8) / 8;
+    if (elen != 0) {
+        *certainly_not_der = 1;
+    }
+    tlen += elen;
+    CHECK(tlen <= 980);
+
+    /* The length of the garbage after the end of the tuple. */
+    glen = der ? 0 : secp256k1_rand_int(990 - tlen) * secp256k1_rand_int(8) / 8;
+    if (glen != 0) {
+        *certainly_not_der = 1;
+    }
+    CHECK(tlen + glen <= 990);
+
+    /* Write the tuple header. */
+    sig[(*len)++] = 0x30;
+    if (indet) {
+        /* Indeterminate length */
+        sig[(*len)++] = 0x80;
+        *certainly_not_der = 1;
+    } else {
+        int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
+        if (!der) {
+            int add = secp256k1_rand_int(127 - tlenlen) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
+            tlenlen += add;
+            if (add != 0) {
+                *certainly_not_der = 1;
+            }
+        }
+        if (tlenlen == 0) {
+            /* Short length notation */
+            sig[(*len)++] = tlen;
+        } else {
+            /* Long length notation */
+            sig[(*len)++] = 128 + tlenlen;
+            assign_big_endian(sig + *len, tlenlen, tlen);
+            *len += tlenlen;
+        }
+        tlen += tlenlen;
+    }
+    tlen += 2;
+    CHECK(tlen + glen <= 1119);
+
+    for (n = 0; n < 2; n++) {
+        /* Write the integer header. */
+        sig[(*len)++] = 0x02;
+        if (nlenlen[n] == 0) {
+            /* Short length notation */
+            sig[(*len)++] = nlen[n] + nzlen[n];
+        } else {
+            /* Long length notation. */
+            sig[(*len)++] = 128 + nlenlen[n];
+            assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]);
+            *len += nlenlen[n];
+        }
+        /* Write zero padding */
+        while (nzlen[n] > 0) {
+            sig[(*len)++] = 0x00;
+            nzlen[n]--;
+        }
+        if (nlen[n] == 32 && !nlow[n]) {
+            /* Special extra 16 0xFF bytes in "high" 32-byte numbers */
+            int i;
+            for (i = 0; i < 16; i++) {
+                sig[(*len)++] = 0xFF;
+            }
+            nlen[n] -= 16;
+        }
+        /* Write first byte of number */
+        if (nlen[n] > 0) {
+            sig[(*len)++] = nhbyte[n];
+            nlen[n]--;
+        }
+        /* Generate remaining random bytes of number */
+        secp256k1_rand_bytes_test(sig + *len, nlen[n]);
+        *len += nlen[n];
+        nlen[n] = 0;
+    }
+
+    /* Generate random garbage inside tuple. */
+    secp256k1_rand_bytes_test(sig + *len, elen);
+    *len += elen;
+
+    /* Generate end-of-contents bytes. */
+    if (indet) {
+        sig[(*len)++] = 0;
+        sig[(*len)++] = 0;
+        tlen += 2;
+    }
+    CHECK(tlen + glen <= 1121);
+
+    /* Generate random garbage outside tuple. */
+    secp256k1_rand_bytes_test(sig + *len, glen);
+    *len += glen;
+    tlen += glen;
+    CHECK(tlen <= 1121);
+    CHECK(tlen == *len);
+}
+
+void run_ecdsa_der_parse(void) {
+    int i,j;
+    for (i = 0; i < 200 * count; i++) {
+        unsigned char buffer[2048];
+        size_t buflen = 0;
+        int certainly_der = 0;
+        int certainly_not_der = 0;
+        random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der);
+        for (j = 0; j < 16; j++) {
+            int ret = 0;
+            if (j > 0) {
+                damage_array(buffer, &buflen);
+                /* We don't know anything anymore about the DERness of the result */
+                certainly_der = 0;
+                certainly_not_der = 0;
+            }
+            ret = test_ecdsa_der_parse(buffer, buflen, certainly_der, certainly_not_der);
+            if (ret != 0) {
+                size_t k;
+                fprintf(stderr, "Failure %x on ", ret);
+                for (k = 0; k < buflen; k++) {
+                    fprintf(stderr, "%02x ", buffer[k]);
+                }
+                fprintf(stderr, "\n");
+            }
+            CHECK(ret == 0);
+        }
+    }
+}
+
 /* Tests several edge cases. */
 void test_ecdsa_edge_cases(void) {
-    const unsigned char msg32[32] = {
-        'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
-        'a', ' ', 'v', 'e', 'r', 'y', ' ', 's',
-        'e', 'c', 'r', 'e', 't', ' ', 'm', 'e',
-        's', 's', 'a', 'g', 'e', '.', '.', '.'
-    };
-    const unsigned char sig64[64] = {
-        /* Generated by signing the above message with nonce 'This is the nonce we will use...'
-         * and secret key 0 (which is not valid), resulting in recid 0. */
-        0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8,
-        0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96,
-        0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63,
-        0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32,
-        0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E,
-        0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD,
-        0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86,
-        0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57
-    };
-    unsigned char pubkey[65];
     int t;
-    int pubkeylen = 65;
-    /* signature (r,s) = (4,4), which can be recovered with all 4 recids. */
-    const unsigned char sigb64[64] = {
-        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
-        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
-    };
-    unsigned char pubkeyb[33];
-    int pubkeyblen = 33;
-    int recid;
+    secp256k1_ecdsa_signature sig;
 
