Merge #9340: [0.13] Update secp256k1 subtree

64dfdde Squashed 'src/secp256k1/' changes from 6c527ec..8225239 (MarcoFalke)

56 files changed, 4463 insertions, 1014 deletions

diff --git a/src/secp256k1/.gitignore b/src/secp256k1/.gitignore
index e0b7b7a48a..87fea161ba 100644
--- a/src/secp256k1/.gitignore
+++ b/src/secp256k1/.gitignore
@@ -6,6 +6,7 @@ bench_schnorr_verify
 bench_recover
 bench_internal
 tests
+exhaustive_tests
 gen_context
 *.exe
 *.so
@@ -25,17 +26,24 @@ config.status
 libtool
 .deps/
 .dirstamp
-build-aux/
 *.lo
 *.o
 *~
 src/libsecp256k1-config.h
 src/libsecp256k1-config.h.in
 src/ecmult_static_context.h
-m4/libtool.m4
-m4/ltoptions.m4
-m4/ltsugar.m4
-m4/ltversion.m4
-m4/lt~obsolete.m4
+build-aux/config.guess
+build-aux/config.sub
+build-aux/depcomp
+build-aux/install-sh
+build-aux/ltmain.sh
+build-aux/m4/libtool.m4
+build-aux/m4/lt~obsolete.m4
+build-aux/m4/ltoptions.m4
+build-aux/m4/ltsugar.m4
+build-aux/m4/ltversion.m4
+build-aux/missing
+build-aux/compile
+build-aux/test-driver
 src/stamp-h1
 libsecp256k1.pc
diff --git a/src/secp256k1/.travis.yml b/src/secp256k1/.travis.yml
index 4e1e73c39f..2439529242 100644
--- a/src/secp256k1/.travis.yml
+++ b/src/secp256k1/.travis.yml
@@ -6,26 +6,30 @@ addons:
 compiler:
   - clang
   - gcc
+cache:
+  directories:
+  - src/java/guava/
 env:
   global:
-    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  schnorr=no  RECOVERY=no
+    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  RECOVERY=no  EXPERIMENTAL=no
+    - GUAVA_URL=https://search.maven.org/remotecontent?filepath=com/google/guava/guava/18.0/guava-18.0.jar GUAVA_JAR=src/java/guava/guava-18.0.jar
   matrix:
     - SCALAR=32bit    RECOVERY=yes
-    - SCALAR=32bit    FIELD=32bit       ECDH=yes
+    - SCALAR=32bit    FIELD=32bit       ECDH=yes  EXPERIMENTAL=yes
     - SCALAR=64bit
     - FIELD=64bit     RECOVERY=yes
     - FIELD=64bit     ENDOMORPHISM=yes
-    - FIELD=64bit     ENDOMORPHISM=yes  ECDH=yes
+    - FIELD=64bit     ENDOMORPHISM=yes  ECDH=yes EXPERIMENTAL=yes
     - FIELD=64bit                       ASM=x86_64
     - FIELD=64bit     ENDOMORPHISM=yes  ASM=x86_64
-    - FIELD=32bit     SCHNORR=yes
     - FIELD=32bit     ENDOMORPHISM=yes
     - BIGNUM=no
-    - BIGNUM=no       ENDOMORPHISM=yes SCHNORR=yes  RECOVERY=yes
+    - BIGNUM=no       ENDOMORPHISM=yes RECOVERY=yes EXPERIMENTAL=yes
     - BIGNUM=no       STATICPRECOMPUTATION=no
     - BUILD=distcheck
     - EXTRAFLAGS=CPPFLAGS=-DDETERMINISTIC
     - EXTRAFLAGS=CFLAGS=-O0
+    - BUILD=check-java ECDH=yes EXPERIMENTAL=yes
 matrix:
   fast_finish: true
   include:
@@ -55,9 +59,11 @@ matrix:
           packages:
             - gcc-multilib
             - libgmp-dev:i386
+before_install: mkdir -p `dirname $GUAVA_JAR`
+install: if [ ! -f $GUAVA_JAR ]; then wget $GUAVA_URL -O $GUAVA_JAR; fi
 before_script: ./autogen.sh
 script:
  - if [ -n "$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=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-schnorr=$SCHNORR --enable-module-recovery=$RECOVERY $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
+ - ./configure --enable-experimental=$EXPERIMENTAL --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --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 7772a4e9d2..e5657f7f31 100644
--- a/src/secp256k1/Makefile.am
+++ b/src/secp256k1/Makefile.am
@@ -1,14 +1,22 @@
 ACLOCAL_AMFLAGS = -I build-aux/m4
 
 lib_LTLIBRARIES = libsecp256k1.la
+if USE_JNI
+JNI_LIB = libsecp256k1_jni.la
+noinst_LTLIBRARIES = $(JNI_LIB)
+else
+JNI_LIB =
+endif
 include_HEADERS = include/secp256k1.h
 noinst_HEADERS =
 noinst_HEADERS += src/scalar.h
 noinst_HEADERS += src/scalar_4x64.h
 noinst_HEADERS += src/scalar_8x32.h
+noinst_HEADERS += src/scalar_low.h
 noinst_HEADERS += src/scalar_impl.h
 noinst_HEADERS += src/scalar_4x64_impl.h
 noinst_HEADERS += src/scalar_8x32_impl.h
+noinst_HEADERS += src/scalar_low_impl.h
 noinst_HEADERS += src/group.h
 noinst_HEADERS += src/group_impl.h
 noinst_HEADERS += src/num_gmp.h
@@ -32,6 +40,7 @@ noinst_HEADERS += src/field_5x52_impl.h
 noinst_HEADERS += src/field_5x52_int128_impl.h
 noinst_HEADERS += src/field_5x52_asm_impl.h
 noinst_HEADERS += src/java/org_bitcoin_NativeSecp256k1.h
+noinst_HEADERS += src/java/org_bitcoin_Secp256k1Context.h
 noinst_HEADERS += src/util.h
 noinst_HEADERS += src/testrand.h
 noinst_HEADERS += src/testrand_impl.h
@@ -45,33 +54,88 @@ noinst_HEADERS += contrib/lax_der_parsing.c
 noinst_HEADERS += contrib/lax_der_privatekey_parsing.h
 noinst_HEADERS += contrib/lax_der_privatekey_parsing.c
 
+if USE_EXTERNAL_ASM
+COMMON_LIB = libsecp256k1_common.la
+noinst_LTLIBRARIES = $(COMMON_LIB)
+else
+COMMON_LIB =
+endif
+
 pkgconfigdir = $(libdir)/pkgconfig
 pkgconfig_DATA = libsecp256k1.pc
 
+if USE_EXTERNAL_ASM
+if USE_ASM_ARM
+libsecp256k1_common_la_SOURCES = src/asm/field_10x26_arm.s
+endif
+endif
+
 libsecp256k1_la_SOURCES = src/secp256k1.c
-libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
-libsecp256k1_la_LIBADD = $(SECP_LIBS)
+libsecp256k1_la_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
+libsecp256k1_la_LIBADD = $(JNI_LIB) $(SECP_LIBS) $(COMMON_LIB)
 
+libsecp256k1_jni_la_SOURCES  = src/java/org_bitcoin_NativeSecp256k1.c src/java/org_bitcoin_Secp256k1Context.c
+libsecp256k1_jni_la_CPPFLAGS = -DSECP256K1_BUILD $(JNI_INCLUDES)
 
 noinst_PROGRAMS =
 if USE_BENCHMARK
 noinst_PROGRAMS += bench_verify bench_sign bench_internal
 bench_verify_SOURCES = src/bench_verify.c
-bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
+bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
 bench_sign_SOURCES = src/bench_sign.c
-bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS)
+bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
 bench_internal_SOURCES = src/bench_internal.c
-bench_internal_LDADD = $(SECP_LIBS)
-bench_internal_CPPFLAGS = $(SECP_INCLUDES)
+bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB)
+bench_internal_CPPFLAGS = -DSECP256K1_BUILD $(SECP_INCLUDES)
 endif
 
+TESTS =
 if USE_TESTS
 noinst_PROGRAMS += tests
 tests_SOURCES = src/tests.c
-tests_CPPFLAGS = -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
-tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS)
+tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
+tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
 tests_LDFLAGS = -static
-TESTS = tests
+TESTS += tests
+endif
+
+if USE_EXHAUSTIVE_TESTS
+noinst_PROGRAMS += exhaustive_tests
+exhaustive_tests_SOURCES = src/tests_exhaustive.c
+exhaustive_tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src $(SECP_INCLUDES)
+exhaustive_tests_LDADD = $(SECP_LIBS)
+exhaustive_tests_LDFLAGS = -static
+TESTS += exhaustive_tests
+endif
+
+JAVAROOT=src/java
+JAVAORG=org/bitcoin
+JAVA_GUAVA=$(srcdir)/$(JAVAROOT)/guava/guava-18.0.jar
+CLASSPATH_ENV=CLASSPATH=$(JAVA_GUAVA)
+JAVA_FILES= \
+  $(JAVAROOT)/$(JAVAORG)/NativeSecp256k1.java \
+  $(JAVAROOT)/$(JAVAORG)/NativeSecp256k1Test.java \
+  $(JAVAROOT)/$(JAVAORG)/NativeSecp256k1Util.java \
+  $(JAVAROOT)/$(JAVAORG)/Secp256k1Context.java
+
+if USE_JNI
+
+$(JAVA_GUAVA):
+	@echo Guava is missing. Fetch it via: \
+	wget https://search.maven.org/remotecontent?filepath=com/google/guava/guava/18.0/guava-18.0.jar -O $(@)
+	@false
+
+.stamp-java: $(JAVA_FILES)
+	@echo   Compiling $^
+	$(AM_V_at)$(CLASSPATH_ENV) javac $^
+	@touch $@
+
+if USE_TESTS
+
+check-java: libsecp256k1.la $(JAVA_GUAVA) .stamp-java
+	$(AM_V_at)java -Djava.library.path="./:./src:./src/.libs:.libs/" -cp "$(JAVA_GUAVA):$(JAVAROOT)" $(JAVAORG)/NativeSecp256k1Test
+
+endif
 endif
 
 if USE_ECMULT_STATIC_PRECOMPUTATION
@@ -93,19 +157,15 @@ $(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
+CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h $(JAVAROOT)/$(JAVAORG)/*.class .stamp-java
 endif
 
-EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h
+EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h $(JAVA_FILES)
 
 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/README.md b/src/secp256k1/README.md
index 6095db4220..8cd344ea81 100644
--- a/src/secp256k1/README.md
+++ b/src/secp256k1/README.md
@@ -1,7 +1,7 @@
 libsecp256k1
 ============
 
-[![Build Status](https://travis-ci.org/bitcoin/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin/secp256k1)
+[![Build Status](https://travis-ci.org/bitcoin-core/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin-core/secp256k1)
 
 Optimized C library for EC operations on curve secp256k1.
 
diff --git a/src/secp256k1/build-aux/m4/ax_jni_include_dir.m4 b/src/secp256k1/build-aux/m4/ax_jni_include_dir.m4
new file mode 100644
index 0000000000..1fc3627614
--- /dev/null
+++ b/src/secp256k1/build-aux/m4/ax_jni_include_dir.m4
@@ -0,0 +1,140 @@
+# ===========================================================================
+#    http://www.gnu.org/software/autoconf-archive/ax_jni_include_dir.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_JNI_INCLUDE_DIR
+#
+# DESCRIPTION
+#
+#   AX_JNI_INCLUDE_DIR finds include directories needed for compiling
+#   programs using the JNI interface.
+#
+#   JNI include directories are usually in the Java distribution. This is
+#   deduced from the value of $JAVA_HOME, $JAVAC, or the path to "javac", in
+#   that order. When this macro completes, a list of directories is left in
+#   the variable JNI_INCLUDE_DIRS.
+#
+#   Example usage follows:
+#
+#     AX_JNI_INCLUDE_DIR
+#
+#     for JNI_INCLUDE_DIR in $JNI_INCLUDE_DIRS
+#     do
+#             CPPFLAGS="$CPPFLAGS -I$JNI_INCLUDE_DIR"
+#     done
+#
+#   If you want to force a specific compiler:
+#
+#   - at the configure.in level, set JAVAC=yourcompiler before calling
+#   AX_JNI_INCLUDE_DIR
+#
+#   - at the configure level, setenv JAVAC
+#
+#   Note: This macro can work with the autoconf M4 macros for Java programs.
+#   This particular macro is not part of the original set of macros.
+#
+# LICENSE
+#
+#   Copyright (c) 2008 Don Anderson <dda@sleepycat.com>
+#
+#   Copying and distribution of this file, with or without modification, are
+#   permitted in any medium without royalty provided the copyright notice
+#   and this notice are preserved. This file is offered as-is, without any
+#   warranty.
+
+#serial 10
+
+AU_ALIAS([AC_JNI_INCLUDE_DIR], [AX_JNI_INCLUDE_DIR])
+AC_DEFUN([AX_JNI_INCLUDE_DIR],[
+
+JNI_INCLUDE_DIRS=""
+
+if test "x$JAVA_HOME" != x; then
+	_JTOPDIR="$JAVA_HOME"
+else
+	if test "x$JAVAC" = x; then
+		JAVAC=javac
+	fi
+	AC_PATH_PROG([_ACJNI_JAVAC], [$JAVAC], [no])
+	if test "x$_ACJNI_JAVAC" = xno; then
+		AC_MSG_WARN([cannot find JDK; try setting \$JAVAC or \$JAVA_HOME])
+	fi
+	_ACJNI_FOLLOW_SYMLINKS("$_ACJNI_JAVAC")
+	_JTOPDIR=`echo "$_ACJNI_FOLLOWED" | sed -e 's://*:/:g' -e 's:/[[^/]]*$::'`
+fi
+
+case "$host_os" in
+        darwin*)        _JTOPDIR=`echo "$_JTOPDIR" | sed -e 's:/[[^/]]*$::'`
+                        _JINC="$_JTOPDIR/Headers";;
+        *)              _JINC="$_JTOPDIR/include";;
+esac
+_AS_ECHO_LOG([_JTOPDIR=$_JTOPDIR])
+_AS_ECHO_LOG([_JINC=$_JINC])
+
+# On Mac OS X 10.6.4, jni.h is a symlink:
+# /System/Library/Frameworks/JavaVM.framework/Versions/Current/Headers/jni.h
+# -> ../../CurrentJDK/Headers/jni.h.
+
+AC_CACHE_CHECK(jni headers, ac_cv_jni_header_path,
+[
+if test -f "$_JINC/jni.h"; then
+  ac_cv_jni_header_path="$_JINC"
+  JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $ac_cv_jni_header_path"
+else
+  _JTOPDIR=`echo "$_JTOPDIR" | sed -e 's:/[[^/]]*$::'`
+  if test -f "$_JTOPDIR/include/jni.h"; then
+    ac_cv_jni_header_path="$_JTOPDIR/include"
+    JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $ac_cv_jni_header_path"
+  else
+    ac_cv_jni_header_path=none
+  fi
+fi
+])
+
+
+
+# get the likely subdirectories for system specific java includes
+case "$host_os" in
+bsdi*)          _JNI_INC_SUBDIRS="bsdos";;
+darwin*)        _JNI_INC_SUBDIRS="darwin";;
+freebsd*)       _JNI_INC_SUBDIRS="freebsd";;
+linux*)         _JNI_INC_SUBDIRS="linux genunix";;
+osf*)           _JNI_INC_SUBDIRS="alpha";;
+solaris*)       _JNI_INC_SUBDIRS="solaris";;
+mingw*)		_JNI_INC_SUBDIRS="win32";;
+cygwin*)	_JNI_INC_SUBDIRS="win32";;
+*)              _JNI_INC_SUBDIRS="genunix";;
+esac
+
+if test "x$ac_cv_jni_header_path" != "xnone"; then
+  # add any subdirectories that are present
+  for JINCSUBDIR in $_JNI_INC_SUBDIRS
+  do
+      if test -d "$_JTOPDIR/include/$JINCSUBDIR"; then
+           JNI_INCLUDE_DIRS="$JNI_INCLUDE_DIRS $_JTOPDIR/include/$JINCSUBDIR"
+      fi
+  done
+fi
+])
+
+# _ACJNI_FOLLOW_SYMLINKS <path>
+# Follows symbolic links on <path>,
+# finally setting variable _ACJNI_FOLLOWED
+# ----------------------------------------
+AC_DEFUN([_ACJNI_FOLLOW_SYMLINKS],[
+# find the include directory relative to the javac executable
+_cur="$1"
+while ls -ld "$_cur" 2>/dev/null | grep " -> " >/dev/null; do
+        AC_MSG_CHECKING([symlink for $_cur])
+        _slink=`ls -ld "$_cur" | sed 's/.* -> //'`
+        case "$_slink" in
+        /*) _cur="$_slink";;
+        # 'X' avoids triggering unwanted echo options.
+        *) _cur=`echo "X$_cur" | sed -e 's/^X//' -e 's:[[^/]]*$::'`"$_slink";;
+        esac
+        AC_MSG_RESULT([$_cur])
+done
+_ACJNI_FOLLOWED="$_cur"
+])# _ACJNI
diff --git a/src/secp256k1/build-aux/m4/bitcoin_secp.m4 b/src/secp256k1/build-aux/m4/bitcoin_secp.m4
index d41bbb6487..b74acb8c13 100644
--- a/src/secp256k1/build-aux/m4/bitcoin_secp.m4
+++ b/src/secp256k1/build-aux/m4/bitcoin_secp.m4
@@ -3,13 +3,13 @@ AC_DEFUN([SECP_INT128_CHECK],[
 has_int128=$ac_cv_type___int128
 ])
 
-dnl 
+dnl escape "$0x" below using the m4 quadrigaph @S|@, and escape it again with a \ for the shell.
 AC_DEFUN([SECP_64BIT_ASM_CHECK],[
 AC_MSG_CHECKING(for x86_64 assembly availability)
 AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
   #include <stdint.h>]],[[
   uint64_t a = 11, tmp;
-  __asm__ __volatile__("movq $0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
+  __asm__ __volatile__("movq \@S|@0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx");
   ]])],[has_64bit_asm=yes],[has_64bit_asm=no])
 AC_MSG_RESULT([$has_64bit_asm])
 ])
@@ -46,6 +46,10 @@ if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then
     ECDSA_sign(0, NULL, 0, NULL, NULL, eckey);
     ECDSA_verify(0, NULL, 0, NULL, 0, eckey);
     EC_KEY_free(eckey);
+    ECDSA_SIG *sig_openssl;
+    sig_openssl = ECDSA_SIG_new();
+    (void)sig_openssl->r;
+    ECDSA_SIG_free(sig_openssl);
   ]])],[has_openssl_ec=yes],[has_openssl_ec=no])
   AC_MSG_RESULT([$has_openssl_ec])
 fi
diff --git a/src/secp256k1/configure.ac b/src/secp256k1/configure.ac
index 786d8dcfb9..ec50ffe3a2 100644
--- a/src/secp256k1/configure.ac
+++ b/src/secp256k1/configure.ac
@@ -29,6 +29,7 @@ AC_PROG_CC_C89
 if test x"$ac_cv_prog_cc_c89" = x"no"; then
   AC_MSG_ERROR([c89 compiler support required])
 fi
+AM_PROG_AS
 
 case $host_os in
   *darwin*)
@@ -93,31 +94,46 @@ AC_ARG_ENABLE(tests,
     [use_tests=$enableval],
     [use_tests=yes])
 
+AC_ARG_ENABLE(openssl_tests,
+    AS_HELP_STRING([--enable-openssl-tests],[enable OpenSSL tests, if OpenSSL is available (default is auto)]),
+    [enable_openssl_tests=$enableval],
+    [enable_openssl_tests=auto])
+
+AC_ARG_ENABLE(experimental,
+    AS_HELP_STRING([--enable-experimental],[allow experimental configure options (default is no)]),
+    [use_experimental=$enableval],
+    [use_experimental=no])
+
+AC_ARG_ENABLE(exhaustive_tests,
+    AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests (default is yes)]),
+    [use_exhaustive_tests=$enableval],
+    [use_exhaustive_tests=yes])
+
 AC_ARG_ENABLE(endomorphism,
     AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
     [use_endomorphism=$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])
+    [use_ecmult_static_precomputation=auto])
 
 AC_ARG_ENABLE(module_ecdh,
-    AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation (default is no)]),
+    AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation (experimental)]),
     [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_ENABLE(jni,
+    AS_HELP_STRING([--enable-jni],[enable libsecp256k1_jni (default is auto)]),
+    [use_jni=$enableval],
+    [use_jni=auto])
+
 AC_ARG_WITH([field], [AS_HELP_STRING([--with-field=64bit|32bit|auto],
 [Specify Field Implementation. Default is auto])],[req_field=$withval], [req_field=auto])
 
@@ -127,8 +143,8 @@ AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|no|auto],
 AC_ARG_WITH([scalar], [AS_HELP_STRING([--with-scalar=64bit|32bit|auto],
 [Specify scalar implementation. Default is auto])],[req_scalar=$withval], [req_scalar=auto])
 
-AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|no|auto]
-[Specify assembly optimizations to use. Default is auto])],[req_asm=$withval], [req_asm=auto])
+AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto]
+[Specify assembly optimizations to use. Default is auto (experimental: arm)])],[req_asm=$withval], [req_asm=auto])
 
 AC_CHECK_TYPES([__int128])
 
@@ -138,6 +154,34 @@ AC_COMPILE_IFELSE([AC_LANG_SOURCE([[void myfunc() {__builtin_expect(0,0);}]])],
     [ AC_MSG_RESULT([no])
     ])
 
+if test x"$use_ecmult_static_precomputation" != x"no"; then
+  save_cross_compiling=$cross_compiling
+  cross_compiling=no
+  TEMP_CC="$CC"
+  CC="$CC_FOR_BUILD"
+  AC_MSG_CHECKING([native compiler: ${CC_FOR_BUILD}])
+  AC_RUN_IFELSE(
+    [AC_LANG_PROGRAM([], [return 0])],
+    [working_native_cc=yes],
+    [working_native_cc=no],[dnl])
+  CC="$TEMP_CC"
+  cross_compiling=$save_cross_compiling
+
+  if test x"$working_native_cc" = x"no"; then
+    set_precomp=no
+    if test x"$use_ecmult_static_precomputation" = x"yes";  then
+      AC_MSG_ERROR([${CC_FOR_BUILD} does not produce working binaries. Please set CC_FOR_BUILD])
+    else
+      AC_MSG_RESULT([${CC_FOR_BUILD} does not produce working binaries. Please set CC_FOR_BUILD])
+    fi
+  else
+    AC_MSG_RESULT([ok])
+    set_precomp=yes
+  fi
+else
+  set_precomp=no
+fi
+
 if test x"$req_asm" = x"auto"; then
   SECP_64BIT_ASM_CHECK
   if test x"$has_64bit_asm" = x"yes"; then
@@ -155,6 +199,8 @@ else
       AC_MSG_ERROR([x86_64 assembly optimization requested but not available])
     fi
     ;;
+  arm)
+    ;;
   no)
     ;;
   *)
@@ -247,10 +293,15 @@ else
 fi
 
 # select assembly optimization
+use_external_asm=no
+
 case $set_asm in
 x86_64)
   AC_DEFINE(USE_ASM_X86_64, 1, [Define this symbol to enable x86_64 assembly optimizations])
   ;;
+arm)
+  use_external_asm=yes
+  ;;
 no)
   ;;
 *)
@@ -305,16 +356,48 @@ esac
 if test x"$use_tests" = x"yes"; then
   SECP_OPENSSL_CHECK
   if test x"$has_openssl_ec" = x"yes"; then
-    AC_DEFINE(ENABLE_OPENSSL_TESTS, 1, [Define this symbol if OpenSSL EC functions are available])
-    SECP_TEST_INCLUDES="$SSL_CFLAGS $CRYPTO_CFLAGS"
-    SECP_TEST_LIBS="$CRYPTO_LIBS"
-
-    case $host in
-    *mingw*)
-      SECP_TEST_LIBS="$SECP_TEST_LIBS -lgdi32"
-      ;;
-    esac
+    if test x"$enable_openssl_tests" != x"no"; then
+      AC_DEFINE(ENABLE_OPENSSL_TESTS, 1, [Define this symbol if OpenSSL EC functions are available])
+      SECP_TEST_INCLUDES="$SSL_CFLAGS $CRYPTO_CFLAGS"
+      SECP_TEST_LIBS="$CRYPTO_LIBS"
+
+      case $host in
+      *mingw*)
+        SECP_TEST_LIBS="$SECP_TEST_LIBS -lgdi32"
+        ;;
+      esac
+    fi
+  else
+    if test x"$enable_openssl_tests" = x"yes"; then
+      AC_MSG_ERROR([OpenSSL tests requested but OpenSSL with EC support is not available])
+    fi
+  fi
+else
+  if test x"$enable_openssl_tests" = x"yes"; then
+    AC_MSG_ERROR([OpenSSL tests requested but tests are not enabled])
+  fi
+fi
 
+if test x"$use_jni" != x"no"; then
+  AX_JNI_INCLUDE_DIR
+  have_jni_dependencies=yes
+  if test x"$enable_module_ecdh" = x"no"; then
+    have_jni_dependencies=no
+  fi
+  if test "x$JNI_INCLUDE_DIRS" = "x"; then
+    have_jni_dependencies=no
+  fi
+  if test "x$have_jni_dependencies" = "xno"; then
+    if test x"$use_jni" = x"yes"; then
+      AC_MSG_ERROR([jni support explicitly requested but headers/dependencies were not found. Enable ECDH and try again.])
+    fi
+    AC_MSG_WARN([jni headers/dependencies not found. jni support disabled])
+    use_jni=no
+  else
+    use_jni=yes
+    for JNI_INCLUDE_DIR in $JNI_INCLUDE_DIRS; do
+      JNI_INCLUDES="$JNI_INCLUDES -I$JNI_INCLUDE_DIR"
+    done
   fi
 fi
 
@@ -327,7 +410,7 @@ if test x"$use_endomorphism" = x"yes"; then
   AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization])
 fi
 
-if test x"$use_ecmult_static_precomputation" = x"yes"; then
+if test x"$set_precomp" = x"yes"; then
   AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table])
 fi
 
@@ -335,38 +418,57 @@ 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()
 
+if test x"$use_external_asm" = x"yes"; then
+  AC_DEFINE(USE_EXTERNAL_ASM, 1, [Define this symbol if an external (non-inline) assembly implementation is used])
+fi
+
+AC_MSG_NOTICE([Using static precomputation: $set_precomp])
 AC_MSG_NOTICE([Using assembly optimizations: $set_asm])
 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_MSG_NOTICE([Using jni: $use_jni])
+
+if test x"$enable_experimental" = x"yes"; then
+  AC_MSG_NOTICE([******])
+  AC_MSG_NOTICE([WARNING: experimental build])
+  AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.])
+  AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
+  AC_MSG_NOTICE([******])
+else
+  if test x"$enable_module_ecdh" = x"yes"; then
+    AC_MSG_ERROR([ECDH module is experimental. Use --enable-experimental to allow.])
+  fi
+  if test x"$set_asm" = x"arm"; then
+    AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.])
+  fi
+fi
 
 AC_CONFIG_HEADERS([src/libsecp256k1-config.h])
 AC_CONFIG_FILES([Makefile libsecp256k1.pc])
+AC_SUBST(JNI_INCLUDES)
 AC_SUBST(SECP_INCLUDES)
 AC_SUBST(SECP_LIBS)
 AC_SUBST(SECP_TEST_LIBS)
 AC_SUBST(SECP_TEST_INCLUDES)
 AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
+AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$use_exhaustive_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([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$set_precomp" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$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"])
+AM_CONDITIONAL([USE_JNI], [test x"$use_jni" == x"yes"])
+AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$use_external_asm" = x"yes"])
+AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"])
 
 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/include/secp256k1.h b/src/secp256k1/include/secp256k1.h
index 7145dbcc54..f268e309d0 100644
--- a/src/secp256k1/include/secp256k1.h
+++ b/src/secp256k1/include/secp256k1.h
@@ -47,11 +47,8 @@ typedef struct secp256k1_context_struct secp256k1_context;
  *  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.
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse.
  */
 typedef struct {
     unsigned char data[64];
@@ -62,12 +59,9 @@ typedef struct {
  *  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
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, 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];
diff --git a/src/secp256k1/include/secp256k1_schnorr.h b/src/secp256k1/include/secp256k1_schnorr.h
deleted file mode 100644
index dc32fec1ea..0000000000
--- a/src/secp256k1/include/secp256k1_schnorr.h
+++ /dev/null
@@ -1,173 +0,0 @@
-#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/libsecp256k1.pc.in b/src/secp256k1/libsecp256k1.pc.in
index 1c72dd0003..a0d006f113 100644
--- a/src/secp256k1/libsecp256k1.pc.in
+++ b/src/secp256k1/libsecp256k1.pc.in
@@ -5,7 +5,7 @@ includedir=@includedir@
 