-    CHECK(!secp256k1_ecdsa_recover_compact(ctx, msg32, sig64, pubkey, &pubkeylen, 0, 0));
-    CHECK(secp256k1_ecdsa_recover_compact(ctx, msg32, sig64, pubkey, &pubkeylen, 0, 1));
-    CHECK(!secp256k1_ecdsa_recover_compact(ctx, msg32, sig64, pubkey, &pubkeylen, 0, 2));
-    CHECK(!secp256k1_ecdsa_recover_compact(ctx, msg32, sig64, pubkey, &pubkeylen, 0, 3));
+    /* Test the case where ECDSA recomputes a point that is infinity. */
+    {
+        secp256k1_gej keyj;
+        secp256k1_ge key;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 1);
+        secp256k1_scalar_negate(&ss, &ss);
+        secp256k1_scalar_inverse(&ss, &ss);
+        secp256k1_scalar_set_int(&sr, 1);
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr);
+        secp256k1_ge_set_gej(&key, &keyj);
+        msg = ss;
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+    }
 
-    for (recid = 0; recid < 4; recid++) {
-        int i;
-        int recid2;
-        /* (4,4) encoded in DER. */
-        unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04};
-        unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01};
-        unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00};
-        unsigned char sigbderalt1[39] = {
-            0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
-        };
-        unsigned char sigbderalt2[39] = {
-            0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+    /* Verify signature with r of zero fails. */
+    {
+        const unsigned char pubkey_mods_zero[33] = {
+            0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
+            0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
+            0x41
         };
-        unsigned char sigbderalt3[40] = {
-            0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00,
+        secp256k1_ge key;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 1);
+        secp256k1_scalar_set_int(&msg, 0);
+        secp256k1_scalar_set_int(&sr, 0);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+    }
+
+    /* Verify signature with s of zero fails. */
+    {
+        const unsigned char pubkey[33] = {
+            0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04,
+            0x01
         };
-        unsigned char sigbderalt4[40] = {
-            0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00,
+        secp256k1_ge key;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 0);
+        secp256k1_scalar_set_int(&msg, 0);
+        secp256k1_scalar_set_int(&sr, 1);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+    }
+
+    /* Verify signature with message 0 passes. */
+    {
+        const unsigned char pubkey[33] = {
+            0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04,
+            0x02
         };
-        /* (order + r,4) encoded in DER. */
-        unsigned char sigbderlong[40] = {
-            0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF,
-            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
-            0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC,
-            0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E,
-            0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04
+        const unsigned char pubkey2[33] = {
+            0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+            0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
+            0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
+            0x43
         };
-        CHECK(secp256k1_ecdsa_recover_compact(ctx, msg32, sigb64, pubkeyb, &pubkeyblen, 1, recid));
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) == 1);
-        for (recid2 = 0; recid2 < 4; recid2++) {
-            unsigned char pubkey2b[33];
-            int pubkey2blen = 33;
-            CHECK(secp256k1_ecdsa_recover_compact(ctx, msg32, sigb64, pubkey2b, &pubkey2blen, 1, recid2));
-            /* Verifying with (order + r,4) should always fail. */
-            CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbderlong, sizeof(sigbderlong), pubkey2b, pubkey2blen) != 1);
-        }
-        /* DER parsing tests. */
-        /* Zero length r/s. */
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigcder_zr, sizeof(sigcder_zr), pubkeyb, pubkeyblen) == -2);