 Name: libsecp256k1
 Description: Optimized C library for EC operations on curve secp256k1
-URL: https://github.com/bitcoin/secp256k1
+URL: https://github.com/bitcoin-core/secp256k1
 Version: @PACKAGE_VERSION@
 Cflags: -I${includedir}
 Libs.private: @SECP_LIBS@
diff --git a/src/secp256k1/sage/group_prover.sage b/src/secp256k1/sage/group_prover.sage
new file mode 100644
index 0000000000..ab580c5b23
--- /dev/null
+++ b/src/secp256k1/sage/group_prover.sage
@@ -0,0 +1,322 @@
+# This code supports verifying group implementations which have branches
+# or conditional statements (like cmovs), by allowing each execution path
+# to independently set assumptions on input or intermediary variables.
+#
+# The general approach is:
+# * A constraint is a tuple of two sets of of symbolic expressions:
+#   the first of which are required to evaluate to zero, the second of which
+#   are required to evaluate to nonzero.
+#   - A constraint is said to be conflicting if any of its nonzero expressions
+#     is in the ideal with basis the zero expressions (in other words: when the
+#     zero expressions imply that one of the nonzero expressions are zero).
+# * There is a list of laws that describe the intended behaviour, including
+#   laws for addition and doubling. Each law is called with the symbolic point
+#   coordinates as arguments, and returns:
+#   - A constraint describing the assumptions under which it is applicable,
+#     called "assumeLaw"
+#   - A constraint describing the requirements of the law, called "require"
+# * Implementations are transliterated into functions that operate as well on
+#   algebraic input points, and are called once per combination of branches
+#   exectured. Each execution returns:
+#   - A constraint describing the assumptions this implementation requires
+#     (such as Z1=1), called "assumeFormula"
+#   - A constraint describing the assumptions this specific branch requires,
+#     but which is by construction guaranteed to cover the entire space by
+#     merging the results from all branches, called "assumeBranch"
+#   - The result of the computation
+# * All combinations of laws with implementation branches are tried, and:
+#   - If the combination of assumeLaw, assumeFormula, and assumeBranch results
+#     in a conflict, it means this law does not apply to this branch, and it is
+#     skipped.
+#   - For others, we try to prove the require constraints hold, assuming the
+#     information in assumeLaw + assumeFormula + assumeBranch, and if this does
+#     not succeed, we fail.
+#     + To prove an expression is zero, we check whether it belongs to the
+#       ideal with the assumed zero expressions as basis. This test is exact.
+#     + To prove an expression is nonzero, we check whether each of its
+#       factors is contained in the set of nonzero assumptions' factors.
+#       This test is not exact, so various combinations of original and
+#       reduced expressions' factors are tried.
+#   - If we succeed, we print out the assumptions from assumeFormula that
+#     weren't implied by assumeLaw already. Those from assumeBranch are skipped,
+#     as we assume that all constraints in it are complementary with each other.
+#
+# Based on the sage verification scripts used in the Explicit-Formulas Database
+# by Tanja Lange and others, see http://hyperelliptic.org/EFD
+
+class fastfrac:
+  """Fractions over rings."""
+
+  def __init__(self,R,top,bot=1):
+    """Construct a fractional, given a ring, a numerator, and denominator."""
+    self.R = R
+    if parent(top) == ZZ or parent(top) == R:
+      self.top = R(top)
+      self.bot = R(bot)
+    elif top.__class__ == fastfrac:
+      self.top = top.top
+      self.bot = top.bot * bot
+    else:
+      self.top = R(numerator(top))
+      self.bot = R(denominator(top)) * bot
+
+  def iszero(self,I):
+    """Return whether this fraction is zero given an ideal."""
+    return self.top in I and self.bot not in I
+
+  def reduce(self,assumeZero):
+    zero = self.R.ideal(map(numerator, assumeZero))
+    return fastfrac(self.R, zero.reduce(self.top)) / fastfrac(self.R, zero.reduce(self.bot))
+
+  def __add__(self,other):
+    """Add two fractions."""
+    if parent(other) == ZZ:
+      return fastfrac(self.R,self.top + self.bot * other,self.bot)
+    if other.__class__ == fastfrac:
+      return fastfrac(self.R,self.top * other.bot + self.bot * other.top,self.bot * other.bot)
+    return NotImplemented
+
+  def __sub__(self,other):
+    """Subtract two fractions."""
+    if parent(other) == ZZ:
+      return fastfrac(self.R,self.top - self.bot * other,self.bot)
+    if other.__class__ == fastfrac:
+      return fastfrac(self.R,self.top * other.bot - self.bot * other.top,self.bot * other.bot)
+    return NotImplemented
+
+  def __neg__(self):
+    """Return the negation of a fraction."""
+    return fastfrac(self.R,-self.top,self.bot)
+
+  def __mul__(self,other):
+    """Multiply two fractions."""
+    if parent(other) == ZZ:
+      return fastfrac(self.R,self.top * other,self.bot)
+    if other.__class__ == fastfrac:
+      return fastfrac(self.R,self.top * other.top,self.bot * other.bot)
+    return NotImplemented
+
+  def __rmul__(self,other):
+    """Multiply something else with a fraction."""
+    return self.__mul__(other)
+
+  def __div__(self,other):
+    """Divide two fractions."""
+    if parent(other) == ZZ:
+      return fastfrac(self.R,self.top,self.bot * other)
+    if other.__class__ == fastfrac:
+      return fastfrac(self.R,self.top * other.bot,self.bot * other.top)
+    return NotImplemented
+
+  def __pow__(self,other):
+    """Compute a power of a fraction."""
+    if parent(other) == ZZ:
+      if other < 0:
+        # Negative powers require flipping top and bottom
+        return fastfrac(self.R,self.bot ^ (-other),self.top ^ (-other))
+      else:
+        return fastfrac(self.R,self.top ^ other,self.bot ^ other)
+    return NotImplemented
+
+  def __str__(self):
+    return "fastfrac((" + str(self.top) + ") / (" + str(self.bot) + "))"
+  def __repr__(self):
+    return "%s" % self
+
+  def numerator(self):
+    return self.top
+
+class constraints:
+  """A set of constraints, consisting of zero and nonzero expressions.
+
+  Constraints can either be used to express knowledge or a requirement.
+
+  Both the fields zero and nonzero are maps from expressions to description
+  strings. The expressions that are the keys in zero are required to be zero,
+  and the expressions that are the keys in nonzero are required to be nonzero.
+
+  Note that (a != 0) and (b != 0) is the same as (a*b != 0), so all keys in
+  nonzero could be multiplied into a single key. This is often much less
+  efficient to work with though, so we keep them separate inside the
+  constraints. This allows higher-level code to do fast checks on the individual
+  nonzero elements, or combine them if needed for stronger checks.
+
+  We can't multiply the different zero elements, as it would suffice for one of
+  the factors to be zero, instead of all of them. Instead, the zero elements are
+  typically combined into an ideal first.
+  """
+
+  def __init__(self, **kwargs):
+    if 'zero' in kwargs:
+      self.zero = dict(kwargs['zero'])
+    else:
+      self.zero = dict()
+    if 'nonzero' in kwargs:
+      self.nonzero = dict(kwargs['nonzero'])
+    else:
+      self.nonzero = dict()
+
+  def negate(self):
+    return constraints(zero=self.nonzero, nonzero=self.zero)
+
+  def __add__(self, other):
+    zero = self.zero.copy()
+    zero.update(other.zero)
+    nonzero = self.nonzero.copy()
+    nonzero.update(other.nonzero)
+    return constraints(zero=zero, nonzero=nonzero)
+
+  def __str__(self):
+    return "constraints(zero=%s,nonzero=%s)" % (self.zero, self.nonzero)
+
+  def __repr__(self):
+    return "%s" % self
+
+
+def conflicts(R, con):
+  """Check whether any of the passed non-zero assumptions is implied by the zero assumptions"""
+  zero = R.ideal(map(numerator, con.zero))
+  if 1 in zero:
+    return True
+  # First a cheap check whether any of the individual nonzero terms conflict on
+  # their own.
+  for nonzero in con.nonzero:
+    if nonzero.iszero(zero):
+      return True
+  # It can be the case that entries in the nonzero set do not individually
+  # conflict with the zero set, but their combination does. For example, knowing
+  # that either x or y is zero is equivalent to having x*y in the zero set.
+  # Having x or y individually in the nonzero set is not a conflict, but both
+  # simultaneously is, so that is the right thing to check for.
+  if reduce(lambda a,b: a * b, con.nonzero, fastfrac(R, 1)).iszero(zero):
+    return True
+  return False
+
+
+def get_nonzero_set(R, assume):
+  """Calculate a simple set of nonzero expressions"""
+  zero = R.ideal(map(numerator, assume.zero))
+  nonzero = set()
+  for nz in map(numerator, assume.nonzero):
+    for (f,n) in nz.factor():
+      nonzero.add(f)
+    rnz = zero.reduce(nz)
+    for (f,n) in rnz.factor():
+      nonzero.add(f)
+  return nonzero
+
+
+def prove_nonzero(R, exprs, assume):
+  """Check whether an expression is provably nonzero, given assumptions"""
+  zero = R.ideal(map(numerator, assume.zero))
+  nonzero = get_nonzero_set(R, assume)
+  expl = set()
+  ok = True
+  for expr in exprs:
+    if numerator(expr) in zero:
+      return (False, [exprs[expr]])
+  allexprs = reduce(lambda a,b: numerator(a)*numerator(b), exprs, 1)
+  for (f, n) in allexprs.factor():
+    if f not in nonzero:
+      ok = False
+  if ok:
+    return (True, None)
+  ok = True
+  for (f, n) in zero.reduce(numerator(allexprs)).factor():
+    if f not in nonzero:
+      ok = False
+  if ok:
+    return (True, None)
+  ok = True
+  for expr in exprs:
+    for (f,n) in numerator(expr).factor():
+      if f not in nonzero:
+        ok = False
+  if ok:
+    return (True, None)
+  ok = True
+  for expr in exprs:
+    for (f,n) in zero.reduce(numerator(expr)).factor():
+      if f not in nonzero:
+        expl.add(exprs[expr])
+  if expl:
+    return (False, list(expl))
+  else:
+    return (True, None)
+
+
+def prove_zero(R, exprs, assume):
+  """Check whether all of the passed expressions are provably zero, given assumptions"""
+  r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume)
+  if not r:
+    return (False, map(lambda x: "Possibly zero denominator: %s" % x, e))
+  zero = R.ideal(map(numerator, assume.zero))
+  nonzero = prod(x for x in assume.nonzero)
+  expl = []
+  for expr in exprs:
+    if not expr.iszero(zero):
+      expl.append(exprs[expr])
+  if not expl:
+    return (True, None)
+  return (False, expl)
+
+
+def describe_extra(R, assume, assumeExtra):
+  """Describe what assumptions are added, given existing assumptions"""
+  zerox = assume.zero.copy()
+  zerox.update(assumeExtra.zero)
+  zero = R.ideal(map(numerator, assume.zero))
+  zeroextra = R.ideal(map(numerator, zerox))
+  nonzero = get_nonzero_set(R, assume)
+  ret = set()
+  # Iterate over the extra zero expressions
+  for base in assumeExtra.zero:
+    if base not in zero:
+      add = []
+      for (f, n) in numerator(base).factor():
+        if f not in nonzero:
+          add += ["%s" % f]
+      if add:
+        ret.add((" * ".join(add)) + " = 0 [%s]" % assumeExtra.zero[base])
+  # Iterate over the extra nonzero expressions
+  for nz in assumeExtra.nonzero:
+    nzr = zeroextra.reduce(numerator(nz))
+    if nzr not in zeroextra:
+      for (f,n) in nzr.factor():
+        if zeroextra.reduce(f) not in nonzero:
+          ret.add("%s != 0" % zeroextra.reduce(f))
+  return ", ".join(x for x in ret)
+
+
+def check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require):
+  """Check a set of zero and nonzero requirements, given a set of zero and nonzero assumptions"""
+  assume = assumeLaw + assumeAssert + assumeBranch
+
+  if conflicts(R, assume):
+    # This formula does not apply
+    return None
+
+  describe = describe_extra(R, assumeLaw + assumeBranch, assumeAssert)
+
+  ok, msg = prove_zero(R, require.zero, assume)
+  if not ok:
+    return "FAIL, %s fails (assuming %s)" % (str(msg), describe)
+
+  res, expl = prove_nonzero(R, require.nonzero, assume)
+  if not res:
+    return "FAIL, %s fails (assuming %s)" % (str(expl), describe)
+
+  if describe != "":
+    return "OK (assuming %s)" % describe
+  else:
+    return "OK"
+
+
+def concrete_verify(c):
+  for k in c.zero:
+    if k != 0:
+      return (False, c.zero[k])
+  for k in c.nonzero:
+    if k == 0:
+      return (False, c.nonzero[k])
+  return (True, None)
diff --git a/src/secp256k1/sage/secp256k1.sage b/src/secp256k1/sage/secp256k1.sage
new file mode 100644
index 0000000000..a97e732f7f
--- /dev/null
+++ b/src/secp256k1/sage/secp256k1.sage
@@ -0,0 +1,306 @@
+# Test libsecp256k1' group operation implementations using prover.sage
+
+import sys
+
+load("group_prover.sage")
+load("weierstrass_prover.sage")
+
+def formula_secp256k1_gej_double_var(a):
+  """libsecp256k1's secp256k1_gej_double_var, used by various addition functions"""
+  rz = a.Z * a.Y
+  rz = rz * 2
+  t1 = a.X^2
+  t1 = t1 * 3
+  t2 = t1^2
+  t3 = a.Y^2
+  t3 = t3 * 2
+  t4 = t3^2
+  t4 = t4 * 2
+  t3 = t3 * a.X
+  rx = t3
+  rx = rx * 4
+  rx = -rx
+  rx = rx + t2
+  t2 = -t2
+  t3 = t3 * 6
+  t3 = t3 + t2
+  ry = t1 * t3
+  t2 = -t4
+  ry = ry + t2
+  return jacobianpoint(rx, ry, rz)
+
+def formula_secp256k1_gej_add_var(branch, a, b):
+  """libsecp256k1's secp256k1_gej_add_var"""
+  if branch == 0:
+    return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), b)
+  if branch == 1:
+    return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
+  z22 = b.Z^2
+  z12 = a.Z^2
+  u1 = a.X * z22
+  u2 = b.X * z12
+  s1 = a.Y * z22
+  s1 = s1 * b.Z
+  s2 = b.Y * z12
+  s2 = s2 * a.Z
+  h = -u1
+  h = h + u2
+  i = -s1
+  i = i + s2
+  if branch == 2:
+    r = formula_secp256k1_gej_double_var(a)
+    return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r)
+  if branch == 3:
+    return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity())
+  i2 = i^2
+  h2 = h^2
+  h3 = h2 * h
+  h = h * b.Z
+  rz = a.Z * h
+  t = u1 * h2
+  rx = t
+  rx = rx * 2
+  rx = rx + h3
+  rx = -rx
+  rx = rx + i2
+  ry = -rx
+  ry = ry + t
+  ry = ry * i
+  h3 = h3 * s1
+  h3 = -h3
+  ry = ry + h3
+  return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
+
+def formula_secp256k1_gej_add_ge_var(branch, a, b):
+  """libsecp256k1's secp256k1_gej_add_ge_var, which assume bz==1"""
+  if branch == 0:
+    return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(nonzero={a.Infinity : 'a_infinite'}), b)
+  if branch == 1:
+    return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
+  z12 = a.Z^2
+  u1 = a.X
+  u2 = b.X * z12
+  s1 = a.Y
+  s2 = b.Y * z12
+  s2 = s2 * a.Z
+  h = -u1
+  h = h + u2
+  i = -s1
+  i = i + s2
+  if (branch == 2):
+    r = formula_secp256k1_gej_double_var(a)
+    return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
+  if (branch == 3):
+    return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
+  i2 = i^2
+  h2 = h^2
+  h3 = h * h2
+  rz = a.Z * h
+  t = u1 * h2
+  rx = t
+  rx = rx * 2
+  rx = rx + h3
+  rx = -rx
+  rx = rx + i2
+  ry = -rx
+  ry = ry + t
+  ry = ry * i
+  h3 = h3 * s1
+  h3 = -h3
+  ry = ry + h3
+  return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
+
+def formula_secp256k1_gej_add_zinv_var(branch, a, b):
+  """libsecp256k1's secp256k1_gej_add_zinv_var"""
+  bzinv = b.Z^(-1)
+  if branch == 0:
+    return (constraints(), constraints(nonzero={b.Infinity : 'b_infinite'}), a)
+  if branch == 1:
+    bzinv2 = bzinv^2
+    bzinv3 = bzinv2 * bzinv
+    rx = b.X * bzinv2
+    ry = b.Y * bzinv3
+    rz = 1
+    return (constraints(), constraints(zero={b.Infinity : 'b_finite'}, nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz))
+  azz = a.Z * bzinv
+  z12 = azz^2
+  u1 = a.X
+  u2 = b.X * z12
+  s1 = a.Y
+  s2 = b.Y * z12
+  s2 = s2 * azz
+  h = -u1
+  h = h + u2
+  i = -s1
+  i = i + s2
+  if branch == 2:
+    r = formula_secp256k1_gej_double_var(a)
+    return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
+  if branch == 3:
+    return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
+  i2 = i^2
+  h2 = h^2
+  h3 = h * h2
+  rz = a.Z
+  rz = rz * h
+  t = u1 * h2
+  rx = t
+  rx = rx * 2
+  rx = rx + h3
+  rx = -rx
+  rx = rx + i2
+  ry = -rx
+  ry = ry + t
+  ry = ry * i
+  h3 = h3 * s1
+  h3 = -h3
+  ry = ry + h3
+  return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
+
+def formula_secp256k1_gej_add_ge(branch, a, b):
+  """libsecp256k1's secp256k1_gej_add_ge"""
+  zeroes = {}
+  nonzeroes = {}
+  a_infinity = False
+  if (branch & 4) != 0:
+    nonzeroes.update({a.Infinity : 'a_infinite'})
+    a_infinity = True
+  else:
+    zeroes.update({a.Infinity : 'a_finite'})
+  zz = a.Z^2
+  u1 = a.X
+  u2 = b.X * zz
+  s1 = a.Y
+  s2 = b.Y * zz
+  s2 = s2 * a.Z
+  t = u1
+  t = t + u2
+  m = s1
+  m = m + s2
+  rr = t^2
+  m_alt = -u2
+  tt = u1 * m_alt
+  rr = rr + tt
+  degenerate = (branch & 3) == 3
+  if (branch & 1) != 0:
+    zeroes.update({m : 'm_zero'})
+  else:
+    nonzeroes.update({m : 'm_nonzero'})
+  if (branch & 2) != 0:
+    zeroes.update({rr : 'rr_zero'})
+  else:
+    nonzeroes.update({rr : 'rr_nonzero'})
+  rr_alt = s1
+  rr_alt = rr_alt * 2
+  m_alt = m_alt + u1
+  if not degenerate:
+    rr_alt = rr
+    m_alt = m
+  n = m_alt^2
+  q = n * t
+  n = n^2
+  if degenerate:
+    n = m
+  t = rr_alt^2
+  rz = a.Z * m_alt
+  infinity = False
+  if (branch & 8) != 0:
+    if not a_infinity:
+      infinity = True
+    zeroes.update({rz : 'r.z=0'})
+  else:
+    nonzeroes.update({rz : 'r.z!=0'})
+  rz = rz * 2
+  q = -q
+  t = t + q
+  rx = t
+  t = t * 2
+  t = t + q
+  t = t * rr_alt
+  t = t + n
+  ry = -t
+  rx = rx * 4
+  ry = ry * 4
+  if a_infinity:
+    rx = b.X
+    ry = b.Y
+    rz = 1
+  if infinity:
+    return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), point_at_infinity())
+  return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), jacobianpoint(rx, ry, rz))
+
+def formula_secp256k1_gej_add_ge_old(branch, a, b):
+  """libsecp256k1's old secp256k1_gej_add_ge, which fails when ay+by=0 but ax!=bx"""
+  a_infinity = (branch & 1) != 0
+  zero = {}
+  nonzero = {}
+  if a_infinity:
+    nonzero.update({a.Infinity : 'a_infinite'})
+  else:
+    zero.update({a.Infinity : 'a_finite'})
+  zz = a.Z^2
+  u1 = a.X
+  u2 = b.X * zz
+  s1 = a.Y
+  s2 = b.Y * zz
+  s2 = s2 * a.Z
+  z = a.Z
+  t = u1
+  t = t + u2
+  m = s1
+  m = m + s2
+  n = m^2
+  q = n * t
+  n = n^2
+  rr = t^2
+  t = u1 * u2
+  t = -t
+  rr = rr + t
+  t = rr^2
+  rz = m * z
+  infinity = False
+  if (branch & 2) != 0:
+    if not a_infinity:
+      infinity = True
+    else:
+      return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(nonzero={z : 'conflict_a'}, zero={z : 'conflict_b'}), point_at_infinity())
+    zero.update({rz : 'r.z=0'})
+  else:
+    nonzero.update({rz : 'r.z!=0'})
+  rz = rz * (0 if a_infinity else 2)
+  rx = t
+  q = -q
+  rx = rx + q
+  q = q * 3
+  t = t * 2
+  t = t + q
+  t = t * rr
+  t = t + n
+  ry = -t
+  rx = rx * (0 if a_infinity else 4)
+  ry = ry * (0 if a_infinity else 4)
+  t = b.X
+  t = t * (1 if a_infinity else 0)
+  rx = rx + t
+  t = b.Y
+  t = t * (1 if a_infinity else 0)
+  ry = ry + t
+  t = (1 if a_infinity else 0)
+  rz = rz + t
+  if infinity:
+    return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), point_at_infinity())
+  return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz))
+
+if __name__ == "__main__":
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var)
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var)
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var)
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge)
+  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old)
+
+  if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive":
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43)
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43)
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43)
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43)
+    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43)
diff --git a/src/secp256k1/sage/weierstrass_prover.sage b/src/secp256k1/sage/weierstrass_prover.sage
new file mode 100644
index 0000000000..03ef2ec901
--- /dev/null
+++ b/src/secp256k1/sage/weierstrass_prover.sage
@@ -0,0 +1,264 @@
+# Prover implementation for Weierstrass curves of the form
+# y^2 = x^3 + A * x + B, specifically with a = 0 and b = 7, with group laws
+# operating on affine and Jacobian coordinates, including the point at infinity
+# represented by a 4th variable in coordinates.
+
+load("group_prover.sage")
+
+
+class affinepoint:
+  def __init__(self, x, y, infinity=0):
+    self.x = x
+    self.y = y
+    self.infinity = infinity
+  def __str__(self):
+    return "affinepoint(x=%s,y=%s,inf=%s)" % (self.x, self.y, self.infinity)
+
+
+class jacobianpoint:
+  def __init__(self, x, y, z, infinity=0):
+    self.X = x
+    self.Y = y
+    self.Z = z
+    self.Infinity = infinity
+  def __str__(self):
+    return "jacobianpoint(X=%s,Y=%s,Z=%s,inf=%s)" % (self.X, self.Y, self.Z, self.Infinity)
+
+
+def point_at_infinity():
+  return jacobianpoint(1, 1, 1, 1)
+
+
+def negate(p):
+  if p.__class__ == affinepoint:
+    return affinepoint(p.x, -p.y)
+  if p.__class__ == jacobianpoint:
+    return jacobianpoint(p.X, -p.Y, p.Z)
+  assert(False)
+
+
+def on_weierstrass_curve(A, B, p):
+  """Return a set of zero-expressions for an affine point to be on the curve"""
+  return constraints(zero={p.x^3 + A*p.x + B - p.y^2: 'on_curve'})
+
+
+def tangential_to_weierstrass_curve(A, B, p12, p3):
+  """Return a set of zero-expressions for ((x12,y12),(x3,y3)) to be a line that is tangential to the curve at (x12,y12)"""
+  return constraints(zero={
+    (p12.y - p3.y) * (p12.y * 2) - (p12.x^2 * 3 + A) * (p12.x - p3.x): 'tangential_to_curve'
+  })
+
+
+def colinear(p1, p2, p3):
+  """Return a set of zero-expressions for ((x1,y1),(x2,y2),(x3,y3)) to be collinear"""
+  return constraints(zero={
+    (p1.y - p2.y) * (p1.x - p3.x) - (p1.y - p3.y) * (p1.x - p2.x): 'colinear_1',
+    (p2.y - p3.y) * (p2.x - p1.x) - (p2.y - p1.y) * (p2.x - p3.x): 'colinear_2',
+    (p3.y - p1.y) * (p3.x - p2.x) - (p3.y - p2.y) * (p3.x - p1.x): 'colinear_3'
+  })
+
+
+def good_affine_point(p):
+  return constraints(nonzero={p.x : 'nonzero_x', p.y : 'nonzero_y'})
+
+
+def good_jacobian_point(p):
+  return constraints(nonzero={p.X : 'nonzero_X', p.Y : 'nonzero_Y', p.Z^6 : 'nonzero_Z'})
+
+
+def good_point(p):
+  return constraints(nonzero={p.Z^6 : 'nonzero_X'})
+
+
+def finite(p, *affine_fns):
+  con = good_point(p) + constraints(zero={p.Infinity : 'finite_point'})
+  if p.Z != 0:
+    return con + reduce(lambda a, b: a + b, (f(affinepoint(p.X / p.Z^2, p.Y / p.Z^3)) for f in affine_fns), con)
+  else:
+    return con
+
+def infinite(p):
+  return constraints(nonzero={p.Infinity : 'infinite_point'})
+
+
+def law_jacobian_weierstrass_add(A, B, pa, pb, pA, pB, pC):
+  """Check whether the passed set of coordinates is a valid Jacobian add, given assumptions"""
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pa) +
+               on_weierstrass_curve(A, B, pb) +
+               finite(pA) +
+               finite(pB) +
+               constraints(nonzero={pa.x - pb.x : 'different_x'}))
+  require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) +
+             colinear(pa, pb, negate(pc))))
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_double(A, B, pa, pb, pA, pB, pC):
+  """Check whether the passed set of coordinates is a valid Jacobian doubling, given assumptions"""
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pa) +
+               on_weierstrass_curve(A, B, pb) +
+               finite(pA) +
+               finite(pB) +
+               constraints(zero={pa.x - pb.x : 'equal_x', pa.y - pb.y : 'equal_y'}))
+  require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) +
+             tangential_to_weierstrass_curve(A, B, pa, negate(pc))))
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_add_opposites(A, B, pa, pb, pA, pB, pC):
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pa) +
+               on_weierstrass_curve(A, B, pb) +
+               finite(pA) +
+               finite(pB) +
+               constraints(zero={pa.x - pb.x : 'equal_x', pa.y + pb.y : 'opposite_y'}))
+  require = infinite(pC)
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_add_infinite_a(A, B, pa, pb, pA, pB, pC):
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pb) +
+               infinite(pA) +
+               finite(pB))
+  require = finite(pC, lambda pc: constraints(zero={pc.x - pb.x : 'c.x=b.x', pc.y - pb.y : 'c.y=b.y'}))
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_add_infinite_b(A, B, pa, pb, pA, pB, pC):
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               on_weierstrass_curve(A, B, pa) +
+               infinite(pB) +
+               finite(pA))
+  require = finite(pC, lambda pc: constraints(zero={pc.x - pa.x : 'c.x=a.x', pc.y - pa.y : 'c.y=a.y'}))
+  return (assumeLaw, require)
+
+
+def law_jacobian_weierstrass_add_infinite_ab(A, B, pa, pb, pA, pB, pC):
+  assumeLaw = (good_affine_point(pa) +
+               good_affine_point(pb) +
+               good_jacobian_point(pA) +
+               good_jacobian_point(pB) +
+               infinite(pA) +
+               infinite(pB))
+  require = infinite(pC)
+  return (assumeLaw, require)
+
+
+laws_jacobian_weierstrass = {
+  'add': law_jacobian_weierstrass_add,
+  'double': law_jacobian_weierstrass_double,
+  'add_opposite': law_jacobian_weierstrass_add_opposites,
+  'add_infinite_a': law_jacobian_weierstrass_add_infinite_a,
+  'add_infinite_b': law_jacobian_weierstrass_add_infinite_b,
+  'add_infinite_ab': law_jacobian_weierstrass_add_infinite_ab
+}
+
+
+def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p):
+  """Verify an implementation of addition of Jacobian points on a Weierstrass curve, by executing and validating the result for every possible addition in a prime field"""
+  F = Integers(p)
+  print "Formula %s on Z%i:" % (name, p)
+  points = []
+  for x in xrange(0, p):
+    for y in xrange(0, p):
+      point = affinepoint(F(x), F(y))
+      r, e = concrete_verify(on_weierstrass_curve(A, B, point))
+      if r:
+        points.append(point)
+
+  for za in xrange(1, p):
+    for zb in xrange(1, p):
+      for pa in points:
+        for pb in points:
+          for ia in xrange(2):
+            for ib in xrange(2):
+              pA = jacobianpoint(pa.x * F(za)^2, pa.y * F(za)^3, F(za), ia)
+              pB = jacobianpoint(pb.x * F(zb)^2, pb.y * F(zb)^3, F(zb), ib)
+              for branch in xrange(0, branches):
+                assumeAssert, assumeBranch, pC = formula(branch, pA, pB)
+                pC.X = F(pC.X)
+                pC.Y = F(pC.Y)
+                pC.Z = F(pC.Z)
+                pC.Infinity = F(pC.Infinity)
+                r, e = concrete_verify(assumeAssert + assumeBranch)
+                if r:
+                  match = False
+                  for key in laws_jacobian_weierstrass:
+                    assumeLaw, require = laws_jacobian_weierstrass[key](A, B, pa, pb, pA, pB, pC)
+                    r, e = concrete_verify(assumeLaw)
+                    if r:
+                      if match:
+                        print "  multiple branches for (%s,%s,%s,%s) + (%s,%s,%s,%s)" % (pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity)
+                      else:
+                        match = True
+                      r, e = concrete_verify(require)
+                      if not r:
+                        print "  failure in branch %i for (%s,%s,%s,%s) + (%s,%s,%s,%s) = (%s,%s,%s,%s): %s" % (branch, pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity, pC.X, pC.Y, pC.Z, pC.Infinity, e)
+  print
+
+
+def check_symbolic_function(R, assumeAssert, assumeBranch, f, A, B, pa, pb, pA, pB, pC):
+  assumeLaw, require = f(A, B, pa, pb, pA, pB, pC)
+  return check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require)
+
+def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula):
+  """Verify an implementation of addition of Jacobian points on a Weierstrass curve symbolically"""
+  R.<ax,bx,ay,by,Az,Bz,Ai,Bi> = PolynomialRing(QQ,8,order='invlex')
+  lift = lambda x: fastfrac(R,x)
+  ax = lift(ax)
+  ay = lift(ay)
+  Az = lift(Az)
+  bx = lift(bx)
+  by = lift(by)
+  Bz = lift(Bz)
+  Ai = lift(Ai)
+  Bi = lift(Bi)
+
+  pa = affinepoint(ax, ay, Ai)
+  pb = affinepoint(bx, by, Bi)
+  pA = jacobianpoint(ax * Az^2, ay * Az^3, Az, Ai)
+  pB = jacobianpoint(bx * Bz^2, by * Bz^3, Bz, Bi)
+
+  res = {}
+
+  for key in laws_jacobian_weierstrass:
+    res[key] = []
+
+  print ("Formula " + name + ":")
+  count = 0
+  for branch in xrange(branches):
+    assumeFormula, assumeBranch, pC = formula(branch, pA, pB)
+    pC.X = lift(pC.X)
+    pC.Y = lift(pC.Y)
+    pC.Z = lift(pC.Z)
+    pC.Infinity = lift(pC.Infinity)
+
+    for key in laws_jacobian_weierstrass:
+      res[key].append((check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC), branch))
+
+  for key in res:
+    print "  %s:" % key
+    val = res[key]
+    for x in val:
+      if x[0] is not None:
+        print "    branch %i: %s" % (x[1], x[0])
+
+  print
diff --git a/src/secp256k1/src/asm/field_10x26_arm.s b/src/secp256k1/src/asm/field_10x26_arm.s
new file mode 100644
index 0000000000..5df561f2fc
--- /dev/null
+++ b/src/secp256k1/src/asm/field_10x26_arm.s
@@ -0,0 +1,919 @@
+@ vim: set tabstop=8 softtabstop=8 shiftwidth=8 noexpandtab syntax=armasm:
+/**********************************************************************
+ * Copyright (c) 2014 Wladimir J. van der Laan                        *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+/*
+ARM implementation of field_10x26 inner loops.
+
+Note:
+
+- To avoid unnecessary loads and make use of available registers, two
+  'passes' have every time been interleaved, with the odd passes accumulating c' and d' 
+  which will be added to c and d respectively in the the even passes
+
+*/
+
+	.syntax unified
+	.arch armv7-a
+	@ eabi attributes - see readelf -A
+	.eabi_attribute 8, 1  @ Tag_ARM_ISA_use = yes
+	.eabi_attribute 9, 0  @ Tag_Thumb_ISA_use = no
+	.eabi_attribute 10, 0 @ Tag_FP_arch = none
+	.eabi_attribute 24, 1 @ Tag_ABI_align_needed = 8-byte
+	.eabi_attribute 25, 1 @ Tag_ABI_align_preserved = 8-byte, except leaf SP
+	.eabi_attribute 30, 2 @ Tag_ABI_optimization_goals = Agressive Speed
+	.eabi_attribute 34, 1 @ Tag_CPU_unaligned_access = v6
+	.text
+
+	@ Field constants
+	.set field_R0, 0x3d10
+	.set field_R1, 0x400
+	.set field_not_M, 0xfc000000	@ ~M = ~0x3ffffff
+
+	.align	2
+	.global secp256k1_fe_mul_inner
+	.type	secp256k1_fe_mul_inner, %function
+	@ Arguments:
+	@  r0  r      Restrict: can overlap with a, not with b
+	@  r1  a
+	@  r2  b
+	@ Stack (total 4+10*4 = 44)
+	@  sp + #0        saved 'r' pointer
+	@  sp + #4 + 4*X  t0,t1,t2,t3,t4,t5,t6,t7,u8,t9
+secp256k1_fe_mul_inner:
+	stmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14}
+	sub	sp, sp, #48			@ frame=44 + alignment
+	str     r0, [sp, #0]			@ save result address, we need it only at the end
+
+	/******************************************
+	 * Main computation code.
+	 ******************************************
+
+	Allocation:
+	    r0,r14,r7,r8   scratch
+	    r1       a (pointer)
+	    r2       b (pointer)
+	    r3:r4    c
+	    r5:r6    d
+	    r11:r12  c'
+	    r9:r10   d'
+
+	Note: do not write to r[] here, it may overlap with a[]
+	*/
+
+	/* A - interleaved with B */
+	ldr	r7, [r1, #0*4]			@ a[0]
+	ldr	r8, [r2, #9*4]			@ b[9]
+	ldr	r0, [r1, #1*4]			@ a[1]
+	umull	r5, r6, r7, r8			@ d = a[0] * b[9]
+	ldr	r14, [r2, #8*4]			@ b[8]
+	umull	r9, r10, r0, r8			@ d' = a[1] * b[9]
+	ldr	r7, [r1, #2*4]			@ a[2]
+	umlal	r5, r6, r0, r14			@ d += a[1] * b[8]
+	ldr	r8, [r2, #7*4] 			@ b[7]
+	umlal	r9, r10, r7, r14		@ d' += a[2] * b[8]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal	r5, r6, r7, r8   		@ d += a[2] * b[7]
+	ldr	r14, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r8  		@ d' += a[3] * b[7]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal	r5, r6, r0, r14   		@ d += a[3] * b[6]
+	ldr	r8, [r2, #5*4]   		@ b[5]
+	umlal	r9, r10, r7, r14  		@ d' += a[4] * b[6]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal	r5, r6, r7, r8   		@ d += a[4] * b[5]
+	ldr	r14, [r2, #4*4]   		@ b[4]
+	umlal	r9, r10, r0, r8  		@ d' += a[5] * b[5]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r5, r6, r0, r14   		@ d += a[5] * b[4]
+	ldr	r8, [r2, #3*4]   		@ b[3]
+	umlal	r9, r10, r7, r14  		@ d' += a[6] * b[4]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r8   		@ d += a[6] * b[3]
+	ldr	r14, [r2, #2*4]   		@ b[2]
+	umlal	r9, r10, r0, r8  		@ d' += a[7] * b[3]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r14   		@ d += a[7] * b[2]
+	ldr	r8, [r2, #1*4]   		@ b[1]
+	umlal	r9, r10, r7, r14  		@ d' += a[8] * b[2]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r8   		@ d += a[8] * b[1]
+	ldr	r14, [r2, #0*4]   		@ b[0]
+	umlal	r9, r10, r0, r8  		@ d' += a[9] * b[1]
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	umlal	r5, r6, r0, r14   		@ d += a[9] * b[0]
+	@ r7,r14 used in B
+
+	bic	r0, r5, field_not_M 		@ t9 = d & M
+	str     r0, [sp, #4 + 4*9]
+	mov	r5, r5, lsr #26     		@ d >>= 26 
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+
+	/* B */
+	umull	r3, r4, r7, r14   		@ c = a[0] * b[0]
+	adds	r5, r5, r9       		@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u0 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u0 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t0 = c & M
+	str	r14, [sp, #4 + 0*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u0 * R1
+	umlal   r3, r4, r0, r14
+
+	/* C - interleaved with D */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[2]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[1]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[0]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal	r5, r6, r7, r14   		@ d += a[2] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14   		@ d' = a[3] * b[9]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal	r5, r6, r0, r8   		@ d += a[3] * b[8]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[4] * b[8]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal	r5, r6, r7, r14   		@ d += a[4] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r14   		@ d' += a[5] * b[7]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r5, r6, r0, r8   		@ d += a[5] * b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umlal	r9, r10, r7, r8   		@ d' += a[6] * b[6]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r14   		@ d += a[6] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal	r9, r10, r0, r14   		@ d' += a[7] * b[5]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r8   		@ d += a[7] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[4]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal	r9, r10, r0, r14   		@ d' += a[9] * b[3]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[2]
+
+	bic	r0, r5, field_not_M 		@ u1 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u1 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t1 = c & M
+	str	r14, [sp, #4 + 1*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u1 * R1
+	umlal   r3, r4, r0, r14
+
+	/* D */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u2 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u2 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t2 = c & M
+	str	r14, [sp, #4 + 2*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u2 * R1
+	umlal   r3, r4, r0, r14
+
+	/* E - interleaved with F */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[4]
+	ldr	r8, [r2, #3*4]   		@ b[3]
+	umlal   r3, r4, r7, r8   		@ c += a[0] * b[3]
+	ldr	r7, [r1, #1*4]   		@ a[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[1] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r3, r4, r7, r8   		@ c += a[1] * b[2]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[2]
+	ldr	r8, [r2, #1*4]   		@ b[1]
+	umlal   r3, r4, r7, r8   		@ c += a[2] * b[1]
+	ldr	r7, [r1, #3*4]   		@ a[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[3] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r3, r4, r7, r8   		@ c += a[3] * b[0]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[0]
+	ldr	r8, [r2, #9*4]   		@ b[9]
+	umlal	r5, r6, r7, r8   		@ d += a[4] * b[9]
+	ldr	r7, [r1, #5*4]   		@ a[5]
+	umull	r9, r10, r7, r8   		@ d' = a[5] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umlal	r5, r6, r7, r8   		@ d += a[5] * b[8]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r9, r10, r7, r8   		@ d' += a[6] * b[8]
+	ldr	r8, [r2, #7*4]   		@ b[7]
+	umlal	r5, r6, r7, r8   		@ d += a[6] * b[7]
+	ldr	r7, [r1, #7*4]   		@ a[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[7] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r5, r6, r7, r8   		@ d += a[7] * b[6]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[6]
+	ldr	r8, [r2, #5*4]   		@ b[5]
+	umlal	r5, r6, r7, r8   		@ d += a[8] * b[5]
+	ldr	r7, [r1, #9*4]   		@ a[9]
+	umlal	r9, r10, r7, r8   		@ d' += a[9] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal	r5, r6, r7, r8   		@ d += a[9] * b[4]
+
+	bic	r0, r5, field_not_M 		@ u3 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u3 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t3 = c & M
+	str	r14, [sp, #4 + 3*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u3 * R1
+	umlal   r3, r4, r0, r14
+
+	/* F */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u4 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u4 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t4 = c & M
+	str	r14, [sp, #4 + 4*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u4 * R1
+	umlal   r3, r4, r0, r14
+
+	/* G - interleaved with H */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[6]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[5]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[4]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal   r3, r4, r7, r14   		@ c += a[2] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r11, r12, r0, r14   		@ c' += a[3] * b[3]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r3, r4, r0, r8   		@ c += a[3] * b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[2]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal   r3, r4, r7, r14   		@ c += a[4] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[5] * b[1]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal   r3, r4, r0, r8   		@ c += a[5] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[6] * b[0]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r14   		@ d += a[6] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14   		@ d' = a[7] * b[9]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r8   		@ d += a[7] * b[8]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[8]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r14   		@ d' += a[9] * b[7]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[6]
+
+	bic	r0, r5, field_not_M 		@ u5 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u5 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t5 = c & M
+	str	r14, [sp, #4 + 5*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u5 * R1
+	umlal   r3, r4, r0, r14
+
+	/* H */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u6 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u6 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t6 = c & M
+	str	r14, [sp, #4 + 6*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u6 * R1
+	umlal   r3, r4, r0, r14
+
+	/* I - interleaved with J */
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umull   r11, r12, r7, r8   		@ c' = a[0] * b[8]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[7]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[6]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal   r3, r4, r7, r14   		@ c += a[2] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal   r11, r12, r0, r14   		@ c' += a[3] * b[5]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r3, r4, r0, r8   		@ c += a[3] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[4]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal   r3, r4, r7, r14   		@ c += a[4] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r11, r12, r0, r14   		@ c' += a[5] * b[3]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal   r3, r4, r0, r8   		@ c += a[5] * b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[6] * b[2]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal   r3, r4, r7, r14   		@ c += a[6] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[7] * b[1]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal   r3, r4, r0, r8   		@ c += a[7] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[8] * b[0]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14  		@ d' = a[9] * b[9]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[8]
+
+	bic	r0, r5, field_not_M 		@ u7 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u7 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t7 = c & M
+	str	r14, [sp, #4 + 7*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u7 * R1
+	umlal   r3, r4, r0, r14
+
+	/* J */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u8 = d & M
+	str	r0, [sp, #4 + 8*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u8 * R0
+	umlal   r3, r4, r0, r14
+
+	/******************************************
+	 * compute and write back result
+	 ******************************************
+	Allocation:
+	    r0    r
+	    r3:r4 c
+	    r5:r6 d
+	    r7    t0
+	    r8    t1
+	    r9    t2
+	    r11   u8
+	    r12   t9
+	    r1,r2,r10,r14 scratch
+
+	Note: do not read from a[] after here, it may overlap with r[]
+	*/
+	ldr	r0, [sp, #0]
+	add	r1, sp, #4 + 3*4		@ r[3..7] = t3..7, r11=u8, r12=t9
+	ldmia	r1, {r2,r7,r8,r9,r10,r11,r12}
+	add	r1, r0, #3*4
+	stmia	r1, {r2,r7,r8,r9,r10}
+
+	bic	r2, r3, field_not_M 		@ r[8] = c & M
+	str	r2, [r0, #8*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u8 * R1
+	umlal   r3, r4, r11, r14
+	movw    r14, field_R0			@ c += d * R0
+	umlal   r3, r4, r5, r14
+	adds	r3, r3, r12			@ c += t9
+	adc	r4, r4, #0
+
+	add	r1, sp, #4 + 0*4		@ r7,r8,r9 = t0,t1,t2
+	ldmia	r1, {r7,r8,r9}
+
+	ubfx	r2, r3, #0, #22     		@ r[9] = c & (M >> 4)
+	str	r2, [r0, #9*4]
+	mov	r3, r3, lsr #22     		@ c >>= 22
+	orr	r3, r3, r4, asl #10
+	mov     r4, r4, lsr #22
+	movw    r14, field_R1 << 4   		@ c += d * (R1 << 4)
+	umlal   r3, r4, r5, r14
+
+	movw    r14, field_R0 >> 4   		@ d = c * (R0 >> 4) + t0 (64x64 multiply+add)
+	umull	r5, r6, r3, r14			@ d = c.lo * (R0 >> 4)
+	adds	r5, r5, r7	    		@ d.lo += t0
+	mla	r6, r14, r4, r6			@ d.hi += c.hi * (R0 >> 4)
+	adc	r6, r6, 0	     		@ d.hi += carry
+
+	bic	r2, r5, field_not_M 		@ r[0] = d & M
+	str	r2, [r0, #0*4]
+
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	
+	movw    r14, field_R1 >> 4   		@ d += c * (R1 >> 4) + t1 (64x64 multiply+add)
+	umull	r1, r2, r3, r14       		@ tmp = c.lo * (R1 >> 4)
+	adds	r5, r5, r8	    		@ d.lo += t1
+	adc	r6, r6, #0	    		@ d.hi += carry
+	adds	r5, r5, r1	    		@ d.lo += tmp.lo
+	mla	r2, r14, r4, r2      		@ tmp.hi += c.hi * (R1 >> 4)
+	adc	r6, r6, r2	   		@ d.hi += carry + tmp.hi
+
+	bic	r2, r5, field_not_M 		@ r[1] = d & M
+	str	r2, [r0, #1*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 (ignore hi)
+	orr	r5, r5, r6, asl #6
+
+	add	r5, r5, r9	  		@ d += t2
+	str	r5, [r0, #2*4]      		@ r[2] = d
+
+	add	sp, sp, #48
+	ldmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc}
+	.size	secp256k1_fe_mul_inner, .-secp256k1_fe_mul_inner
+
+	.align	2
+	.global secp256k1_fe_sqr_inner
+	.type	secp256k1_fe_sqr_inner, %function
+	@ Arguments:
+	@  r0  r	 Can overlap with a
+	@  r1  a
+	@ Stack (total 4+10*4 = 44)
+	@  sp + #0        saved 'r' pointer
+	@  sp + #4 + 4*X  t0,t1,t2,t3,t4,t5,t6,t7,u8,t9
+secp256k1_fe_sqr_inner:
+	stmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14}
+	sub	sp, sp, #48			@ frame=44 + alignment
+	str     r0, [sp, #0]			@ save result address, we need it only at the end
+	/******************************************
+	 * Main computation code.
+	 ******************************************
+
+	Allocation:
+	    r0,r14,r2,r7,r8   scratch
+	    r1       a (pointer)
+	    r3:r4    c
+	    r5:r6    d
+	    r11:r12  c'
+	    r9:r10   d'
+
+	Note: do not write to r[] here, it may overlap with a[]
+	*/
+	/* A interleaved with B */
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	ldr	r7, [r1, #0*4]			@ a[0]
+	mov	r0, r0, asl #1
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umull	r3, r4, r7, r7			@ c = a[0] * a[0]
+	ldr	r8, [r1, #8*4]			@ a[8]
+	mov	r7, r7, asl #1
+	umull	r5, r6, r7, r14			@ d = a[0]*2 * a[9]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umull	r9, r10, r0, r14		@ d' = a[1]*2 * a[9]
+	ldr	r14, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r8			@ d += a[1]*2 * a[8]
+	mov	r7, r7, asl #1
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	umlal	r9, r10, r7, r8			@ d' += a[2]*2 * a[8]
+	ldr	r8, [r1, #6*4]			@ a[6]
+	umlal	r5, r6, r7, r14			@ d += a[2]*2 * a[7]
+	mov	r0, r0, asl #1
+	ldr	r7, [r1, #4*4]			@ a[4]*2
+	umlal	r9, r10, r0, r14		@ d' += a[3]*2 * a[7]
+	ldr	r14, [r1, #5*4]			@ a[5]
+	mov	r7, r7, asl #1
+	umlal	r5, r6, r0, r8			@ d += a[3]*2 * a[6]
+	umlal	r9, r10, r7, r8			@ d' += a[4]*2 * a[6]
+	umlal	r5, r6, r7, r14			@ d += a[4]*2 * a[5]
+	umlal	r9, r10, r14, r14		@ d' += a[5] * a[5]
+
+	bic	r0, r5, field_not_M 		@ t9 = d & M
+	str     r0, [sp, #4 + 9*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+
+	/* B */
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u0 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u0 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t0 = c & M
+	str	r14, [sp, #4 + 0*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u0 * R1
+	umlal   r3, r4, r0, r14
+
+	/* C interleaved with D */
+	ldr	r0, [r1, #0*4]			@ a[0]*2
+	ldr	r14, [r1, #1*4]			@ a[1]
+	mov	r0, r0, asl #1
+	ldr	r8, [r1, #2*4]			@ a[2]
+	umlal	r3, r4, r0, r14			@ c += a[0]*2 * a[1]
+	mov	r7, r8, asl #1                  @ a[2]*2
+	umull	r11, r12, r14, r14		@ c' = a[1] * a[1]
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umlal	r11, r12, r0, r8		@ c' += a[0]*2 * a[2]
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	ldr	r8, [r1, #8*4]			@ a[8]
+	umlal	r5, r6, r7, r14			@ d += a[2]*2 * a[9]
+	mov	r0, r0, asl #1
+	ldr	r7, [r1, #4*4]			@ a[4]*2
+	umull	r9, r10, r0, r14		@ d' = a[3]*2 * a[9]
+	ldr	r14, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r8			@ d += a[3]*2 * a[8]
+	mov	r7, r7, asl #1
+	ldr	r0, [r1, #5*4]			@ a[5]*2
+	umlal	r9, r10, r7, r8			@ d' += a[4]*2 * a[8]
+	ldr	r8, [r1, #6*4]			@ a[6]
+	mov	r0, r0, asl #1
+	umlal	r5, r6, r7, r14			@ d += a[4]*2 * a[7]
+	umlal	r9, r10, r0, r14		@ d' += a[5]*2 * a[7]
+	umlal	r5, r6, r0, r8			@ d += a[5]*2 * a[6]
+	umlal	r9, r10, r8, r8			@ d' += a[6] * a[6]
+
+	bic	r0, r5, field_not_M 		@ u1 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u1 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t1 = c & M
+	str	r14, [sp, #4 + 1*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u1 * R1
+	umlal   r3, r4, r0, r14
+
+	/* D */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u2 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u2 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t2 = c & M
+	str	r14, [sp, #4 + 2*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u2 * R1
+	umlal   r3, r4, r0, r14
+
+	/* E interleaved with F */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	ldr	r14, [r1, #2*4]			@ a[2]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #3*4]			@ a[3]
+	ldr	r2, [r1, #4*4]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[3]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[4]
+	mov	r2, r2, asl #1			@ a[4]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[3]
+	ldr	r8, [r1, #9*4]			@ a[9]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[2]
+	ldr	r0, [r1, #5*4]			@ a[5]*2
+	umlal	r11, r12, r14, r14		@ c' += a[2] * a[2]
+	ldr	r14, [r1, #8*4]			@ a[8]
+	mov	r0, r0, asl #1
+	umlal	r5, r6, r2, r8			@ d += a[4]*2 * a[9]
+	ldr	r7, [r1, #6*4]			@ a[6]*2
+	umull	r9, r10, r0, r8			@ d' = a[5]*2 * a[9]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r14			@ d += a[5]*2 * a[8]
+	umlal	r9, r10, r7, r14		@ d' += a[6]*2 * a[8]
+	umlal	r5, r6, r7, r8			@ d += a[6]*2 * a[7]
+	umlal	r9, r10, r8, r8			@ d' += a[7] * a[7]
+
+	bic	r0, r5, field_not_M 		@ u3 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u3 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t3 = c & M
+	str	r14, [sp, #4 + 3*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u3 * R1
+	umlal   r3, r4, r0, r14
+
+	/* F */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u4 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u4 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t4 = c & M
+	str	r14, [sp, #4 + 4*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u4 * R1
+	umlal   r3, r4, r0, r14
+
+	/* G interleaved with H */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #5*4]			@ a[5]
+	ldr	r2, [r1, #6*4]			@ a[6]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[5]
+	ldr	r14, [r1, #4*4]			@ a[4]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[6]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[5]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #3*4]			@ a[3]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[4]
+	mov	r0, r2, asl #1			@ a[6]*2
+	umlal	r11, r12, r7, r14		@ c' += a[2]*2 * a[4]
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umlal	r3, r4, r7, r8			@ c += a[2]*2 * a[3]
+	ldr	r7, [r1, #7*4]			@ a[7]*2
+	umlal	r11, r12, r8, r8		@ c' += a[3] * a[3]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #8*4]			@ a[8]
+	umlal	r5, r6, r0, r14			@ d += a[6]*2 * a[9]
+	umull	r9, r10, r7, r14		@ d' = a[7]*2 * a[9]
+	umlal	r5, r6, r7, r8			@ d += a[7]*2 * a[8]
+	umlal	r9, r10, r8, r8			@ d' += a[8] * a[8]
+
+	bic	r0, r5, field_not_M 		@ u5 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u5 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t5 = c & M
+	str	r14, [sp, #4 + 5*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u5 * R1
+	umlal   r3, r4, r0, r14
+
+	/* H */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u6 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u6 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t6 = c & M
+	str	r14, [sp, #4 + 6*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u6 * R1
+	umlal   r3, r4, r0, r14
+
+	/* I interleaved with J */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #7*4]			@ a[7]
+	ldr	r2, [r1, #8*4]			@ a[8]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[7]
+	ldr	r14, [r1, #6*4]			@ a[6]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[8]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[7]
+	ldr	r8, [r1, #5*4]			@ a[5]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[6]
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	mov	r7, r7, asl #1
+	umlal	r11, r12, r7, r14		@ c' += a[2]*2 * a[6]
+	ldr	r14, [r1, #4*4]			@ a[4]
+	mov	r0, r0, asl #1
+	umlal	r3, r4, r7, r8			@ c += a[2]*2 * a[5]
+	mov	r2, r2, asl #1			@ a[8]*2
+	umlal	r11, r12, r0, r8		@ c' += a[3]*2 * a[5]
+	umlal	r3, r4, r0, r14			@ c += a[3]*2 * a[4]
+	umlal	r11, r12, r14, r14		@ c' += a[4] * a[4]
+	ldr	r8, [r1, #9*4]			@ a[9]
+	umlal	r5, r6, r2, r8			@ d += a[8]*2 * a[9]
+	@ r8 will be used in J
+
+	bic	r0, r5, field_not_M 		@ u7 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u7 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t7 = c & M
+	str	r14, [sp, #4 + 7*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u7 * R1
+	umlal   r3, r4, r0, r14
+
+	/* J */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	umlal	r5, r6, r8, r8			@ d += a[9] * a[9]
+
+	bic	r0, r5, field_not_M 		@ u8 = d & M
+	str	r0, [sp, #4 + 8*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u8 * R0
+	umlal   r3, r4, r0, r14
+
+	/******************************************
+	 * compute and write back result
+	 ******************************************
+	Allocation:
+	    r0    r
+	    r3:r4 c
+	    r5:r6 d
+	    r7    t0
+	    r8    t1
+	    r9    t2
+	    r11   u8
+	    r12   t9
+	    r1,r2,r10,r14 scratch
+
+	Note: do not read from a[] after here, it may overlap with r[]
+	*/
+	ldr	r0, [sp, #0]
+	add	r1, sp, #4 + 3*4		@ r[3..7] = t3..7, r11=u8, r12=t9
+	ldmia	r1, {r2,r7,r8,r9,r10,r11,r12}
+	add	r1, r0, #3*4
+	stmia	r1, {r2,r7,r8,r9,r10}
+
+	bic	r2, r3, field_not_M 		@ r[8] = c & M
+	str	r2, [r0, #8*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u8 * R1
+	umlal   r3, r4, r11, r14
+	movw    r14, field_R0			@ c += d * R0
+	umlal   r3, r4, r5, r14
+	adds	r3, r3, r12			@ c += t9
+	adc	r4, r4, #0
+
+	add	r1, sp, #4 + 0*4		@ r7,r8,r9 = t0,t1,t2
+	ldmia	r1, {r7,r8,r9}
+
+	ubfx	r2, r3, #0, #22     		@ r[9] = c & (M >> 4)
+	str	r2, [r0, #9*4]
+	mov	r3, r3, lsr #22     		@ c >>= 22
+	orr	r3, r3, r4, asl #10
+	mov     r4, r4, lsr #22
+	movw    r14, field_R1 << 4   		@ c += d * (R1 << 4)
+	umlal   r3, r4, r5, r14
+
+	movw    r14, field_R0 >> 4   		@ d = c * (R0 >> 4) + t0 (64x64 multiply+add)
+	umull	r5, r6, r3, r14			@ d = c.lo * (R0 >> 4)
+	adds	r5, r5, r7	    		@ d.lo += t0
+	mla	r6, r14, r4, r6			@ d.hi += c.hi * (R0 >> 4)
+	adc	r6, r6, 0	     		@ d.hi += carry
+
+	bic	r2, r5, field_not_M 		@ r[0] = d & M
+	str	r2, [r0, #0*4]
+
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	
+	movw    r14, field_R1 >> 4   		@ d += c * (R1 >> 4) + t1 (64x64 multiply+add)
+	umull	r1, r2, r3, r14       		@ tmp = c.lo * (R1 >> 4)
+	adds	r5, r5, r8	    		@ d.lo += t1
+	adc	r6, r6, #0	    		@ d.hi += carry
+	adds	r5, r5, r1	    		@ d.lo += tmp.lo
+	mla	r2, r14, r4, r2      		@ tmp.hi += c.hi * (R1 >> 4)
+	adc	r6, r6, r2	   		@ d.hi += carry + tmp.hi
+
+	bic	r2, r5, field_not_M 		@ r[1] = d & M
+	str	r2, [r0, #1*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 (ignore hi)
+	orr	r5, r5, r6, asl #6
+
+	add	r5, r5, r9	  		@ d += t2
+	str	r5, [r0, #2*4]      		@ r[2] = d
+
+	add	sp, sp, #48
+	ldmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc}
+	.size	secp256k1_fe_sqr_inner, .-secp256k1_fe_sqr_inner
+
diff --git a/src/secp256k1/src/bench_ecdh.c b/src/secp256k1/src/bench_ecdh.c
index 5a7c6376e0..cde5e2dbb4 100644
--- a/src/secp256k1/src/bench_ecdh.c
+++ b/src/secp256k1/src/bench_ecdh.c
@@ -28,7 +28,8 @@ static void bench_ecdh_setup(void* arg) {
         0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f
     };
 