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigcder_zs, sizeof(sigcder_zs), pubkeyb, pubkeyblen) == -2);
-        /* Leading zeros. */
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbderalt1, sizeof(sigbderalt1), pubkeyb, pubkeyblen) == 1);
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbderalt2, sizeof(sigbderalt2), pubkeyb, pubkeyblen) == 1);
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbderalt3, sizeof(sigbderalt3), pubkeyb, pubkeyblen) == 1);
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbderalt4, sizeof(sigbderalt4), pubkeyb, pubkeyblen) == 1);
-        sigbderalt3[4] = 1;
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbderalt3, sizeof(sigbderalt3), pubkeyb, pubkeyblen) == -2);
-        sigbderalt4[7] = 1;
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbderalt4, sizeof(sigbderalt4), pubkeyb, pubkeyblen) == -2);
-        /* Damage signature. */
-        sigbder[7]++;
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) == 0);
-        sigbder[7]--;
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbder, 6, pubkeyb, pubkeyblen) == -2);
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbder, sizeof(sigbder)-1, pubkeyb, pubkeyblen) == -2);
-        for(i = 0; i < 8; i++) {
-            int c;
-            unsigned char orig = sigbder[i];
-            /*Try every single-byte change.*/
-            for (c = 0; c < 256; c++) {
-                if (c == orig ) {
-                    continue;
-                }
-                sigbder[i] = c;
-                CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigbder, sizeof(sigbder), pubkeyb, pubkeyblen) ==
-                  (i==4 || i==7) ? 0 : -2 );
-            }
-            sigbder[i] = orig;
-        }
+        secp256k1_ge key;
+        secp256k1_ge key2;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 2);
+        secp256k1_scalar_set_int(&msg, 0);
+        secp256k1_scalar_set_int(&sr, 2);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+        CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        secp256k1_scalar_negate(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        secp256k1_scalar_set_int(&ss, 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
     }
 
-    /* Test the case where ECDSA recomputes a point that is infinity. */
+    /* Verify signature with message 1 passes. */
     {
-        secp256k1_gej_t keyj;
-        secp256k1_ge_t key;
-        secp256k1_scalar_t msg;
-        secp256k1_ecdsa_sig_t sig;
-        secp256k1_scalar_set_int(&sig.s, 1);
-        secp256k1_scalar_negate(&sig.s, &sig.s);
-        secp256k1_scalar_inverse(&sig.s, &sig.s);
-        secp256k1_scalar_set_int(&sig.r, 1);
-        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sig.r);
-        secp256k1_ge_set_gej(&key, &keyj);
-        msg = sig.s;
-        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sig, &key, &msg) == 0);
+        const unsigned char pubkey[33] = {
+            0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22,
+            0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05,
+            0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c,
+            0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76,
+            0x25
+        };
+        const unsigned char pubkey2[33] = {
+            0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40,
+            0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae,
+            0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f,
+            0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10,
+            0x62
+        };
+        const unsigned char csr[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+            0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb
+        };
+        secp256k1_ge key;
+        secp256k1_ge key2;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 1);
+        secp256k1_scalar_set_int(&msg, 1);
+        secp256k1_scalar_set_b32(&sr, csr, NULL);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+        CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        secp256k1_scalar_negate(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
+        secp256k1_scalar_set_int(&ss, 2);
+        secp256k1_scalar_inverse_var(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
     }
 