-    data->ctx = secp256k1_context_create(0);
+    /* create a context with no capabilities */
+    data->ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT);
     for (i = 0; i < 32; i++) {
         data->scalar[i] = i + 1;
     }
diff --git a/src/secp256k1/src/bench_internal.c b/src/secp256k1/src/bench_internal.c
index 7809f5f8cf..0809f77bda 100644
--- a/src/secp256k1/src/bench_internal.c
+++ b/src/secp256k1/src/bench_internal.c
@@ -181,12 +181,12 @@ void bench_field_inverse_var(void* arg) {
     }
 }
 
-void bench_field_sqrt_var(void* arg) {
+void bench_field_sqrt(void* arg) {
     int i;
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_fe_sqrt_var(&data->fe_x, &data->fe_x);
+        secp256k1_fe_sqrt(&data->fe_x, &data->fe_x);
         secp256k1_fe_add(&data->fe_x, &data->fe_y);
     }
 }
@@ -227,6 +227,15 @@ void bench_group_add_affine_var(void* arg) {
     }
 }
 
+void bench_group_jacobi_var(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        secp256k1_gej_has_quad_y_var(&data->gej_x);
+    }
+}
+
 void bench_ecmult_wnaf(void* arg) {
     int i;
     bench_inv_t *data = (bench_inv_t*)arg;
@@ -299,6 +308,21 @@ void bench_context_sign(void* arg) {
     }
 }
 
+#ifndef USE_NUM_NONE
+void bench_num_jacobi(void* arg) {
+    int i;
+    bench_inv_t *data = (bench_inv_t*)arg;
+    secp256k1_num nx, norder;
+
+    secp256k1_scalar_get_num(&nx, &data->scalar_x);
+    secp256k1_scalar_order_get_num(&norder);
+    secp256k1_scalar_get_num(&norder, &data->scalar_y);
+
+    for (i = 0; i < 200000; i++) {
+        secp256k1_num_jacobi(&nx, &norder);
+    }
+}
+#endif
 
 int have_flag(int argc, char** argv, char *flag) {
     char** argm = argv + argc;
@@ -333,12 +357,13 @@ int main(int argc, char **argv) {
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, 20000);
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt_var", bench_field_sqrt_var, bench_setup, NULL, &data, 10, 20000);
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, 20000);
 
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, 200000);
     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, "group") || have_flag(argc, argv, "jacobi")) run_benchmark("group_jacobi_var", bench_group_jacobi_var, bench_setup, NULL, &data, 10, 20000);
 
     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);
@@ -350,5 +375,8 @@ int main(int argc, char **argv) {
     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);
 
+#ifndef USE_NUM_NONE
+    if (have_flag(argc, argv, "num") || have_flag(argc, argv, "jacobi")) run_benchmark("num_jacobi", bench_num_jacobi, bench_setup, NULL, &data, 10, 200000);
+#endif
     return 0;
 }
diff --git a/src/secp256k1/src/bench_verify.c b/src/secp256k1/src/bench_verify.c
index 5718320cda..418defa0aa 100644
--- a/src/secp256k1/src/bench_verify.c
+++ b/src/secp256k1/src/bench_verify.c
@@ -11,6 +11,12 @@
 #include "util.h"
 #include "bench.h"
 
+#ifdef ENABLE_OPENSSL_TESTS
+#include <openssl/bn.h>
+#include <openssl/ecdsa.h>
+#include <openssl/obj_mac.h>
+#endif
+
 typedef struct {
     secp256k1_context *ctx;
     unsigned char msg[32];
@@ -19,6 +25,9 @@ typedef struct {
     size_t siglen;
     unsigned char pubkey[33];
     size_t pubkeylen;
+#ifdef ENABLE_OPENSSL_TESTS
+    EC_GROUP* ec_group;
+#endif
 } benchmark_verify_t;
 
 static void benchmark_verify(void* arg) {
@@ -40,6 +49,36 @@ static void benchmark_verify(void* arg) {
     }
 }
 