-    /* Test r/s equal to zero */
+    /* Verify signature with message -1 passes. */
     {
-        /* (1,1) encoded in DER. */
-        unsigned char sigcder[8] = {0x30, 0x06, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01};
-        unsigned char sigc64[64] = {
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
-            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        const unsigned char pubkey[33] = {
+            0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0,
+            0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52,
+            0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27,
+            0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20,
+            0xf1
+        };
+        const unsigned char csr[32] = {
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
+            0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee
         };
-        unsigned char pubkeyc[65];
-        int pubkeyclen = 65;
-        CHECK(secp256k1_ecdsa_recover_compact(ctx, msg32, sigc64, pubkeyc, &pubkeyclen, 0, 0) == 1);
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigcder, sizeof(sigcder), pubkeyc, pubkeyclen) == 1);
-        sigcder[4] = 0;
-        sigc64[31] = 0;
-        CHECK(secp256k1_ecdsa_recover_compact(ctx, msg32, sigc64, pubkeyb, &pubkeyblen, 1, 0) == 0);
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigcder, sizeof(sigcder), pubkeyc, pubkeyclen) == 0);
-        sigcder[4] = 1;
-        sigcder[7] = 0;
-        sigc64[31] = 1;
-        sigc64[63] = 0;
-        CHECK(secp256k1_ecdsa_recover_compact(ctx, msg32, sigc64, pubkeyb, &pubkeyblen, 1, 0) == 0);
-        CHECK(secp256k1_ecdsa_verify(ctx, msg32, sigcder, sizeof(sigcder), pubkeyc, pubkeyclen) == 0);
-    }
-
-    /*Signature where s would be zero.*/
+        secp256k1_ge key;
+        secp256k1_scalar msg;
+        secp256k1_scalar sr, ss;
+        secp256k1_scalar_set_int(&ss, 1);
+        secp256k1_scalar_set_int(&msg, 1);
+        secp256k1_scalar_negate(&msg, &msg);
+        secp256k1_scalar_set_b32(&sr, csr, NULL);
+        CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        secp256k1_scalar_negate(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
+        secp256k1_scalar_set_int(&ss, 3);
+        secp256k1_scalar_inverse_var(&ss, &ss);
+        CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
+    }
+
+    /* Signature where s would be zero. */
     {
-        const unsigned char nonce[32] = {
+        secp256k1_pubkey pubkey;
+        size_t siglen;
+        int32_t ecount;
+        unsigned char signature[72];
+        static const unsigned char nonce[32] = {
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
@@ -1810,21 +4004,72 @@ void test_ecdsa_edge_cases(void) {
             0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62,
             0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9,
         };
-        unsigned char sig[72];
-        int siglen = 72;
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, precomputed_nonce_function, nonce) == 0);
-        CHECK(siglen == 0);
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, precomputed_nonce_function, nonce2) == 0);
-        CHECK(siglen == 0);
+        ecount = 0;
+        secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0);
         msg[31] = 0xaa;
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1);
+        CHECK(ecount == 0);
+        CHECK(secp256k1_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0);
+        CHECK(ecount == 1);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0);
+        CHECK(ecount == 2);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0);
+        CHECK(ecount == 3);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1);
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, key) == 1);
+        CHECK(secp256k1_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0);
+        CHECK(ecount == 4);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0);
+        CHECK(ecount == 5);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, NULL) == 0);
+        CHECK(ecount == 6);
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1);
+        CHECK(ecount == 6);
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
+        CHECK(ecount == 7);
+        /* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */
+        CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0);
+        CHECK(ecount == 8);
         siglen = 72;
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, precomputed_nonce_function, nonce) == 1);
-        CHECK(siglen > 0);
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, precomputed_nonce_function, nonce2) == 1);
-        CHECK(siglen > 0);
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0);
+        CHECK(ecount == 9);
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0);
+        CHECK(ecount == 10);
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0);
+        CHECK(ecount == 11);
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1);
+        CHECK(ecount == 11);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0);
+        CHECK(ecount == 12);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0);
+        CHECK(ecount == 13);
+        CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, signature, siglen) == 1);
+        CHECK(ecount == 13);
         siglen = 10;
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, precomputed_nonce_function, nonce) != 1);
-        CHECK(siglen == 0);
+        /* Too little room for a signature does not fail via ARGCHECK. */
+        CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0);
+        CHECK(ecount == 13);
+        ecount = 0;
+        CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, NULL) == 0);
+        CHECK(ecount == 1);
+        CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0);
+        CHECK(ecount == 2);
+        CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0);
+        CHECK(ecount == 3);
+        CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1);
+        CHECK(ecount == 3);
+        CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0);
+        CHECK(ecount == 4);
+        CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0);
+        CHECK(ecount == 5);
+        CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1);
+        CHECK(ecount == 5);
+        memset(signature, 255, 64);
+        CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0);
+        CHECK(ecount == 5);
+        secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
     }
 
     /* Nonce function corner cases. */
@@ -1833,65 +4078,43 @@ void test_ecdsa_edge_cases(void) {
         int i;
         unsigned char key[32];
         unsigned char msg[32];
-        unsigned char sig[72];
-        unsigned char sig2[72];
-        secp256k1_ecdsa_sig_t s[512];
-        int siglen = 72;
-        int siglen2 = 72;
-        int recid2;
+        secp256k1_ecdsa_signature sig2;
+        secp256k1_scalar sr[512], ss;
         const unsigned char *extra;
         extra = t == 0 ? NULL : zero;
         memset(msg, 0, 32);
         msg[31] = 1;
         /* High key results in signature failure. */
         memset(key, 0xFF, 32);
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, NULL, extra) == 0);
-        CHECK(siglen == 0);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
+        CHECK(is_empty_signature(&sig));
         /* Zero key results in signature failure. */
         memset(key, 0, 32);
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, NULL, extra) == 0);
-        CHECK(siglen == 0);
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
+        CHECK(is_empty_signature(&sig));
         /* Nonce function failure results in signature failure. */
         key[31] = 1;
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, nonce_function_test_fail, extra) == 0);
-        CHECK(siglen == 0);
-        CHECK(secp256k1_ecdsa_sign_compact(ctx, msg, sig, key, nonce_function_test_fail, extra, &recid) == 0);
-        CHECK(is_empty_compact_signature(sig));
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_fail, extra) == 0);
+        CHECK(is_empty_signature(&sig));
         /* The retry loop successfully makes its way to the first good value. */
-        siglen = 72;
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, nonce_function_test_retry, extra) == 1);
-        CHECK(siglen > 0);
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig2, &siglen2, key, nonce_function_rfc6979, extra) == 1);
-        CHECK(siglen > 0);
-        CHECK((siglen == siglen2) && (memcmp(sig, sig2, siglen) == 0));
-        CHECK(secp256k1_ecdsa_sign_compact(ctx, msg, sig, key, nonce_function_test_retry, extra, &recid) == 1);
-        CHECK(!is_empty_compact_signature(sig));
-        CHECK(secp256k1_ecdsa_sign_compact(ctx, msg, sig2, key, nonce_function_rfc6979, extra, &recid2) == 1);
-        CHECK(!is_empty_compact_signature(sig2));
-        CHECK((recid == recid2) && (memcmp(sig, sig2, 64) == 0));
-        /* The default nonce function is determinstic. */
-        siglen = 72;
-        siglen2 = 72;
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig, &siglen, key, NULL, extra) == 1);
-        CHECK(siglen > 0);
-        CHECK(secp256k1_ecdsa_sign(ctx, msg, sig2, &siglen2, key, NULL, extra) == 1);
-        CHECK(siglen2 > 0);
-        CHECK((siglen == siglen2) && (memcmp(sig, sig2, siglen) == 0));
-        CHECK(secp256k1_ecdsa_sign_compact(ctx, msg, sig, key, NULL, extra, &recid) == 1);
-        CHECK(!is_empty_compact_signature(sig));
-        CHECK(secp256k1_ecdsa_sign_compact(ctx, msg, sig2, key, NULL, extra, &recid2) == 1);
-        CHECK(!is_empty_compact_signature(sig));
-        CHECK((recid == recid2) && (memcmp(sig, sig2, 64) == 0));
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1);
+        CHECK(!is_empty_signature(&sig));
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1);
+        CHECK(!is_empty_signature(&sig2));
+        CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
+        /* The default nonce function is deterministic. */
+        CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+        CHECK(!is_empty_signature(&sig2));
+        CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
         /* The default nonce function changes output with different messages. */
         for(i = 0; i < 256; i++) {
             int j;
-            siglen2 = 72;
             msg[0] = i;
-            CHECK(secp256k1_ecdsa_sign(ctx, msg, sig2, &siglen2, key, NULL, extra) == 1);
-            CHECK(!is_empty_compact_signature(sig));
-            CHECK(secp256k1_ecdsa_sig_parse(&s[i], sig2, siglen2));
+            CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+            CHECK(!is_empty_signature(&sig2));
+            secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
             for (j = 0; j < i; j++) {
-                CHECK(!secp256k1_scalar_eq(&s[i].r, &s[j].r));
+                CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
             }
         }
         msg[0] = 0;
@@ -1899,17 +4122,45 @@ void test_ecdsa_edge_cases(void) {
         /* The default nonce function changes output with different keys. */
         for(i = 256; i < 512; i++) {
             int j;
-            siglen2 = 72;
             key[0] = i - 256;
-            CHECK(secp256k1_ecdsa_sign(ctx, msg, sig2, &siglen2, key, NULL, extra) == 1);
-            CHECK(secp256k1_ecdsa_sig_parse(&s[i], sig2, siglen2));
+            CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
+            CHECK(!is_empty_signature(&sig2));
+            secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
             for (j = 0; j < i; j++) {
-                CHECK(!secp256k1_scalar_eq(&s[i].r, &s[j].r));
+                CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
             }
         }
         key[0] = 0;
     }
 