+#ifdef ENABLE_OPENSSL_TESTS
+static void benchmark_verify_openssl(void* arg) {
+    int i;
+    benchmark_verify_t* data = (benchmark_verify_t*)arg;
+
+    for (i = 0; i < 20000; i++) {
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+        {
+            EC_KEY *pkey = EC_KEY_new();
+            const unsigned char *pubkey = &data->pubkey[0];
+            int result;
+
+            CHECK(pkey != NULL);
+            result = EC_KEY_set_group(pkey, data->ec_group);
+            CHECK(result);
+            result = (o2i_ECPublicKey(&pkey, &pubkey, data->pubkeylen)) != NULL;
+            CHECK(result);
+            result = ECDSA_verify(0, &data->msg[0], sizeof(data->msg), &data->sig[0], data->siglen, pkey) == (i == 0);
+            CHECK(result);
+            EC_KEY_free(pkey);
+        }
+        data->sig[data->siglen - 1] ^= (i & 0xFF);
+        data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF);
+        data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF);
+    }
+}
+#endif
+
 int main(void) {
     int i;
     secp256k1_pubkey pubkey;
@@ -62,6 +101,11 @@ int main(void) {
     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);
+#ifdef ENABLE_OPENSSL_TESTS
+    data.ec_group = EC_GROUP_new_by_curve_name(NID_secp256k1);
+    run_benchmark("ecdsa_verify_openssl", benchmark_verify_openssl, NULL, NULL, &data, 10, 20000);
+    EC_GROUP_free(data.ec_group);
+#endif
 
     secp256k1_context_destroy(data.ctx);
     return 0;
diff --git a/src/secp256k1/src/ecdsa_impl.h b/src/secp256k1/src/ecdsa_impl.h
index d110b4bb1d..9a42e519bd 100644
--- a/src/secp256k1/src/ecdsa_impl.h
+++ b/src/secp256k1/src/ecdsa_impl.h
@@ -203,7 +203,9 @@ static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const
 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 sn, u1, u2;
+#if !defined(EXHAUSTIVE_TEST_ORDER)
     secp256k1_fe xr;
+#endif
     secp256k1_gej pubkeyj;
     secp256k1_gej pr;
 
@@ -219,6 +221,21 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
     if (secp256k1_gej_is_infinity(&pr)) {
         return 0;
     }
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+{
+    secp256k1_scalar computed_r;
+    int overflow = 0;
+    secp256k1_ge pr_ge;
+    secp256k1_ge_set_gej(&pr_ge, &pr);
+    secp256k1_fe_normalize(&pr_ge.x);
+
+    secp256k1_fe_get_b32(c, &pr_ge.x);
+    secp256k1_scalar_set_b32(&computed_r, c, &overflow);
+    /* we fully expect overflow */
+    return secp256k1_scalar_eq(sigr, &computed_r);
+}
+#else
     secp256k1_scalar_get_b32(c, sigr);
     secp256k1_fe_set_b32(&xr, c);
 
@@ -252,6 +269,7 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
         return 1;
     }
     return 0;
+#endif
 }
 
 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) {
diff --git a/src/secp256k1/src/ecmult_const_impl.h b/src/secp256k1/src/ecmult_const_impl.h
index 90ac94770e..0db314c48e 100644
--- a/src/secp256k1/src/ecmult_const_impl.h
+++ b/src/secp256k1/src/ecmult_const_impl.h
@@ -58,25 +58,27 @@ 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
+    /* Note that we cannot handle even numbers by negating them to be odd, as is
+     * done in other implementations, since if our scalars were specified to have
+     * width < 256 for performance reasons, their negations would have width 256
+     * and we'd lose any performance benefit. 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 */
+     * or 2 (for odd) to the number we are encoding, returning a skew value indicating
+     * this, and having the caller compensate after doing the multiplication. */
+
+    /* Negative numbers will be negated to keep their bit representation below the maximum width */
     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);
+    bit = flip ^ !secp256k1_scalar_is_even(&s);
     /* 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);
@@ -89,11 +91,6 @@ static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
     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);
@@ -127,15 +124,13 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
     secp256k1_ge tmpa;
     secp256k1_fe Z;
 
+    int skew_1;
+    int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
 #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;
@@ -145,18 +140,10 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
 #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);
+    skew_1   = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1);
 #endif
 
     /* Calculate odd multiples of a.
@@ -179,21 +166,15 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
     /* 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);
-
+#ifdef USE_ENDOMORPHISM
     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--) {
@@ -202,59 +183,57 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
         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);
-
+#ifdef USE_ENDOMORPHISM
         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;
+#ifdef USE_ENDOMORPHISM
         secp256k1_ge_storage correction_lam_stor;
+#endif
         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);
+#ifdef USE_ENDOMORPHISM
         secp256k1_ge_to_storage(&correction_lam_stor, a);
+#endif
         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);
+#ifdef USE_ENDOMORPHISM
         secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
+#endif
 
         /* Apply the correction */
         secp256k1_ge_from_storage(&correction, &correction_1_stor);
         secp256k1_ge_neg(&correction, &correction);
         secp256k1_gej_add_ge(r, r, &correction);
 
+#ifdef USE_ENDOMORPHISM
         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_impl.h b/src/secp256k1/src/ecmult_gen_impl.h
index b63c4d8662..35f2546077 100644
--- a/src/secp256k1/src/ecmult_gen_impl.h
+++ b/src/secp256k1/src/ecmult_gen_impl.h
@@ -77,7 +77,7 @@ static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx
                 secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
             }
         }
-        secp256k1_ge_set_all_gej_var(1024, prec, precj, cb);
+        secp256k1_ge_set_all_gej_var(prec, precj, 1024, cb);
     }
     for (j = 0; j < 64; j++) {
         for (i = 0; i < 16; i++) {
diff --git a/src/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h
index e6e5f47188..4e40104ad4 100644
--- a/src/secp256k1/src/ecmult_impl.h
+++ b/src/secp256k1/src/ecmult_impl.h
@@ -7,13 +7,29 @@
 #ifndef _SECP256K1_ECMULT_IMPL_H_
 #define _SECP256K1_ECMULT_IMPL_H_
 
+#include <string.h>
+
 #include "group.h"
 #include "scalar.h"
 #include "ecmult.h"
 
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/* We need to lower these values for exhaustive tests because
+ * the tables cannot have infinities in them (this breaks the
+ * affine-isomorphism stuff which tracks z-ratios) */
+#  if EXHAUSTIVE_TEST_ORDER > 128
+#    define WINDOW_A 5
+#    define WINDOW_G 8
+#  elif EXHAUSTIVE_TEST_ORDER > 8
+#    define WINDOW_A 4
+#    define WINDOW_G 4
+#  else
+#    define WINDOW_A 2
+#    define WINDOW_G 2
+#  endif
+#else
 /* optimal for 128-bit and 256-bit exponents. */
 #define WINDOW_A 5
-
 /** larger numbers may result in slightly better performance, at the cost of
     exponentially larger precomputed tables. */
 #ifdef USE_ENDOMORPHISM
@@ -23,6 +39,7 @@
 /** One table for window size 16: 1.375 MiB. */
 #define WINDOW_G 16
 #endif
+#endif
 
 /** The number of entries a table with precomputed multiples needs to have. */
 #define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
@@ -101,7 +118,7 @@ static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge
     /* 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);
+    secp256k1_ge_set_table_gej_var(prea, prej, zr, n);
     /* Convert them to compact storage form. */
     for (i = 0; i < n; i++) {
         secp256k1_ge_to_storage(&pre[i], &prea[i]);
diff --git a/src/secp256k1/src/field.h b/src/secp256k1/src/field.h
index 2d52af5e36..bbb1ee866c 100644
--- a/src/secp256k1/src/field.h
+++ b/src/secp256k1/src/field.h
@@ -30,6 +30,8 @@
 #error "Please select field implementation"
 #endif
 
+#include "util.h"
+
 /** Normalize a field element. */
 static void secp256k1_fe_normalize(secp256k1_fe *r);
 
@@ -50,6 +52,9 @@ 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 *r, int a);
 
+/** Sets a field element equal to zero, initializing all fields. */
+static void secp256k1_fe_clear(secp256k1_fe *a);
+
 /** Verify whether a field element is zero. Requires the input to be normalized. */
 static int secp256k1_fe_is_zero(const secp256k1_fe *a);
 
@@ -57,6 +62,9 @@ static int secp256k1_fe_is_zero(const secp256k1_fe *a);
 static int secp256k1_fe_is_odd(const secp256k1_fe *a);
 
 /** Compare two field elements. Requires magnitude-1 inputs. */
+static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Same as secp256k1_fe_equal, but may be variable time. */
 static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
 
 /** Compare two field elements. Requires both inputs to be normalized */
@@ -92,7 +100,10 @@ static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
  *  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);
+static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Checks whether a field element is a quadratic residue. */
+static int secp256k1_fe_is_quad_var(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). */
@@ -104,7 +115,7 @@ 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 *r, const secp256k1_fe *a);
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len);
 
 /** Convert a field element to the storage type. */
 static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
diff --git a/src/secp256k1/src/field_10x26_impl.h b/src/secp256k1/src/field_10x26_impl.h
index 212cc5396a..7b8c079608 100644
--- a/src/secp256k1/src/field_10x26_impl.h
+++ b/src/secp256k1/src/field_10x26_impl.h
@@ -7,8 +7,6 @@
 #ifndef _SECP256K1_FIELD_REPR_IMPL_H_
 #define _SECP256K1_FIELD_REPR_IMPL_H_
 
-#include <stdio.h>
-#include <string.h>
 #include "util.h"
 #include "num.h"
 #include "field.h"
@@ -429,6 +427,14 @@ SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_f
 #endif
 }
 
+#if defined(USE_EXTERNAL_ASM)
+
+/* External assembler implementation */
+void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
+void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
+
+#else
+
 #ifdef VERIFY
 #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
 #else
@@ -1037,7 +1043,7 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t
     VERIFY_BITS(r[2], 27);
     /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
 }
-
+#endif
 
 static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
 #ifdef VERIFY
diff --git a/src/secp256k1/src/field_5x52_impl.h b/src/secp256k1/src/field_5x52_impl.h
index b31e24ab81..7a99eb21ec 100644
--- a/src/secp256k1/src/field_5x52_impl.h
+++ b/src/secp256k1/src/field_5x52_impl.h
@@ -11,7 +11,6 @@
 #include "libsecp256k1-config.h"
 #endif
 
-#include <string.h>
 #include "util.h"
 #include "num.h"
 #include "field.h"
diff --git a/src/secp256k1/src/field_5x52_int128_impl.h b/src/secp256k1/src/field_5x52_int128_impl.h
index 9280bb5ea2..0bf22bdd3e 100644
--- a/src/secp256k1/src/field_5x52_int128_impl.h
+++ b/src/secp256k1/src/field_5x52_int128_impl.h
@@ -137,7 +137,7 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
     VERIFY_BITS(r[2], 52);
     VERIFY_BITS(c, 63);
     /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    c   += d * R + t3;;
+    c   += d * R + t3;
     VERIFY_BITS(c, 100);
     /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
     r[3] = c & M; c >>= 52;
@@ -259,7 +259,7 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t
     VERIFY_BITS(c, 63);
     /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
 
-    c   += d * R + t3;;
+    c   += d * R + t3;
     VERIFY_BITS(c, 100);
     /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
     r[3] = c & M; c >>= 52;
diff --git a/src/secp256k1/src/field_impl.h b/src/secp256k1/src/field_impl.h
index 77f4aae2f9..5127b279bc 100644
--- a/src/secp256k1/src/field_impl.h
+++ b/src/secp256k1/src/field_impl.h
@@ -21,6 +21,13 @@
 #error "Please select field implementation"
 #endif
 
+SECP256K1_INLINE static int secp256k1_fe_equal(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(&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);
@@ -28,7 +35,7 @@ SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const
     return secp256k1_fe_normalizes_to_zero_var(&na);
 }
 
-static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a) {
+static int secp256k1_fe_sqrt(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.
      *
@@ -123,7 +130,7 @@ static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a) {
     /* Check that a square root was actually calculated */
 
     secp256k1_fe_sqr(&t1, r);
-    return secp256k1_fe_equal_var(&t1, a);
+    return secp256k1_fe_equal(&t1, a);
 }
 
 static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
@@ -253,7 +260,7 @@ static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
 #endif
 }
 
-static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a) {
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) {
     secp256k1_fe u;
     size_t i;
     if (len < 1) {
@@ -280,4 +287,29 @@ static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k
     r[0] = u;
 }
 
+static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) {
+#ifndef USE_NUM_NONE
+    unsigned char b[32];
+    secp256k1_num n;
+    secp256k1_num m;
+    /* 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,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
+    };
+
+    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);
+    return secp256k1_num_jacobi(&n, &m) >= 0;
+#else
+    secp256k1_fe r;
+    return secp256k1_fe_sqrt(&r, a);
+#endif
+}
+
 #endif
diff --git a/src/secp256k1/src/group.h b/src/secp256k1/src/group.h
index ebfe1ca70c..4957b248fe 100644
--- a/src/secp256k1/src/group.h
+++ b/src/secp256k1/src/group.h
@@ -47,7 +47,7 @@ static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const se
  *  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);
+static int secp256k1_ge_set_xquad(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. */
@@ -65,12 +65,12 @@ static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *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 *r, const secp256k1_gej *a, const secp256k1_callback *cb);
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, 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);
+static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len);
 
 /** 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
@@ -94,6 +94,9 @@ 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 *a);
 
+/** Check whether a group element's y coordinate is a quadratic residue. */
+static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *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);
diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h
index 42e2f6e6eb..2e192b62fd 100644
--- a/src/secp256k1/src/group_impl.h
+++ b/src/secp256k1/src/group_impl.h
@@ -7,12 +7,57 @@
 #ifndef _SECP256K1_GROUP_IMPL_H_
 #define _SECP256K1_GROUP_IMPL_H_
 
-#include <string.h>
-
 #include "num.h"
 #include "field.h"
 #include "group.h"
 
+/* These points can be generated in sage as follows:
+ *
+ * 0. Setup a worksheet with the following parameters.
+ *   b = 4  # whatever CURVE_B will be set to
+ *   F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
+ *   C = EllipticCurve ([F (0), F (b)])
+ *
+ * 1. Determine all the small orders available to you. (If there are
+ *    no satisfactory ones, go back and change b.)
+ *   print C.order().factor(limit=1000)
+ *
+ * 2. Choose an order as one of the prime factors listed in the above step.
+ *    (You can also multiply some to get a composite order, though the
+ *    tests will crash trying to invert scalars during signing.) We take a
+ *    random point and scale it to drop its order to the desired value.
+ *    There is some probability this won't work; just try again.
+ *   order = 199
+ *   P = C.random_point()
+ *   P = (int(P.order()) / int(order)) * P
+ *   assert(P.order() == order)
+ *
+ * 3. Print the values. You'll need to use a vim macro or something to
+ *    split the hex output into 4-byte chunks.
+ *   print "%x %x" % P.xy()
+ */
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#  if EXHAUSTIVE_TEST_ORDER == 199
+const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0xFA7CC9A7, 0x0737F2DB, 0xA749DD39, 0x2B4FB069,
+    0x3B017A7D, 0xA808C2F1, 0xFB12940C, 0x9EA66C18,
+    0x78AC123A, 0x5ED8AEF3, 0x8732BC91, 0x1F3A2868,
+    0x48DF246C, 0x808DAE72, 0xCFE52572, 0x7F0501ED
+);
+
+const int CURVE_B = 4;
+#  elif EXHAUSTIVE_TEST_ORDER == 13
+const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0xedc60018, 0xa51a786b, 0x2ea91f4d, 0x4c9416c0,
+    0x9de54c3b, 0xa1316554, 0x6cf4345c, 0x7277ef15,
+    0x54cb1b6b, 0xdc8c1273, 0x087844ea, 0x43f4603e,
+    0x0eaf9a43, 0xf6effe55, 0x939f806d, 0x37adf8ac
+);
+const int CURVE_B = 2;
+#  else
+#    error No known generator for the specified exhaustive test group order.
+#  endif
+#else
 /** Generator for secp256k1, value 'g' defined in
  *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
  */
@@ -23,8 +68,11 @@ static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
     0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
 );
 
+const int CURVE_B = 7;
+#endif
+
 static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
-    secp256k1_fe zi2; 
+    secp256k1_fe zi2;
     secp256k1_fe zi3;
     secp256k1_fe_sqr(&zi2, zi);
     secp256k1_fe_mul(&zi3, &zi2, zi);
@@ -78,7 +126,7 @@ static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
     r->y = a->y;
 }
 
-static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb) {
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, const secp256k1_callback *cb) {
     secp256k1_fe *az;
     secp256k1_fe *azi;
     size_t i;
@@ -91,7 +139,7 @@ static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp
     }
 
     azi = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * count);
-    secp256k1_fe_inv_all_var(count, azi, az);
+    secp256k1_fe_inv_all_var(azi, az, count);
     free(az);
 
     count = 0;
@@ -104,7 +152,7 @@ static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp
     free(azi);
 }
 
-static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr) {
+static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len) {
     size_t i = len - 1;
     secp256k1_fe zi;
 
@@ -147,9 +195,15 @@ static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp
 
 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);
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+    secp256k1_fe_clear(&r->z);
+}
+
+static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
+    r->infinity = 1;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
 }
 
 static void secp256k1_gej_clear(secp256k1_gej *r) {
@@ -165,19 +219,19 @@ static void secp256k1_ge_clear(secp256k1_ge *r) {
     secp256k1_fe_clear(&r->y);
 }
 
-static int secp256k1_ge_set_xquad_var(secp256k1_ge *r, const secp256k1_fe *x) {
+static int secp256k1_ge_set_xquad(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_set_int(&c, CURVE_B);
     secp256k1_fe_add(&c, &x3);
-    return secp256k1_fe_sqrt_var(&r->y, &c);
+    return secp256k1_fe_sqrt(&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)) {
+    if (!secp256k1_ge_set_xquad(r, x)) {
         return 0;
     }
     secp256k1_fe_normalize_var(&r->y);
@@ -230,7 +284,7 @@ static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
     secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
     secp256k1_fe_sqr(&z2, &a->z);
     secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
-    secp256k1_fe_mul_int(&z6, 7);
+    secp256k1_fe_mul_int(&z6, CURVE_B);
     secp256k1_fe_add(&x3, &z6);
     secp256k1_fe_normalize_weak(&x3);
     return secp256k1_fe_equal_var(&y2, &x3);
@@ -244,18 +298,30 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
     /* y^2 = x^3 + 7 */
     secp256k1_fe_sqr(&y2, &a->y);
     secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
-    secp256k1_fe_set_int(&c, 7);
+    secp256k1_fe_set_int(&c, CURVE_B);
     secp256k1_fe_add(&x3, &c);
     secp256k1_fe_normalize_weak(&x3);
     return secp256k1_fe_equal_var(&y2, &x3);
 }
 
 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 */
+    /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate.
+     *
+     * Note that there is an implementation described at
+     *     https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
+     * which trades a multiply for a square, but in practice this is actually slower,
+     * mainly because it requires more normalizations.
+     */
     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.
+     *
+     *  Having said this, if this function receives a point on a sextic twist, e.g. by
+     *  a fault attack, it is possible for y to be 0. This happens for y^2 = x^3 + 6,
+     *  since -6 does have a cube root mod p. For this point, this function will not set
+     *  the infinity flag even though the point doubles to infinity, and the result
+     *  point will be gibberish (z = 0 but infinity = 0).
      */
     r->infinity = a->infinity;
     if (r->infinity) {
@@ -623,4 +689,18 @@ static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
 }
 #endif
 
+static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a) {
+    secp256k1_fe yz;
+
+    if (a->infinity) {
+        return 0;
+    }
+
+    /* We rely on the fact that the Jacobi symbol of 1 / a->z^3 is the same as
+     * that of a->z. Thus a->y / a->z^3 is a quadratic residue iff a->y * a->z
+       is */
+    secp256k1_fe_mul(&yz, &a->y, &a->z);
+    return secp256k1_fe_is_quad_var(&yz);
+}
+
 #endif
diff --git a/src/secp256k1/src/hash.h b/src/secp256k1/src/hash.h
index 0ff01e63fa..fca98cab9f 100644
--- a/src/secp256k1/src/hash.h
+++ b/src/secp256k1/src/hash.h
@@ -11,7 +11,7 @@
 #include <stdint.h>
 
 typedef struct {
-    uint32_t s[32];
+    uint32_t s[8];
     uint32_t buf[16]; /* In big endian */
     size_t bytes;
 } secp256k1_sha256_t;
diff --git a/src/secp256k1/src/hash_impl.h b/src/secp256k1/src/hash_impl.h
index ae55df6d8a..b47e65f830 100644
--- a/src/secp256k1/src/hash_impl.h
+++ b/src/secp256k1/src/hash_impl.h
@@ -269,15 +269,13 @@ static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256
     rng->retry = 0;
 }
 
-
+#undef BE32
 #undef Round
-#undef sigma0
 #undef sigma1
-#undef Sigma0
+#undef sigma0
 #undef Sigma1
-#undef Ch
+#undef Sigma0
 #undef Maj
-#undef ReadBE32
-#undef WriteBE32
+#undef Ch
 
 #endif
diff --git a/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java b/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java
index 90a498eaa2..1c67802fba 100644
--- a/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java
+++ b/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java
@@ -1,60 +1,446 @@
+/*
+ * Copyright 2013 Google Inc.
+ * Copyright 2014-2016 the libsecp256k1 contributors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
 package org.bitcoin;
 
 import java.nio.ByteBuffer;
 import java.nio.ByteOrder;
 
+import java.math.BigInteger;
 import com.google.common.base.Preconditions;
-
+import java.util.concurrent.locks.Lock;
+import java.util.concurrent.locks.ReentrantReadWriteLock;
+import static org.bitcoin.NativeSecp256k1Util.*;
 
 /**
- * This class holds native methods to handle ECDSA verification.
- * You can find an example library that can be used for this at
- * https://github.com/sipa/secp256k1
+ * <p>This class holds native methods to handle ECDSA verification.</p>
+ *
+ * <p>You can find an example library that can be used for this at https://github.com/bitcoin/secp256k1</p>
+ *
+ * <p>To build secp256k1 for use with bitcoinj, run
+ * `./configure --enable-jni --enable-experimental --enable-module-ecdh`
+ * and `make` then copy `.libs/libsecp256k1.so` to your system library path
+ * or point the JVM to the folder containing it with -Djava.library.path
+ * </p>
  */
 public class NativeSecp256k1 {
-    public static final boolean enabled;
-    static {
-        boolean isEnabled = true;
-        try {
-            System.loadLibrary("javasecp256k1");
-        } catch (UnsatisfiedLinkError e) {
-            isEnabled = false;
-        }
-        enabled = isEnabled;
-    }
-    
+
+    private static final ReentrantReadWriteLock rwl = new ReentrantReadWriteLock();
+    private static final Lock r = rwl.readLock();
+    private static final Lock w = rwl.writeLock();
     private static ThreadLocal<ByteBuffer> nativeECDSABuffer = new ThreadLocal<ByteBuffer>();
     /**
      * Verifies the given secp256k1 signature in native code.
      * Calling when enabled == false is undefined (probably library not loaded)
-     * 
+     *
      * @param data The data which was signed, must be exactly 32 bytes
      * @param signature The signature
      * @param pub The public key which did the signing
      */
-    public static boolean verify(byte[] data, byte[] signature, byte[] pub) {
+    public static boolean verify(byte[] data, byte[] signature, byte[] pub) throws AssertFailException{
         Preconditions.checkArgument(data.length == 32 && signature.length <= 520 && pub.length <= 520);
 