+    {
+        /* Check that optional nonce arguments do not have equivalent effect. */
+        const unsigned char zeros[32] = {0};
+        unsigned char nonce[32];
+        unsigned char nonce2[32];
+        unsigned char nonce3[32];
+        unsigned char nonce4[32];
+        VG_UNDEF(nonce,32);
+        VG_UNDEF(nonce2,32);
+        VG_UNDEF(nonce3,32);
+        VG_UNDEF(nonce4,32);
+        CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1);
+        VG_CHECK(nonce,32);
+        CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1);
+        VG_CHECK(nonce2,32);
+        CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1);
+        VG_CHECK(nonce3,32);
+        CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1);
+        VG_CHECK(nonce4,32);
+        CHECK(memcmp(nonce, nonce2, 32) != 0);
+        CHECK(memcmp(nonce, nonce3, 32) != 0);
+        CHECK(memcmp(nonce, nonce4, 32) != 0);
+        CHECK(memcmp(nonce2, nonce3, 32) != 0);
+        CHECK(memcmp(nonce2, nonce4, 32) != 0);
+        CHECK(memcmp(nonce3, nonce4, 32) != 0);
+    }
+
+
     /* Privkey export where pubkey is the point at infinity. */
     {
         unsigned char privkey[300];
@@ -1919,9 +4170,10 @@ void test_ecdsa_edge_cases(void) {
             0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
             0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41,
         };
-        int outlen = 300;
-        CHECK(!secp256k1_ec_privkey_export(ctx, seckey, privkey, &outlen, 0));
-        CHECK(!secp256k1_ec_privkey_export(ctx, seckey, privkey, &outlen, 1));
+        size_t outlen = 300;
+        CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 0));
+        outlen = 300;
+        CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 1));
     }
 }
 