         ByteBuffer byteBuff = nativeECDSABuffer.get();
-        if (byteBuff == null) {
-            byteBuff = ByteBuffer.allocateDirect(32 + 8 + 520 + 520);
+        if (byteBuff == null || byteBuff.capacity() < 520) {
+            byteBuff = ByteBuffer.allocateDirect(520);
             byteBuff.order(ByteOrder.nativeOrder());
             nativeECDSABuffer.set(byteBuff);
         }
         byteBuff.rewind();
         byteBuff.put(data);
-        byteBuff.putInt(signature.length);
-        byteBuff.putInt(pub.length);
         byteBuff.put(signature);
         byteBuff.put(pub);
-        return secp256k1_ecdsa_verify(byteBuff) == 1;
+
+        byte[][] retByteArray;
+
+        r.lock();
+        try {
+          return secp256k1_ecdsa_verify(byteBuff, Secp256k1Context.getContext(), signature.length, pub.length) == 1;
+        } finally {
+          r.unlock();
+        }
+    }
+
+    /**
+     * libsecp256k1 Create an ECDSA signature.
+     *
+     * @param data Message hash, 32 bytes
+     * @param key Secret key, 32 bytes
+     *
+     * Return values
+     * @param sig byte array of signature
+     */
+    public static byte[] sign(byte[] data, byte[] sec) throws AssertFailException{
+        Preconditions.checkArgument(data.length == 32 && sec.length <= 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < 32 + 32) {
+            byteBuff = ByteBuffer.allocateDirect(32 + 32);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(data);
+        byteBuff.put(sec);
+
+        byte[][] retByteArray;
+
+        r.lock();
+        try {
+          retByteArray = secp256k1_ecdsa_sign(byteBuff, Secp256k1Context.getContext());
+        } finally {
+          r.unlock();
+        }
+
+        byte[] sigArr = retByteArray[0];
+        int sigLen = new BigInteger(new byte[] { retByteArray[1][0] }).intValue();
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(sigArr.length, sigLen, "Got bad signature length.");
+
+        return retVal == 0 ? new byte[0] : sigArr;
+    }
+
+    /**
+     * libsecp256k1 Seckey Verify - returns 1 if valid, 0 if invalid
+     *
+     * @param seckey ECDSA Secret key, 32 bytes
+     */
+    public static boolean secKeyVerify(byte[] seckey) {
+        Preconditions.checkArgument(seckey.length == 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < seckey.length) {
+            byteBuff = ByteBuffer.allocateDirect(seckey.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(seckey);
+
+        r.lock();
+        try {
+          return secp256k1_ec_seckey_verify(byteBuff,Secp256k1Context.getContext()) == 1;
+        } finally {
+          r.unlock();
+        }
+    }
+
+
+    /**
+     * libsecp256k1 Compute Pubkey - computes public key from secret key
+     *
+     * @param seckey ECDSA Secret key, 32 bytes
+     *
+     * Return values
+     * @param pubkey ECDSA Public key, 33 or 65 bytes
+     */
+    //TODO add a 'compressed' arg
+    public static byte[] computePubkey(byte[] seckey) throws AssertFailException{
+        Preconditions.checkArgument(seckey.length == 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < seckey.length) {
+            byteBuff = ByteBuffer.allocateDirect(seckey.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(seckey);
+
+        byte[][] retByteArray;
+
+        r.lock();
+        try {
+          retByteArray = secp256k1_ec_pubkey_create(byteBuff, Secp256k1Context.getContext());
+        } finally {
+          r.unlock();
+        }
+
+        byte[] pubArr = retByteArray[0];
+        int pubLen = new BigInteger(new byte[] { retByteArray[1][0] }).intValue();
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(pubArr.length, pubLen, "Got bad pubkey length.");
+
+        return retVal == 0 ? new byte[0]: pubArr;
+    }
+
+    /**
+     * libsecp256k1 Cleanup - This destroys the secp256k1 context object
+     * This should be called at the end of the program for proper cleanup of the context.
+     */
+    public static synchronized void cleanup() {
+        w.lock();
+        try {
+          secp256k1_destroy_context(Secp256k1Context.getContext());
+        } finally {
+          w.unlock();
+        }
+    }
+
+    public static long cloneContext() {
+       r.lock();
+       try {
+        return secp256k1_ctx_clone(Secp256k1Context.getContext());
+       } finally { r.unlock(); }
+    }
+
+    /**
+     * libsecp256k1 PrivKey Tweak-Mul - Tweak privkey by multiplying to it
+     *
+     * @param tweak some bytes to tweak with
+     * @param seckey 32-byte seckey
+     */
+    public static byte[] privKeyTweakMul(byte[] privkey, byte[] tweak) throws AssertFailException{
+        Preconditions.checkArgument(privkey.length == 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < privkey.length + tweak.length) {
+            byteBuff = ByteBuffer.allocateDirect(privkey.length + tweak.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(privkey);
+        byteBuff.put(tweak);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_privkey_tweak_mul(byteBuff,Secp256k1Context.getContext());
+        } finally {
+          r.unlock();
+        }
+
+        byte[] privArr = retByteArray[0];
+
+        int privLen = (byte) new BigInteger(new byte[] { retByteArray[1][0] }).intValue() & 0xFF;
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(privArr.length, privLen, "Got bad pubkey length.");
+
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return privArr;
+    }
+
+    /**
+     * libsecp256k1 PrivKey Tweak-Add - Tweak privkey by adding to it
+     *
+     * @param tweak some bytes to tweak with
+     * @param seckey 32-byte seckey
+     */
+    public static byte[] privKeyTweakAdd(byte[] privkey, byte[] tweak) throws AssertFailException{
+        Preconditions.checkArgument(privkey.length == 32);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < privkey.length + tweak.length) {
+            byteBuff = ByteBuffer.allocateDirect(privkey.length + tweak.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(privkey);
+        byteBuff.put(tweak);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_privkey_tweak_add(byteBuff,Secp256k1Context.getContext());
+        } finally {
+          r.unlock();
+        }
+
+        byte[] privArr = retByteArray[0];
+
+        int privLen = (byte) new BigInteger(new byte[] { retByteArray[1][0] }).intValue() & 0xFF;
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(privArr.length, privLen, "Got bad pubkey length.");
+
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return privArr;
+    }
+
+    /**
+     * libsecp256k1 PubKey Tweak-Add - Tweak pubkey by adding to it
+     *
+     * @param tweak some bytes to tweak with
+     * @param pubkey 32-byte seckey
+     */
+    public static byte[] pubKeyTweakAdd(byte[] pubkey, byte[] tweak) throws AssertFailException{
+        Preconditions.checkArgument(pubkey.length == 33 || pubkey.length == 65);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < pubkey.length + tweak.length) {
+            byteBuff = ByteBuffer.allocateDirect(pubkey.length + tweak.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(pubkey);
+        byteBuff.put(tweak);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_pubkey_tweak_add(byteBuff,Secp256k1Context.getContext(), pubkey.length);
+        } finally {
+          r.unlock();
+        }
+
+        byte[] pubArr = retByteArray[0];
+
+        int pubLen = (byte) new BigInteger(new byte[] { retByteArray[1][0] }).intValue() & 0xFF;
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(pubArr.length, pubLen, "Got bad pubkey length.");
+
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return pubArr;
+    }
+
+    /**
+     * libsecp256k1 PubKey Tweak-Mul - Tweak pubkey by multiplying to it
+     *
+     * @param tweak some bytes to tweak with
+     * @param pubkey 32-byte seckey
+     */
+    public static byte[] pubKeyTweakMul(byte[] pubkey, byte[] tweak) throws AssertFailException{
+        Preconditions.checkArgument(pubkey.length == 33 || pubkey.length == 65);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < pubkey.length + tweak.length) {
+            byteBuff = ByteBuffer.allocateDirect(pubkey.length + tweak.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(pubkey);
+        byteBuff.put(tweak);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_pubkey_tweak_mul(byteBuff,Secp256k1Context.getContext(), pubkey.length);
+        } finally {
+          r.unlock();
+        }
+
+        byte[] pubArr = retByteArray[0];
+
+        int pubLen = (byte) new BigInteger(new byte[] { retByteArray[1][0] }).intValue() & 0xFF;
+        int retVal = new BigInteger(new byte[] { retByteArray[1][1] }).intValue();
+
+        assertEquals(pubArr.length, pubLen, "Got bad pubkey length.");
+
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return pubArr;
     }
 
     /**
-     * @param byteBuff signature format is byte[32] data,
-     *        native-endian int signatureLength, native-endian int pubkeyLength,
-     *        byte[signatureLength] signature, byte[pubkeyLength] pub
-     * @returns 1 for valid signature, anything else for invalid
+     * libsecp256k1 create ECDH secret - constant time ECDH calculation
+     *
+     * @param seckey byte array of secret key used in exponentiaion
+     * @param pubkey byte array of public key used in exponentiaion
      */
-    private static native int secp256k1_ecdsa_verify(ByteBuffer byteBuff);
+    public static byte[] createECDHSecret(byte[] seckey, byte[] pubkey) throws AssertFailException{
+        Preconditions.checkArgument(seckey.length <= 32 && pubkey.length <= 65);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < 32 + pubkey.length) {
+            byteBuff = ByteBuffer.allocateDirect(32 + pubkey.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(seckey);
+        byteBuff.put(pubkey);
+
+        byte[][] retByteArray;
+        r.lock();
+        try {
+          retByteArray = secp256k1_ecdh(byteBuff, Secp256k1Context.getContext(), pubkey.length);
+        } finally {
+          r.unlock();
+        }
+
+        byte[] resArr = retByteArray[0];
+        int retVal = new BigInteger(new byte[] { retByteArray[1][0] }).intValue();
+
+        assertEquals(resArr.length, 32, "Got bad result length.");
+        assertEquals(retVal, 1, "Failed return value check.");
+
+        return resArr;
+    }
+
+    /**
+     * libsecp256k1 randomize - updates the context randomization
+     *
+     * @param seed 32-byte random seed
+     */
+    public static synchronized boolean randomize(byte[] seed) throws AssertFailException{
+        Preconditions.checkArgument(seed.length == 32 || seed == null);
+
+        ByteBuffer byteBuff = nativeECDSABuffer.get();
+        if (byteBuff == null || byteBuff.capacity() < seed.length) {
+            byteBuff = ByteBuffer.allocateDirect(seed.length);
+            byteBuff.order(ByteOrder.nativeOrder());
+            nativeECDSABuffer.set(byteBuff);
+        }
+        byteBuff.rewind();
+        byteBuff.put(seed);
+
+        w.lock();
+        try {
+          return secp256k1_context_randomize(byteBuff, Secp256k1Context.getContext()) == 1;
+        } finally {
+          w.unlock();
+        }
+    }
+
+    private static native long secp256k1_ctx_clone(long context);
+
+    private static native int secp256k1_context_randomize(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_privkey_tweak_add(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_privkey_tweak_mul(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_pubkey_tweak_add(ByteBuffer byteBuff, long context, int pubLen);
+
+    private static native byte[][] secp256k1_pubkey_tweak_mul(ByteBuffer byteBuff, long context, int pubLen);
+
+    private static native void secp256k1_destroy_context(long context);
+
+    private static native int secp256k1_ecdsa_verify(ByteBuffer byteBuff, long context, int sigLen, int pubLen);
+
+    private static native byte[][] secp256k1_ecdsa_sign(ByteBuffer byteBuff, long context);
+
+    private static native int secp256k1_ec_seckey_verify(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_ec_pubkey_create(ByteBuffer byteBuff, long context);
+
+    private static native byte[][] secp256k1_ec_pubkey_parse(ByteBuffer byteBuff, long context, int inputLen);
+
+    private static native byte[][] secp256k1_ecdh(ByteBuffer byteBuff, long context, int inputLen);
+
 }
diff --git a/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Test.java b/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Test.java
new file mode 100644
index 0000000000..c00d08899b
--- /dev/null
+++ b/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Test.java
@@ -0,0 +1,226 @@
+package org.bitcoin;
+
+import com.google.common.io.BaseEncoding;
+import java.util.Arrays;
+import java.math.BigInteger;
+import javax.xml.bind.DatatypeConverter;
+import static org.bitcoin.NativeSecp256k1Util.*;
+
+/**
+ * This class holds test cases defined for testing this library.
+ */
+public class NativeSecp256k1Test {
+
+    //TODO improve comments/add more tests
+    /**
+      * This tests verify() for a valid signature
+      */
+    public static void testVerifyPos() throws AssertFailException{
+        boolean result = false;
+        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A90".toLowerCase()); //sha256hash of "testing"
+        byte[] sig = BaseEncoding.base16().lowerCase().decode("3044022079BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F817980220294F14E883B3F525B5367756C2A11EF6CF84B730B36C17CB0C56F0AAB2C98589".toLowerCase());
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+
+        result = NativeSecp256k1.verify( data, sig, pub);
+        assertEquals( result, true , "testVerifyPos");
+    }
+
+    /**
+      * This tests verify() for a non-valid signature
+      */
+    public static void testVerifyNeg() throws AssertFailException{
+        boolean result = false;
+        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A91".toLowerCase()); //sha256hash of "testing"
+        byte[] sig = BaseEncoding.base16().lowerCase().decode("3044022079BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F817980220294F14E883B3F525B5367756C2A11EF6CF84B730B36C17CB0C56F0AAB2C98589".toLowerCase());
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+
+        result = NativeSecp256k1.verify( data, sig, pub);
+        //System.out.println(" TEST " + new BigInteger(1, resultbytes).toString(16));
+        assertEquals( result, false , "testVerifyNeg");
+    }
+
+    /**
+      * This tests secret key verify() for a valid secretkey
+      */
+    public static void testSecKeyVerifyPos() throws AssertFailException{
+        boolean result = false;
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+
+        result = NativeSecp256k1.secKeyVerify( sec );
+        //System.out.println(" TEST " + new BigInteger(1, resultbytes).toString(16));
+        assertEquals( result, true , "testSecKeyVerifyPos");
+    }
+
+    /**
+      * This tests secret key verify() for a invalid secretkey
+      */
+    public static void testSecKeyVerifyNeg() throws AssertFailException{
+        boolean result = false;
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF".toLowerCase());
+
+        result = NativeSecp256k1.secKeyVerify( sec );
+        //System.out.println(" TEST " + new BigInteger(1, resultbytes).toString(16));
+        assertEquals( result, false , "testSecKeyVerifyNeg");
+    }
+
+    /**
+      * This tests public key create() for a valid secretkey
+      */
+    public static void testPubKeyCreatePos() throws AssertFailException{
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+
+        byte[] resultArr = NativeSecp256k1.computePubkey( sec);
+        String pubkeyString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( pubkeyString , "04C591A8FF19AC9C4E4E5793673B83123437E975285E7B442F4EE2654DFFCA5E2D2103ED494718C697AC9AEBCFD19612E224DB46661011863ED2FC54E71861E2A6" , "testPubKeyCreatePos");
+    }
+
+    /**
+      * This tests public key create() for a invalid secretkey
+      */
+    public static void testPubKeyCreateNeg() throws AssertFailException{
+       byte[] sec = BaseEncoding.base16().lowerCase().decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF".toLowerCase());
+
+       byte[] resultArr = NativeSecp256k1.computePubkey( sec);
+       String pubkeyString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+       assertEquals( pubkeyString, "" , "testPubKeyCreateNeg");
+    }
+
+    /**
+      * This tests sign() for a valid secretkey
+      */
+    public static void testSignPos() throws AssertFailException{
+
+        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A90".toLowerCase()); //sha256hash of "testing"
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+
+        byte[] resultArr = NativeSecp256k1.sign(data, sec);
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString, "30440220182A108E1448DC8F1FB467D06A0F3BB8EA0533584CB954EF8DA112F1D60E39A202201C66F36DA211C087F3AF88B50EDF4F9BDAA6CF5FD6817E74DCA34DB12390C6E9" , "testSignPos");
+    }
+
+    /**
+      * This tests sign() for a invalid secretkey
+      */
+    public static void testSignNeg() throws AssertFailException{
+        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A90".toLowerCase()); //sha256hash of "testing"
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF".toLowerCase());
+
+        byte[] resultArr = NativeSecp256k1.sign(data, sec);
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString, "" , "testSignNeg");
+    }
+
+    /**
+      * This tests private key tweak-add
+      */
+    public static void testPrivKeyTweakAdd_1() throws AssertFailException {
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+        byte[] data = BaseEncoding.base16().lowerCase().decode("3982F19BEF1615BCCFBB05E321C10E1D4CBA3DF0E841C2E41EEB6016347653C3".toLowerCase()); //sha256hash of "tweak"
+
+        byte[] resultArr = NativeSecp256k1.privKeyTweakAdd( sec , data );
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString , "A168571E189E6F9A7E2D657A4B53AE99B909F7E712D1C23CED28093CD57C88F3" , "testPrivKeyAdd_1");
+    }
+
+    /**
+      * This tests private key tweak-mul
+      */
+    public static void testPrivKeyTweakMul_1() throws AssertFailException {
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+        byte[] data = BaseEncoding.base16().lowerCase().decode("3982F19BEF1615BCCFBB05E321C10E1D4CBA3DF0E841C2E41EEB6016347653C3".toLowerCase()); //sha256hash of "tweak"
+
+        byte[] resultArr = NativeSecp256k1.privKeyTweakMul( sec , data );
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString , "97F8184235F101550F3C71C927507651BD3F1CDB4A5A33B8986ACF0DEE20FFFC" , "testPrivKeyMul_1");
+    }
+
+    /**
+      * This tests private key tweak-add uncompressed
+      */
+    public static void testPrivKeyTweakAdd_2() throws AssertFailException {
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+        byte[] data = BaseEncoding.base16().lowerCase().decode("3982F19BEF1615BCCFBB05E321C10E1D4CBA3DF0E841C2E41EEB6016347653C3".toLowerCase()); //sha256hash of "tweak"
+
+        byte[] resultArr = NativeSecp256k1.pubKeyTweakAdd( pub , data );
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString , "0411C6790F4B663CCE607BAAE08C43557EDC1A4D11D88DFCB3D841D0C6A941AF525A268E2A863C148555C48FB5FBA368E88718A46E205FABC3DBA2CCFFAB0796EF" , "testPrivKeyAdd_2");
+    }
+
+    /**
+      * This tests private key tweak-mul uncompressed
+      */
+    public static void testPrivKeyTweakMul_2() throws AssertFailException {
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+        byte[] data = BaseEncoding.base16().lowerCase().decode("3982F19BEF1615BCCFBB05E321C10E1D4CBA3DF0E841C2E41EEB6016347653C3".toLowerCase()); //sha256hash of "tweak"
+
+        byte[] resultArr = NativeSecp256k1.pubKeyTweakMul( pub , data );
+        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( sigString , "04E0FE6FE55EBCA626B98A807F6CAF654139E14E5E3698F01A9A658E21DC1D2791EC060D4F412A794D5370F672BC94B722640B5F76914151CFCA6E712CA48CC589" , "testPrivKeyMul_2");
+    }
+
+    /**
+      * This tests seed randomization
+      */
+    public static void testRandomize() throws AssertFailException {
+        byte[] seed = BaseEncoding.base16().lowerCase().decode("A441B15FE9A3CF56661190A0B93B9DEC7D04127288CC87250967CF3B52894D11".toLowerCase()); //sha256hash of "random"
+        boolean result = NativeSecp256k1.randomize(seed);
+        assertEquals( result, true, "testRandomize");
+    }
+
+    public static void testCreateECDHSecret() throws AssertFailException{
+
+        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
+        byte[] pub = BaseEncoding.base16().lowerCase().decode("040A629506E1B65CD9D2E0BA9C75DF9C4FED0DB16DC9625ED14397F0AFC836FAE595DC53F8B0EFE61E703075BD9B143BAC75EC0E19F82A2208CAEB32BE53414C40".toLowerCase());
+
+        byte[] resultArr = NativeSecp256k1.createECDHSecret(sec, pub);
+        String ecdhString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
+        assertEquals( ecdhString, "2A2A67007A926E6594AF3EB564FC74005B37A9C8AEF2033C4552051B5C87F043" , "testCreateECDHSecret");
+    }
+
+    public static void main(String[] args) throws AssertFailException{
+
+
+        System.out.println("\n libsecp256k1 enabled: " + Secp256k1Context.isEnabled() + "\n");
+
+        assertEquals( Secp256k1Context.isEnabled(), true, "isEnabled" );
+
+        //Test verify() success/fail
+        testVerifyPos();
+        testVerifyNeg();
+
+        //Test secKeyVerify() success/fail
+        testSecKeyVerifyPos();
+        testSecKeyVerifyNeg();
+
+        //Test computePubkey() success/fail
+        testPubKeyCreatePos();
+        testPubKeyCreateNeg();
+
+        //Test sign() success/fail
+        testSignPos();
+        testSignNeg();
+
+        //Test privKeyTweakAdd() 1
+        testPrivKeyTweakAdd_1();
+
+        //Test privKeyTweakMul() 2
+        testPrivKeyTweakMul_1();
+
+        //Test privKeyTweakAdd() 3
+        testPrivKeyTweakAdd_2();
+
+        //Test privKeyTweakMul() 4
+        testPrivKeyTweakMul_2();
+
+        //Test randomize()
+        testRandomize();
+
+        //Test ECDH
+        testCreateECDHSecret();
+
+        NativeSecp256k1.cleanup();
+
+        System.out.println(" All tests passed." );
+
+    }
+}
diff --git a/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Util.java b/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Util.java
new file mode 100644
index 0000000000..04732ba044
--- /dev/null
+++ b/src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Util.java
@@ -0,0 +1,45 @@
+/*
+ * Copyright 2014-2016 the libsecp256k1 contributors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.bitcoin;
+
+public class NativeSecp256k1Util{
+
+    public static void assertEquals( int val, int val2, String message ) throws AssertFailException{
+      if( val != val2 )
+        throw new AssertFailException("FAIL: " + message);
+    }
+
+    public static void assertEquals( boolean val, boolean val2, String message ) throws AssertFailException{
+      if( val != val2 )
+        throw new AssertFailException("FAIL: " + message);
+      else
+        System.out.println("PASS: " + message);
+    }
+
+    public static void assertEquals( String val, String val2, String message ) throws AssertFailException{
+      if( !val.equals(val2) )
+        throw new AssertFailException("FAIL: " + message);
+      else
+        System.out.println("PASS: " + message);
+    }
+
+    public static class AssertFailException extends Exception {
+      public AssertFailException(String message) {
+        super( message );
+      }
+    }
+}
diff --git a/src/secp256k1/src/java/org/bitcoin/Secp256k1Context.java b/src/secp256k1/src/java/org/bitcoin/Secp256k1Context.java
new file mode 100644
index 0000000000..216c986a8b
--- /dev/null
+++ b/src/secp256k1/src/java/org/bitcoin/Secp256k1Context.java
@@ -0,0 +1,51 @@
+/*
+ * Copyright 2014-2016 the libsecp256k1 contributors
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.bitcoin;
+
+/**
+ * This class holds the context reference used in native methods 
+ * to handle ECDSA operations.
+ */
+public class Secp256k1Context {
+  private static final boolean enabled; //true if the library is loaded
+  private static final long context; //ref to pointer to context obj
+
+  static { //static initializer
+      boolean isEnabled = true;
+      long contextRef = -1;
+      try {
+          System.loadLibrary("secp256k1");
+          contextRef = secp256k1_init_context();
+      } catch (UnsatisfiedLinkError e) {
+          System.out.println("UnsatisfiedLinkError: " + e.toString());
+          isEnabled = false;
+      }
+      enabled = isEnabled;
+      context = contextRef;
+  }
+
+  public static boolean isEnabled() {
+     return enabled;
+  }
+
+  public static long getContext() {
+     if(!enabled) return -1; //sanity check
+     return context;
+  }
+
+  private static native long secp256k1_init_context();
+}
diff --git a/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c b/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c
index bb4cd70728..bcef7b32ce 100644
--- a/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c
+++ b/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c
@@ -1,23 +1,377 @@
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
 #include "org_bitcoin_NativeSecp256k1.h"
 #include "include/secp256k1.h"
+#include "include/secp256k1_ecdh.h"
+#include "include/secp256k1_recovery.h"
 
-JNIEXPORT jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify
-  (JNIEnv* env, jclass classObject, jobject byteBufferObject)
+
+SECP256K1_API jlong JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ctx_1clone
+  (JNIEnv* env, jclass classObject, jlong ctx_l)
+{
+  const secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+
+  jlong ctx_clone_l = (uintptr_t) secp256k1_context_clone(ctx);
+
+  (void)classObject;(void)env;
+
+  return ctx_clone_l;
+
+}
+
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1context_1randomize
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
 {
-	unsigned char* data = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
-	int sigLen = *((int*)(data + 32));
-	int pubLen = *((int*)(data + 32 + 4));
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+
+  const unsigned char* seed = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+
+  (void)classObject;
+
+  return secp256k1_context_randomize(ctx, seed);
 
-	return secp256k1_ecdsa_verify(data, 32, data+32+8, sigLen, data+32+8+sigLen, pubLen);
 }
 
-static void __javasecp256k1_attach(void) __attribute__((constructor));
-static void __javasecp256k1_detach(void) __attribute__((destructor));
+SECP256K1_API void JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1destroy_1context
+  (JNIEnv* env, jclass classObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+
+  secp256k1_context_destroy(ctx);
 
-static void __javasecp256k1_attach(void) {
-	secp256k1_start(SECP256K1_START_VERIFY);
+  (void)classObject;(void)env;
 }
 
-static void __javasecp256k1_detach(void) {
-	secp256k1_stop();
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint siglen, jint publen)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+
+  unsigned char* data = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* sigdata = {  (unsigned char*) (data + 32) };
+  const unsigned char* pubdata = { (unsigned char*) (data + siglen + 32) };
+
+  secp256k1_ecdsa_signature sig;
+  secp256k1_pubkey pubkey;
+
+  int ret = secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigdata, siglen);
+
+  if( ret ) {
+    ret = secp256k1_ec_pubkey_parse(ctx, &pubkey, pubdata, publen);
+
+    if( ret ) {
+      ret = secp256k1_ecdsa_verify(ctx, &sig, data, &pubkey);
+    }
+  }
+
+  (void)classObject;
+
+  return ret;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1sign
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* data = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  unsigned char* secKey = (unsigned char*) (data + 32);
+
+  jobjectArray retArray;
+  jbyteArray sigArray, intsByteArray;
+  unsigned char intsarray[2];
+
+  secp256k1_ecdsa_signature sig[72];
+
+  int ret = secp256k1_ecdsa_sign(ctx, sig, data, secKey, NULL, NULL );
+
+  unsigned char outputSer[72];
+  size_t outputLen = 72;
+
+  if( ret ) {
+    int ret2 = secp256k1_ecdsa_signature_serialize_der(ctx,outputSer, &outputLen, sig ); (void)ret2;
+  }
+
+  intsarray[0] = outputLen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  sigArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, sigArray, 0, outputLen, (jbyte*)outputSer);
+  (*env)->SetObjectArrayElement(env, retArray, 0, sigArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1seckey_1verify
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* secKey = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+
+  (void)classObject;
+
+  return secp256k1_ec_seckey_verify(ctx, secKey);
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1pubkey_1create
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  const unsigned char* secKey = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+
+  secp256k1_pubkey pubkey;
+
+  jobjectArray retArray;
+  jbyteArray pubkeyArray, intsByteArray;
+  unsigned char intsarray[2];
+
+  int ret = secp256k1_ec_pubkey_create(ctx, &pubkey, secKey);
+
+  unsigned char outputSer[65];
+  size_t outputLen = 65;
+
+  if( ret ) {
+    int ret2 = secp256k1_ec_pubkey_serialize(ctx,outputSer, &outputLen, &pubkey,SECP256K1_EC_UNCOMPRESSED );(void)ret2;
+  }
+
+  intsarray[0] = outputLen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  pubkeyArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, pubkeyArray, 0, outputLen, (jbyte*)outputSer);
+  (*env)->SetObjectArrayElement(env, retArray, 0, pubkeyArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1privkey_1tweak_1add
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* privkey = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* tweak = (unsigned char*) (privkey + 32);
+
+  jobjectArray retArray;
+  jbyteArray privArray, intsByteArray;
+  unsigned char intsarray[2];
+
+  int privkeylen = 32;
+
+  int ret = secp256k1_ec_privkey_tweak_add(ctx, privkey, tweak);
+
+  intsarray[0] = privkeylen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  privArray = (*env)->NewByteArray(env, privkeylen);
+  (*env)->SetByteArrayRegion(env, privArray, 0, privkeylen, (jbyte*)privkey);
+  (*env)->SetObjectArrayElement(env, retArray, 0, privArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1privkey_1tweak_1mul
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* privkey = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* tweak = (unsigned char*) (privkey + 32);
+
+  jobjectArray retArray;
+  jbyteArray privArray, intsByteArray;
+  unsigned char intsarray[2];
+
+  int privkeylen = 32;
+
+  int ret = secp256k1_ec_privkey_tweak_mul(ctx, privkey, tweak);
+
+  intsarray[0] = privkeylen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  privArray = (*env)->NewByteArray(env, privkeylen);
+  (*env)->SetByteArrayRegion(env, privArray, 0, privkeylen, (jbyte*)privkey);
+  (*env)->SetObjectArrayElement(env, retArray, 0, privArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1pubkey_1tweak_1add
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+/*  secp256k1_pubkey* pubkey = (secp256k1_pubkey*) (*env)->GetDirectBufferAddress(env, byteBufferObject);*/
+  unsigned char* pkey = (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* tweak = (unsigned char*) (pkey + publen);
+
+  jobjectArray retArray;
+  jbyteArray pubArray, intsByteArray;
+  unsigned char intsarray[2];
+  unsigned char outputSer[65];
+  size_t outputLen = 65;
+
+  secp256k1_pubkey pubkey;
+  int ret = secp256k1_ec_pubkey_parse(ctx, &pubkey, pkey, publen);
+
+  if( ret ) {
+    ret = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, tweak);
+  }
+
+  if( ret ) {
+    int ret2 = secp256k1_ec_pubkey_serialize(ctx,outputSer, &outputLen, &pubkey,SECP256K1_EC_UNCOMPRESSED );(void)ret2;
+  }
+
+  intsarray[0] = outputLen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  pubArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, pubArray, 0, outputLen, (jbyte*)outputSer);
+  (*env)->SetObjectArrayElement(env, retArray, 0, pubArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1pubkey_1tweak_1mul
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  unsigned char* pkey = (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* tweak = (unsigned char*) (pkey + publen);
+
+  jobjectArray retArray;
+  jbyteArray pubArray, intsByteArray;
+  unsigned char intsarray[2];
+  unsigned char outputSer[65];
+  size_t outputLen = 65;
+
+  secp256k1_pubkey pubkey;
+  int ret = secp256k1_ec_pubkey_parse(ctx, &pubkey, pkey, publen);
+
+  if ( ret ) {
+    ret = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, tweak);
+  }
+
+  if( ret ) {
+    int ret2 = secp256k1_ec_pubkey_serialize(ctx,outputSer, &outputLen, &pubkey,SECP256K1_EC_UNCOMPRESSED );(void)ret2;
+  }
+
+  intsarray[0] = outputLen;
+  intsarray[1] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  pubArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, pubArray, 0, outputLen, (jbyte*)outputSer);
+  (*env)->SetObjectArrayElement(env, retArray, 0, pubArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 2);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 2, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
+}
+
+SECP256K1_API jlong JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1pubkey_1combine
+  (JNIEnv * env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint numkeys)
+{
+  (void)classObject;(void)env;(void)byteBufferObject;(void)ctx_l;(void)numkeys;
+
+  return 0;
+}
+
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdh
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen)
+{
+  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
+  const unsigned char* secdata = (*env)->GetDirectBufferAddress(env, byteBufferObject);
+  const unsigned char* pubdata = (const unsigned char*) (secdata + 32);
+
+  jobjectArray retArray;
+  jbyteArray outArray, intsByteArray;
+  unsigned char intsarray[1];
+  secp256k1_pubkey pubkey;
+  unsigned char nonce_res[32];
+  size_t outputLen = 32;
+
+  int ret = secp256k1_ec_pubkey_parse(ctx, &pubkey, pubdata, publen);
+
+  if (ret) {
+    ret = secp256k1_ecdh(
+      ctx,
+      nonce_res,
+      &pubkey,
+      secdata
+    );
+  }
+
+  intsarray[0] = ret;
+
+  retArray = (*env)->NewObjectArray(env, 2,
+    (*env)->FindClass(env, "[B"),
+    (*env)->NewByteArray(env, 1));
+
+  outArray = (*env)->NewByteArray(env, outputLen);
+  (*env)->SetByteArrayRegion(env, outArray, 0, 32, (jbyte*)nonce_res);
+  (*env)->SetObjectArrayElement(env, retArray, 0, outArray);
+
+  intsByteArray = (*env)->NewByteArray(env, 1);
+  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 1, (jbyte*)intsarray);
+  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
+
+  (void)classObject;
+
+  return retArray;
 }
diff --git a/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h b/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h
index d7fb004fa8..fe613c9e9e 100644
--- a/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h
+++ b/src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h
@@ -1,5 +1,6 @@
 /* DO NOT EDIT THIS FILE - it is machine generated */
 #include <jni.h>
+#include "include/secp256k1.h"
 /* Header for class org_bitcoin_NativeSecp256k1 */
 
 #ifndef _Included_org_bitcoin_NativeSecp256k1
@@ -9,11 +10,108 @@ extern "C" {
 #endif
 /*
  * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ctx_clone
+ * Signature: (J)J
+ */
+SECP256K1_API jlong JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ctx_1clone
+  (JNIEnv *, jclass, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_context_randomize
+ * Signature: (Ljava/nio/ByteBuffer;J)I
+ */
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1context_1randomize
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_privkey_tweak_add
+ * Signature: (Ljava/nio/ByteBuffer;J)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1privkey_1tweak_1add
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_privkey_tweak_mul
+ * Signature: (Ljava/nio/ByteBuffer;J)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1privkey_1tweak_1mul
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_pubkey_tweak_add
+ * Signature: (Ljava/nio/ByteBuffer;JI)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1pubkey_1tweak_1add
+  (JNIEnv *, jclass, jobject, jlong, jint);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_pubkey_tweak_mul
+ * Signature: (Ljava/nio/ByteBuffer;JI)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1pubkey_1tweak_1mul
+  (JNIEnv *, jclass, jobject, jlong, jint);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_destroy_context
+ * Signature: (J)V
+ */
+SECP256K1_API void JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1destroy_1context
+  (JNIEnv *, jclass, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
  * Method:    secp256k1_ecdsa_verify
- * Signature: (Ljava/nio/ByteBuffer;)I
+ * Signature: (Ljava/nio/ByteBuffer;JII)I
+ */
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify
+  (JNIEnv *, jclass, jobject, jlong, jint, jint);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ecdsa_sign
+ * Signature: (Ljava/nio/ByteBuffer;J)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1sign
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ec_seckey_verify
+ * Signature: (Ljava/nio/ByteBuffer;J)I
+ */
+SECP256K1_API jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1seckey_1verify
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ec_pubkey_create
+ * Signature: (Ljava/nio/ByteBuffer;J)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1pubkey_1create
+  (JNIEnv *, jclass, jobject, jlong);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ec_pubkey_parse
+ * Signature: (Ljava/nio/ByteBuffer;JI)[[B
+ */
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1pubkey_1parse
+  (JNIEnv *, jclass, jobject, jlong, jint);
+
+/*
+ * Class:     org_bitcoin_NativeSecp256k1
+ * Method:    secp256k1_ecdh
+ * Signature: (Ljava/nio/ByteBuffer;JI)[[B
  */
-JNIEXPORT jint JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1verify
-  (JNIEnv *, jclass, jobject);
+SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdh
+  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen);
+
 
 #ifdef __cplusplus
 }
diff --git a/src/secp256k1/src/java/org_bitcoin_Secp256k1Context.c b/src/secp256k1/src/java/org_bitcoin_Secp256k1Context.c
new file mode 100644
index 0000000000..a52939e7e7
--- /dev/null
+++ b/src/secp256k1/src/java/org_bitcoin_Secp256k1Context.c
@@ -0,0 +1,15 @@
+#include <stdlib.h>
+#include <stdint.h>
+#include "org_bitcoin_Secp256k1Context.h"
+#include "include/secp256k1.h"
+
+SECP256K1_API jlong JNICALL Java_org_bitcoin_Secp256k1Context_secp256k1_1init_1context
+  (JNIEnv* env, jclass classObject)
+{
+  secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+  (void)classObject;(void)env;
+
+  return (uintptr_t)ctx;
+}
+
diff --git a/src/secp256k1/src/java/org_bitcoin_Secp256k1Context.h b/src/secp256k1/src/java/org_bitcoin_Secp256k1Context.h
new file mode 100644
index 0000000000..0d2bc84b7f
--- /dev/null
+++ b/src/secp256k1/src/java/org_bitcoin_Secp256k1Context.h
@@ -0,0 +1,22 @@
+/* DO NOT EDIT THIS FILE - it is machine generated */
+#include <jni.h>
+#include "include/secp256k1.h"
+/* Header for class org_bitcoin_Secp256k1Context */
+
+#ifndef _Included_org_bitcoin_Secp256k1Context
+#define _Included_org_bitcoin_Secp256k1Context
+#ifdef __cplusplus
+extern "C" {
+#endif
+/*
+ * Class:     org_bitcoin_Secp256k1Context
+ * Method:    secp256k1_init_context
+ * Signature: ()J
+ */
+SECP256K1_API jlong JNICALL Java_org_bitcoin_Secp256k1Context_secp256k1_1init_1context
+  (JNIEnv *, jclass);
+
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/src/secp256k1/src/modules/ecdh/Makefile.am.include b/src/secp256k1/src/modules/ecdh/Makefile.am.include
index 670b9c1152..e3088b4697 100644
--- a/src/secp256k1/src/modules/ecdh/Makefile.am.include
+++ b/src/secp256k1/src/modules/ecdh/Makefile.am.include
@@ -4,5 +4,5 @@ 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)
+bench_ecdh_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
 endif
diff --git a/src/secp256k1/src/modules/recovery/Makefile.am.include b/src/secp256k1/src/modules/recovery/Makefile.am.include
index 5de3ea33ea..bf23c26e71 100644
--- a/src/secp256k1/src/modules/recovery/Makefile.am.include
+++ b/src/secp256k1/src/modules/recovery/Makefile.am.include
@@ -4,5 +4,5 @@ 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)
+bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
 endif
diff --git a/src/secp256k1/src/modules/recovery/main_impl.h b/src/secp256k1/src/modules/recovery/main_impl.h
index ec42f4bb6c..86f2f0cb2b 100644..100755
--- a/src/secp256k1/src/modules/recovery/main_impl.h
+++ b/src/secp256k1/src/modules/recovery/main_impl.h
@@ -138,16 +138,15 @@ int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecd
     secp256k1_scalar_set_b32(&sec, seckey, &overflow);
     /* Fail if the secret key is invalid. */
     if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned char nonce32[32];
         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;
@@ -155,6 +154,7 @@ int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecd
             }
             count++;
         }
+        memset(nonce32, 0, 32);
         secp256k1_scalar_clear(&msg);
         secp256k1_scalar_clear(&non);
         secp256k1_scalar_clear(&sec);
diff --git a/src/secp256k1/src/modules/schnorr/Makefile.am.include b/src/secp256k1/src/modules/schnorr/Makefile.am.include
deleted file mode 100644
index b3bfa7d5cc..0000000000
--- a/src/secp256k1/src/modules/schnorr/Makefile.am.include
+++ /dev/null
@@ -1,10 +0,0 @@
-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
deleted file mode 100644
index fa176a1767..0000000000
--- a/src/secp256k1/src/modules/schnorr/main_impl.h
+++ /dev/null
@@ -1,164 +0,0 @@
-/**********************************************************************
- * 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
deleted file mode 100644
index de18147bd5..0000000000
--- a/src/secp256k1/src/modules/schnorr/schnorr.h
+++ /dev/null
@@ -1,20 +0,0 @@
-/***********************************************************************
- * 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
deleted file mode 100644
index e13ab6db7c..0000000000
--- a/src/secp256k1/src/modules/schnorr/schnorr_impl.h
+++ /dev/null
@@ -1,207 +0,0 @@
-/***********************************************************************
- * 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
deleted file mode 100644
index 5bd14a03e3..0000000000
--- a/src/secp256k1/src/modules/schnorr/tests_impl.h
+++ /dev/null
@@ -1,175 +0,0 @@
-/**********************************************************************
- * 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 ebfa71eb44..7bb9c5be8c 100644
--- a/src/secp256k1/src/num.h
+++ b/src/secp256k1/src/num.h
@@ -32,6 +32,9 @@ static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsi
 /** Compute a modular inverse. The input must be less than the modulus. */
 static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m);
 
+/** Compute the jacobi symbol (a|b). b must be positive and odd. */
+static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b);
+
 /** Compare the absolute value of two numbers. */
 static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b);
 
@@ -57,6 +60,9 @@ 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 *a);
 
+/** Check whether a number is one. */
+static int secp256k1_num_is_one(const secp256k1_num *a);
+
 /** Check whether a number is strictly negative. */
 static int secp256k1_num_is_neg(const secp256k1_num *a);
 
diff --git a/src/secp256k1/src/num_gmp_impl.h b/src/secp256k1/src/num_gmp_impl.h
index 7b6a89719a..3a46495eea 100644
--- a/src/secp256k1/src/num_gmp_impl.h
+++ b/src/secp256k1/src/num_gmp_impl.h
@@ -144,6 +144,32 @@ static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a,
     memset(v, 0, sizeof(v));
 }
 
+static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b) {
+    int ret;
+    mpz_t ga, gb;
+    secp256k1_num_sanity(a);
+    secp256k1_num_sanity(b);
+    VERIFY_CHECK(!b->neg && (b->limbs > 0) && (b->data[0] & 1));
+
+    mpz_inits(ga, gb, NULL);
+
+    mpz_import(gb, b->limbs, -1, sizeof(mp_limb_t), 0, 0, b->data);
+    mpz_import(ga, a->limbs, -1, sizeof(mp_limb_t), 0, 0, a->data);
+    if (a->neg) {
+        mpz_neg(ga, ga);
+    }
+
+    ret = mpz_jacobi(ga, gb);
+
+    mpz_clears(ga, gb, NULL);
+
+    return ret;
+}
+
+static int secp256k1_num_is_one(const secp256k1_num *a) {
+    return (a->limbs == 1 && a->data[0] == 1);
+}
+
 static int secp256k1_num_is_zero(const secp256k1_num *a) {
     return (a->limbs == 1 && a->data[0] == 0);
 }
diff --git a/src/secp256k1/src/scalar.h b/src/secp256k1/src/scalar.h
index b590ccd6dd..27e9d8375e 100644
--- a/src/secp256k1/src/scalar.h
+++ b/src/secp256k1/src/scalar.h
@@ -13,7 +13,9 @@
 #include "libsecp256k1-config.h"
 #endif
 
-#if defined(USE_SCALAR_4X64)
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low.h"
+#elif defined(USE_SCALAR_4X64)
 #include "scalar_4x64.h"
 #elif defined(USE_SCALAR_8X32)
 #include "scalar_8x32.h"
diff --git a/src/secp256k1/src/scalar_4x64_impl.h b/src/secp256k1/src/scalar_4x64_impl.h
index aa2703dd23..56e7bd82af 100644
--- a/src/secp256k1/src/scalar_4x64_impl.h
+++ b/src/secp256k1/src/scalar_4x64_impl.h
@@ -282,8 +282,8 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "movq 56(%%rsi), %%r14\n"
     /* Initialize r8,r9,r10 */
     "movq 0(%%rsi), %%r8\n"
-    "movq $0, %%r9\n"
-    "movq $0, %%r10\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
     /* (r8,r9) += n0 * c0 */
     "movq %8, %%rax\n"
     "mulq %%r11\n"
@@ -291,7 +291,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq %%rdx, %%r9\n"
     /* extract m0 */
     "movq %%r8, %q0\n"
-    "movq $0, %%r8\n"
+    "xorq %%r8, %%r8\n"
     /* (r9,r10) += l1 */
     "addq 8(%%rsi), %%r9\n"
     "adcq $0, %%r10\n"
@@ -309,7 +309,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r8\n"
     /* extract m1 */
     "movq %%r9, %q1\n"
-    "movq $0, %%r9\n"
+    "xorq %%r9, %%r9\n"
     /* (r10,r8,r9) += l2 */
     "addq 16(%%rsi), %%r10\n"
     "adcq $0, %%r8\n"
@@ -332,7 +332,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r9\n"
     /* extract m2 */
     "movq %%r10, %q2\n"
-    "movq $0, %%r10\n"
+    "xorq %%r10, %%r10\n"
     /* (r8,r9,r10) += l3 */
     "addq 24(%%rsi), %%r8\n"
     "adcq $0, %%r9\n"
@@ -355,7 +355,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r10\n"
     /* extract m3 */
     "movq %%r8, %q3\n"
-    "movq $0, %%r8\n"
+    "xorq %%r8, %%r8\n"
     /* (r9,r10,r8) += n3 * c1 */
     "movq %9, %%rax\n"
     "mulq %%r14\n"
@@ -387,8 +387,8 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "movq %q11, %%r13\n"
     /* Initialize (r8,r9,r10) */
     "movq %q5, %%r8\n"
-    "movq $0, %%r9\n"
-    "movq $0, %%r10\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
     /* (r8,r9) += m4 * c0 */
     "movq %12, %%rax\n"
     "mulq %%r11\n"
@@ -396,7 +396,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq %%rdx, %%r9\n"
     /* extract p0 */
     "movq %%r8, %q0\n"
-    "movq $0, %%r8\n"
+    "xorq %%r8, %%r8\n"
     /* (r9,r10) += m1 */
     "addq %q6, %%r9\n"
     "adcq $0, %%r10\n"
@@ -414,7 +414,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r8\n"
     /* extract p1 */
     "movq %%r9, %q1\n"
-    "movq $0, %%r9\n"
+    "xorq %%r9, %%r9\n"
     /* (r10,r8,r9) += m2 */
     "addq %q7, %%r10\n"
     "adcq $0, %%r8\n"
@@ -472,7 +472,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "movq %%rax, 0(%q6)\n"
     /* Move to (r8,r9) */
     "movq %%rdx, %%r8\n"
-    "movq $0, %%r9\n"
+    "xorq %%r9, %%r9\n"
     /* (r8,r9) += p1 */
     "addq %q2, %%r8\n"
     "adcq $0, %%r9\n"
@@ -483,7 +483,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq %%rdx, %%r9\n"
     /* Extract r1 */
     "movq %%r8, 8(%q6)\n"
-    "movq $0, %%r8\n"
+    "xorq %%r8, %%r8\n"
     /* (r9,r8) += p4 */
     "addq %%r10, %%r9\n"
     "adcq $0, %%r8\n"
@@ -492,7 +492,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r8\n"
     /* Extract r2 */
     "movq %%r9, 16(%q6)\n"
-    "movq $0, %%r9\n"
+    "xorq %%r9, %%r9\n"
     /* (r8,r9) += p3 */
     "addq %q4, %%r8\n"
     "adcq $0, %%r9\n"
diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h
index 88ea97de86..f5b2376407 100644
--- a/src/secp256k1/src/scalar_impl.h
+++ b/src/secp256k1/src/scalar_impl.h
@@ -7,8 +7,6 @@
 #ifndef _SECP256K1_SCALAR_IMPL_H_
 #define _SECP256K1_SCALAR_IMPL_H_
 