@@ -1930,46 +4182,48 @@ void run_ecdsa_edge_cases(void) {
 }
 
 #ifdef ENABLE_OPENSSL_TESTS
-EC_KEY *get_openssl_key(const secp256k1_scalar_t *key) {
+EC_KEY *get_openssl_key(const unsigned char *key32) {
     unsigned char privkey[300];
-    int privkeylen;
+    size_t privkeylen;
     const unsigned char* pbegin = privkey;
-    int compr = secp256k1_rand32() & 1;
+    int compr = secp256k1_rand_bits(1);
     EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1);
-    CHECK(secp256k1_eckey_privkey_serialize(&ctx->ecmult_gen_ctx, privkey, &privkeylen, key, compr));
+    CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr));
     CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen));
     CHECK(EC_KEY_check_key(ec_key));
     return ec_key;
 }
 
 void test_ecdsa_openssl(void) {
-    secp256k1_gej_t qj;
-    secp256k1_ge_t q;
-    secp256k1_ecdsa_sig_t sig;
-    secp256k1_scalar_t one;
-    secp256k1_scalar_t msg2;
-    secp256k1_scalar_t key, msg;
+    secp256k1_gej qj;
+    secp256k1_ge q;
+    secp256k1_scalar sigr, sigs;
+    secp256k1_scalar one;
+    secp256k1_scalar msg2;
+    secp256k1_scalar key, msg;
     EC_KEY *ec_key;
     unsigned int sigsize = 80;
-    int secp_sigsize = 80;
+    size_t secp_sigsize = 80;
     unsigned char message[32];
     unsigned char signature[80];
+    unsigned char key32[32];
     secp256k1_rand256_test(message);
     secp256k1_scalar_set_b32(&msg, message, NULL);
     random_scalar_order_test(&key);
+    secp256k1_scalar_get_b32(key32, &key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key);
     secp256k1_ge_set_gej(&q, &qj);
-    ec_key = get_openssl_key(&key);
-    CHECK(ec_key);
+    ec_key = get_openssl_key(key32);
+    CHECK(ec_key != NULL);
     CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
-    CHECK(secp256k1_ecdsa_sig_parse(&sig, signature, sigsize));
-    CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sig, &q, &msg));
+    CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize));
+    CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg));
     secp256k1_scalar_set_int(&one, 1);
     secp256k1_scalar_add(&msg2, &msg, &one);
-    CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sig, &q, &msg2));
+    CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2));
 
-    random_sign(&sig, &key, &msg, NULL);
-    CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sig));
+    random_sign(&sigr, &sigs, &key, &msg, NULL);
+    CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs));
     CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1);
 
     EC_KEY_free(ec_key);
@@ -1983,6 +4237,18 @@ void run_ecdsa_openssl(void) {
 }
 #endif
 
+#ifdef ENABLE_MODULE_ECDH
+# include "modules/ecdh/tests_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_SCHNORR
+# include "modules/schnorr/tests_impl.h"
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+# include "modules/recovery/tests_impl.h"
+#endif
+
 int main(int argc, char **argv) {
     unsigned char seed16[16] = {0};
     unsigned char run32[32] = {0};
@@ -2007,7 +4273,7 @@ int main(int argc, char **argv) {
         }
     } else {
         FILE *frand = fopen("/dev/urandom", "r");
-        if (!frand || !fread(&seed16, sizeof(seed16), 1, frand)) {
+        if ((frand == NULL) || !fread(&seed16, sizeof(seed16), 1, frand)) {
             uint64_t t = time(NULL) * (uint64_t)1337;
             seed16[0] ^= t;
             seed16[1] ^= t >> 8;
@@ -2028,12 +4294,14 @@ int main(int argc, char **argv) {
     /* initialize */
     run_context_tests();
     ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
-
-    if (secp256k1_rand32() & 1) {
+    if (secp256k1_rand_bits(1)) {
         secp256k1_rand256(run32);
-        CHECK(secp256k1_context_randomize(ctx, secp256k1_rand32() & 1 ? run32 : NULL));
+        CHECK(secp256k1_context_randomize(ctx, secp256k1_rand_bits(1) ? run32 : NULL));
     }
 
+    run_rand_bits();
+    run_rand_int();
+
     run_sha256_tests();
     run_hmac_sha256_tests();
     run_rfc6979_hmac_sha256_tests();
@@ -2057,6 +4325,7 @@ int main(int argc, char **argv) {
 
     /* group tests */
     run_ge();
+    run_group_decompress();
 
     /* ecmult tests */
     run_wnaf();
@@ -2064,9 +4333,28 @@ int main(int argc, char **argv) {
     run_ecmult_chain();
     run_ecmult_constants();
     run_ecmult_gen_blind();
+    run_ecmult_const_tests();
+    run_ec_combine();
+
+    /* endomorphism tests */
+#ifdef USE_ENDOMORPHISM
+    run_endomorphism_tests();
+#endif
+
+    /* EC point parser test */
+    run_ec_pubkey_parse_test();
+
+    /* EC key edge cases */
+    run_eckey_edge_case_test();
+
+#ifdef ENABLE_MODULE_ECDH
+    /* ecdh tests */
+    run_ecdh_tests();
+#endif
 
     /* ecdsa tests */
     run_random_pubkeys();
+    run_ecdsa_der_parse();
     run_ecdsa_sign_verify();
     run_ecdsa_end_to_end();
     run_ecdsa_edge_cases();
@@ -2074,10 +4362,22 @@ int main(int argc, char **argv) {
     run_ecdsa_openssl();
 #endif
 
+#ifdef ENABLE_MODULE_SCHNORR
+    /* Schnorr tests */
+    run_schnorr_tests();
+#endif
+
+#ifdef ENABLE_MODULE_RECOVERY
+    /* ECDSA pubkey recovery tests */
+    run_recovery_tests();
+#endif
+
     secp256k1_rand256(run32);
     printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]);
 
     /* shutdown */
     secp256k1_context_destroy(ctx);
+
+    printf("no problems found\n");
     return 0;
 }
diff --git a/src/secp256k1/src/util.h b/src/secp256k1/src/util.h
index ae98639f7c..4eef4ded47 100644
--- a/src/secp256k1/src/util.h
+++ b/src/secp256k1/src/util.h
@@ -15,6 +15,15 @@
 #include <stdint.h>
 #include <stdio.h>
 
+typedef struct {
+    void (*fn)(const char *text, void* data);
+    const void* data;
+} secp256k1_callback;
+
+static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) {
+    cb->fn(text, (void*)cb->data);
+}
+
 #ifdef DETERMINISTIC
 #define TEST_FAILURE(msg) do { \
     fprintf(stderr, "%s\n", msg); \
@@ -47,23 +56,20 @@
 } while(0)
 #endif
 
-/* Like assert(), but safe to use on expressions with side effects. */
-#ifndef NDEBUG
-#define DEBUG_CHECK CHECK
-#else
-#define DEBUG_CHECK(cond) do { (void)(cond); } while(0)
-#endif
-
-/* Like DEBUG_CHECK(), but when VERIFY is defined instead of NDEBUG not defined. */
+/* Like assert(), but when VERIFY is defined, and side-effect safe. */
 #ifdef VERIFY
 #define VERIFY_CHECK CHECK
+#define VERIFY_SETUP(stmt) do { stmt; } while(0)
 #else
 #define VERIFY_CHECK(cond) do { (void)(cond); } while(0)
+#define VERIFY_SETUP(stmt)
 #endif
 
-static SECP256K1_INLINE void *checked_malloc(size_t size) {
+static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) {
     void *ret = malloc(size);
-    CHECK(ret != NULL);
+    if (ret == NULL) {
+        secp256k1_callback_call(cb, "Out of memory");
+    }
     return ret;
 }