-#include <string.h>
-
 #include "group.h"
 #include "scalar.h"
 
@@ -16,7 +14,9 @@
 #include "libsecp256k1-config.h"
 #endif
 
-#if defined(USE_SCALAR_4X64)
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low_impl.h"
+#elif defined(USE_SCALAR_4X64)
 #include "scalar_4x64_impl.h"
 #elif defined(USE_SCALAR_8X32)
 #include "scalar_8x32_impl.h"
@@ -33,17 +33,37 @@ static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a
 
 /** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
 static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    static const unsigned char order[32] = {
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER
+    };
+#else
     static const unsigned char order[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
     };
+#endif
     secp256k1_num_set_bin(r, order, 32);
 }
 #endif
 
 static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    int i;
+    *r = 0;
+    for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++)
+        if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1)
+            *r = i;
+    /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus
+     * have a composite group order; fix it in exhaustive_tests.c). */
+    VERIFY_CHECK(*r != 0);
+}
+#else
     secp256k1_scalar *t;
     int i;
     /* First compute x ^ (2^N - 1) for some values of N. */
@@ -235,9 +255,9 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
 }
 
 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);
 }
+#endif
 
 static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
 #if defined(USE_SCALAR_INV_BUILTIN)
@@ -261,6 +281,18 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_sc
 }
 
 #ifdef USE_ENDOMORPHISM
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/**
+ * Find k1 and k2 given k, such that k1 + k2 * lambda == k mod n; unlike in the
+ * full case we don't bother making k1 and k2 be small, we just want them to be
+ * nontrivial to get full test coverage for the exhaustive tests. We therefore
+ * (arbitrarily) set k2 = k + 5 and k1 = k - k2 * lambda.
+ */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r2 = (*a + 5) % EXHAUSTIVE_TEST_ORDER;
+    *r1 = (*a + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER;
+}
+#else
 /**
  * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
  * lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
@@ -333,5 +365,6 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar
     secp256k1_scalar_add(r1, r1, a);
 }
 #endif
+#endif
 
 #endif
diff --git a/src/secp256k1/src/scalar_low.h b/src/secp256k1/src/scalar_low.h
new file mode 100644
index 0000000000..5574c44c7a
--- /dev/null
+++ b/src/secp256k1/src/scalar_low.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_SCALAR_REPR_
+#define _SECP256K1_SCALAR_REPR_
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef uint32_t secp256k1_scalar;
+
+#endif
diff --git a/src/secp256k1/src/scalar_low_impl.h b/src/secp256k1/src/scalar_low_impl.h
new file mode 100644
index 0000000000..4f94441f49
--- /dev/null
+++ b/src/secp256k1/src/scalar_low_impl.h
@@ -0,0 +1,114 @@
+/**********************************************************************
+ * 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_SCALAR_REPR_IMPL_H_
+#define _SECP256K1_SCALAR_REPR_IMPL_H_
+
+#include "scalar.h"
+
+#include <string.h>
+
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    return !(*a & 1);
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { *r = 0; }
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { *r = v; }
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    if (offset < 32)
+        return ((*a >> offset) & ((((uint32_t)1) << count) - 1));
+    else
+        return 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    return secp256k1_scalar_get_bits(a, offset, count);
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { return *a >= EXHAUSTIVE_TEST_ORDER; }
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a + *b) % EXHAUSTIVE_TEST_ORDER;
+    return *r < *b;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    if (flag && bit < 32)
+        *r += (1 << bit);
+#ifdef VERIFY
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    const int base = 0x100 % EXHAUSTIVE_TEST_ORDER;
+    int i;
+    *r = 0;
+    for (i = 0; i < 32; i++) {
+       *r = ((*r * base) + b32[i]) % EXHAUSTIVE_TEST_ORDER;
+    }
+    /* just deny overflow, it basically always happens */
+    if (overflow) *overflow = 0;
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    memset(bin, 0, 32);
+    bin[28] = *a >> 24; bin[29] = *a >> 16; bin[30] = *a >> 8; bin[31] = *a;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return *a == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    if (*a == 0) {
+        *r = 0;
+    } else {
+        *r = EXHAUSTIVE_TEST_ORDER - *a;
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return *a == 1;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    return *a > EXHAUSTIVE_TEST_ORDER / 2;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    if (flag) secp256k1_scalar_negate(r, r);
+    return flag ? -1 : 1;
+}
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a * *b) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = *r & ((1 << n) - 1);
+    *r >>= n;
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    *r = (*a * *a) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r1 = *a;
+    *r2 = 0;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return *a == *b;
+}
+
+#endif
diff --git a/src/secp256k1/src/secp256k1.c b/src/secp256k1/src/secp256k1.c
index 62d192baeb..fb8b882faa 100644..100755
--- a/src/secp256k1/src/secp256k1.c
+++ b/src/secp256k1/src/secp256k1.c
@@ -4,8 +4,6 @@
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
 
-#define SECP256K1_BUILD (1)
-
 #include "include/secp256k1.h"
 
 #include "util.h"
@@ -152,7 +150,6 @@ static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) {
 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));
@@ -170,7 +167,6 @@ int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *o
     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));
@@ -216,7 +212,7 @@ static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const
 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;
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(sig != NULL);
     ARG_CHECK(input != NULL);
 
@@ -234,7 +230,7 @@ int secp256k1_ecdsa_signature_parse_compact(const secp256k1_context* ctx, secp25
     int ret = 1;
     int overflow = 0;
 
-    (void)ctx;
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(sig != NULL);
     ARG_CHECK(input64 != NULL);
 
@@ -253,7 +249,7 @@ int secp256k1_ecdsa_signature_parse_compact(const secp256k1_context* ctx, secp25
 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;
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(output != NULL);
     ARG_CHECK(outputlen != NULL);
     ARG_CHECK(sig != NULL);
@@ -265,7 +261,7 @@ int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsign
 int secp256k1_ecdsa_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, const secp256k1_ecdsa_signature* sig) {
     secp256k1_scalar r, s;
 
-    (void)ctx;
+    VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(output64 != NULL);
     ARG_CHECK(sig != NULL);
 
@@ -363,16 +359,15 @@ int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature
     secp256k1_scalar_set_b32(&sec, seckey, &overflow);
     /* Fail if the secret key is invalid. */
     if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned char nonce32[32];
         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 (!overflow && !secp256k1_scalar_is_zero(&non)) {
                 if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL)) {
                     break;
@@ -380,6 +375,7 @@ int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature
             }
             count++;
         }
+        memset(nonce32, 0, 32);
         secp256k1_scalar_clear(&msg);
         secp256k1_scalar_clear(&non);
         secp256k1_scalar_clear(&sec);
@@ -398,7 +394,6 @@ int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char
     int overflow;
     VERIFY_CHECK(ctx != NULL);
     ARG_CHECK(seckey != NULL);
-    (void)ctx;
 
     secp256k1_scalar_set_b32(&sec, seckey, &overflow);
     ret = !overflow && !secp256k1_scalar_is_zero(&sec);
@@ -437,7 +432,6 @@ int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *
     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);
@@ -485,7 +479,6 @@ int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *
     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);
diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
index 687a5f2fdd..9ae7d30281 100644
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/src/tests.c
@@ -473,6 +473,8 @@ void test_num_negate(void) {
 }
 
 void test_num_add_sub(void) {
+    int i;
+    secp256k1_scalar s;
     secp256k1_num n1;
     secp256k1_num n2;
     secp256k1_num n1p2, n2p1, n1m2, n2m1;
@@ -498,6 +500,110 @@ void test_num_add_sub(void) {
     CHECK(!secp256k1_num_eq(&n2p1, &n1));
     secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */
     CHECK(secp256k1_num_eq(&n2p1, &n1));
+
+    /* check is_one */
+    secp256k1_scalar_set_int(&s, 1);
+    secp256k1_scalar_get_num(&n1, &s);
+    CHECK(secp256k1_num_is_one(&n1));
+    /* check that 2^n + 1 is never 1 */
+    secp256k1_scalar_get_num(&n2, &s);
+    for (i = 0; i < 250; ++i) {
+        secp256k1_num_add(&n1, &n1, &n1);    /* n1 *= 2 */
+        secp256k1_num_add(&n1p2, &n1, &n2);  /* n1p2 = n1 + 1 */
+        CHECK(!secp256k1_num_is_one(&n1p2));
+    }
+}
+
+void test_num_mod(void) {
+    int i;
+    secp256k1_scalar s;
+    secp256k1_num order, n;
+
+    /* check that 0 mod anything is 0 */
+    random_scalar_order_test(&s);
+    secp256k1_scalar_get_num(&order, &s);
+    secp256k1_scalar_set_int(&s, 0);
+    secp256k1_scalar_get_num(&n, &s);
+    secp256k1_num_mod(&n, &order);
+    CHECK(secp256k1_num_is_zero(&n));
+
+    /* check that anything mod 1 is 0 */
+    secp256k1_scalar_set_int(&s, 1);
+    secp256k1_scalar_get_num(&order, &s);
+    secp256k1_scalar_get_num(&n, &s);
+    secp256k1_num_mod(&n, &order);
+    CHECK(secp256k1_num_is_zero(&n));
+
+    /* check that increasing the number past 2^256 does not break this */
+    random_scalar_order_test(&s);
+    secp256k1_scalar_get_num(&n, &s);
+    /* multiply by 2^8, which'll test this case with high probability */
+    for (i = 0; i < 8; ++i) {
+        secp256k1_num_add(&n, &n, &n);
+    }
+    secp256k1_num_mod(&n, &order);
+    CHECK(secp256k1_num_is_zero(&n));
+}
+
+void test_num_jacobi(void) {
+    secp256k1_scalar sqr;
+    secp256k1_scalar small;
+    secp256k1_scalar five;  /* five is not a quadratic residue */
+    secp256k1_num order, n;
+    int i;
+    /* squares mod 5 are 1, 4 */
+    const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 };
+
+    /* check some small values with 5 as the order */
+    secp256k1_scalar_set_int(&five, 5);
+    secp256k1_scalar_get_num(&order, &five);
+    for (i = 0; i < 10; ++i) {
+        secp256k1_scalar_set_int(&small, i);
+        secp256k1_scalar_get_num(&n, &small);
+        CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]);
+    }
+
+    /** test large values with 5 as group order */
+    secp256k1_scalar_get_num(&order, &five);
+    /* we first need a scalar which is not a multiple of 5 */
+    do {
+        secp256k1_num fiven;
+        random_scalar_order_test(&sqr);
+        secp256k1_scalar_get_num(&fiven, &five);
+        secp256k1_scalar_get_num(&n, &sqr);
+        secp256k1_num_mod(&n, &fiven);
+    } while (secp256k1_num_is_zero(&n));
+    /* next force it to be a residue. 2 is a nonresidue mod 5 so we can
+     * just multiply by two, i.e. add the number to itself */
+    if (secp256k1_num_jacobi(&n, &order) == -1) {
+        secp256k1_num_add(&n, &n, &n);
+    }
+
+    /* test residue */
+    CHECK(secp256k1_num_jacobi(&n, &order) == 1);
+    /* test nonresidue */
+    secp256k1_num_add(&n, &n, &n);
+    CHECK(secp256k1_num_jacobi(&n, &order) == -1);
+
+    /** test with secp group order as order */
+    secp256k1_scalar_order_get_num(&order);
+    random_scalar_order_test(&sqr);
+    secp256k1_scalar_sqr(&sqr, &sqr);
+    /* test residue */
+    secp256k1_scalar_get_num(&n, &sqr);
+    CHECK(secp256k1_num_jacobi(&n, &order) == 1);
+    /* test nonresidue */
+    secp256k1_scalar_mul(&sqr, &sqr, &five);
+    secp256k1_scalar_get_num(&n, &sqr);
+    CHECK(secp256k1_num_jacobi(&n, &order) == -1);
+    /* test multiple of the order*/
+    CHECK(secp256k1_num_jacobi(&order, &order) == 0);
+
+    /* check one less than the order */
+    secp256k1_scalar_set_int(&small, 1);
+    secp256k1_scalar_get_num(&n, &small);
+    secp256k1_num_sub(&n, &order, &n);
+    CHECK(secp256k1_num_jacobi(&n, &order) == 1);  /* sage confirms this is 1 */
 }
 
 void run_num_smalltests(void) {
@@ -505,6 +611,8 @@ void run_num_smalltests(void) {
     for (i = 0; i < 100*count; i++) {
         test_num_negate();
         test_num_add_sub();
+        test_num_mod();
+        test_num_jacobi();
     }
 }
 #endif
@@ -689,6 +797,10 @@ void scalar_test(void) {
             secp256k1_scalar_inverse(&inv, &inv);
             /* Inverting one must result in one. */
             CHECK(secp256k1_scalar_is_one(&inv));
+#ifndef USE_NUM_NONE
+            secp256k1_scalar_get_num(&invnum, &inv);
+            CHECK(secp256k1_num_is_one(&invnum));
+#endif
         }
     }
 
@@ -855,7 +967,7 @@ void run_scalar_tests(void) {
         secp256k1_scalar zzv;
 #endif
         int overflow;
-        unsigned char chal[32][2][32] = {
+        unsigned char chal[33][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,
@@ -1111,9 +1223,17 @@ void run_scalar_tests(void) {
              {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}}
+              0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}},
+            {{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+              0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
+              0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03},
+             {0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+              0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
+              0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
+              0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}}
         };
-        unsigned char res[32][2][32] = {
+        unsigned char res[33][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,
@@ -1369,10 +1489,18 @@ void run_scalar_tests(void) {
              {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}}
+              0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}},
+            {{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
+              0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
+              0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
+              0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5},
+             {0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
+              0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
+              0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
+              0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}}
         };
         secp256k1_scalar_set_int(&one, 1);
-        for (i = 0; i < 32; i++) {
+        for (i = 0; i < 33; i++) {
             secp256k1_scalar_set_b32(&x, chal[i][0], &overflow);
             CHECK(!overflow);
             secp256k1_scalar_set_b32(&y, chal[i][1], &overflow);
@@ -1446,7 +1574,7 @@ void random_fe_non_zero(secp256k1_fe *nz) {
 void random_fe_non_square(secp256k1_fe *ns) {
     secp256k1_fe r;
     random_fe_non_zero(ns);
-    if (secp256k1_fe_sqrt_var(&r, ns)) {
+    if (secp256k1_fe_sqrt(&r, ns)) {
         secp256k1_fe_negate(ns, ns, 1);
     }
 }
@@ -1605,18 +1733,18 @@ void run_field_inv_all_var(void) {
     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);
+    secp256k1_fe_inv_all_var(xi, x, 0);
     for (i = 0; i < count; i++) {
         size_t j;
         size_t len = secp256k1_rand_int(15) + 1;
         for (j = 0; j < len; j++) {
             random_fe_non_zero(&x[j]);
         }
-        secp256k1_fe_inv_all_var(len, xi, x);
+        secp256k1_fe_inv_all_var(xi, x, len);
         for (j = 0; j < len; j++) {
             CHECK(check_fe_inverse(&x[j], &xi[j]));
         }
-        secp256k1_fe_inv_all_var(len, xii, xi);
+        secp256k1_fe_inv_all_var(xii, xi, len);
         for (j = 0; j < len; j++) {
             CHECK(check_fe_equal(&x[j], &xii[j]));
         }
@@ -1641,7 +1769,7 @@ void run_sqr(void) {
 
 void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) {
     secp256k1_fe r1, r2;
-    int v = secp256k1_fe_sqrt_var(&r1, a);
+    int v = secp256k1_fe_sqrt(&r1, a);
     CHECK((v == 0) == (k == NULL));
 
     if (k != NULL) {
@@ -1802,7 +1930,7 @@ void test_ge(void) {
                 zs[i] = gej[i].z;
             }
         }
-        secp256k1_fe_inv_all_var(4 * runs + 1, zinv, zs);
+        secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1);
         free(zs);
     }
 
@@ -1922,8 +2050,8 @@ void test_ge(void) {
                 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);
+        secp256k1_ge_set_table_gej_var(ge_set_table, gej, zr, 4 * runs + 1);
+        secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1, &ctx->error_callback);
         for (i = 0; i < 4 * runs + 1; i++) {
             secp256k1_fe s;
             random_fe_non_zero(&s);
@@ -1951,8 +2079,8 @@ void test_add_neg_y_diff_x(void) {
      * 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.
+     * root of https://github.com/bitcoin-core/secp256k1/issues/257
+     * which this test is a regression test for.
      *
      * These points were generated in sage as
      * # secp256k1 params
@@ -2051,15 +2179,16 @@ void run_ec_combine(void) {
 void test_group_decompress(const secp256k1_fe* x) {
     /* The input itself, normalized. */
     secp256k1_fe fex = *x;
-    secp256k1_fe tmp;
+    secp256k1_fe fez;
     /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */
     secp256k1_ge ge_quad, ge_even, ge_odd;
+    secp256k1_gej gej_quad;
     /* 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_quad = secp256k1_ge_set_xquad(&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);
 
@@ -2085,13 +2214,29 @@ void test_group_decompress(const secp256k1_fe* 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(secp256k1_fe_is_quad_var(&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));
+
+        /* Check secp256k1_gej_has_quad_y_var. */
+        secp256k1_gej_set_ge(&gej_quad, &ge_quad);
+        CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
+        do {
+            random_fe_test(&fez);
+        } while (secp256k1_fe_is_zero(&fez));
+        secp256k1_gej_rescale(&gej_quad, &fez);
+        CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
+        secp256k1_gej_neg(&gej_quad, &gej_quad);
+        CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
+        do {
+            random_fe_test(&fez);
+        } while (secp256k1_fe_is_zero(&fez));
+        secp256k1_gej_rescale(&gej_quad, &fez);
+        CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
+        secp256k1_gej_neg(&gej_quad, &gej_quad);
+        CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
     }
 }
 
@@ -2383,9 +2528,7 @@ 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);
@@ -2395,10 +2538,8 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) {
     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
+    skew = secp256k1_wnaf_const(wnaf, num, w);
 
     for (i = WNAF_SIZE(w); i >= 0; --i) {
         secp256k1_scalar t;
@@ -2417,10 +2558,8 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) {
         }
         secp256k1_scalar_add(&x, &x, &t);
     }
-#ifdef USE_ENDOMORPHISM
-    /* Skew num because when encoding 128-bit numbers as odd we use an offset */
+    /* Skew num because when encoding numbers as odd we use an offset */
     secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
-#endif
     CHECK(secp256k1_scalar_eq(&x, &num));
 }
 
@@ -3484,12 +3623,14 @@ 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};
+#ifdef ENABLE_OPENSSL_TESTS
     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
     };
+#endif
 
     int ret = 0;
 
@@ -3607,13 +3748,13 @@ static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) {
 static void damage_array(unsigned char *sig, size_t *len) {
     int pos;
     int action = secp256k1_rand_bits(3);
-    if (action < 1) {
+    if (action < 1 && *len > 3) {
         /* Delete a byte. */
         pos = secp256k1_rand_int(*len);
         memmove(sig + pos, sig + pos + 1, *len - pos - 1);
         (*len)--;
         return;
-    } else if (action < 2) {
+    } else if (action < 2 && *len < 2048) {
         /* Insert a byte. */
         pos = secp256k1_rand_int(1 + *len);
         memmove(sig + pos + 1, sig + pos, *len - pos);
@@ -3785,6 +3926,7 @@ void run_ecdsa_der_parse(void) {
         int certainly_der = 0;
         int certainly_not_der = 0;
         random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der);
+        CHECK(buflen <= 2048);
         for (j = 0; j < 16; j++) {
             int ret = 0;
             if (j > 0) {
diff --git a/src/secp256k1/src/tests_exhaustive.c b/src/secp256k1/src/tests_exhaustive.c
new file mode 100644
index 0000000000..bda6ee475c
--- /dev/null
+++ b/src/secp256k1/src/tests_exhaustive.c
@@ -0,0 +1,329 @@
+/***********************************************************************
+ * Copyright (c) 2016 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <time.h>
+
+#undef USE_ECMULT_STATIC_PRECOMPUTATION
+
+#ifndef EXHAUSTIVE_TEST_ORDER
+/* see group_impl.h for allowable values */
+#define EXHAUSTIVE_TEST_ORDER 13
+#define EXHAUSTIVE_TEST_LAMBDA 9   /* cube root of 1 mod 13 */
+#endif
+
+#include "include/secp256k1.h"
+#include "group.h"
+#include "secp256k1.c"
+#include "testrand_impl.h"
+
+/** stolen from tests.c */
+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(&a->y, &b->y));
+}
+
+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;
+    }
+    /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
+    secp256k1_fe_sqr(&z2s, &b->z);
+    secp256k1_fe_mul(&u1, &a->x, &z2s);
+    u2 = b->x; secp256k1_fe_normalize_weak(&u2);
+    secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
+    s2 = b->y; secp256k1_fe_normalize_weak(&s2);
+    CHECK(secp256k1_fe_equal_var(&u1, &u2));
+    CHECK(secp256k1_fe_equal_var(&s1, &s2));
+}
+
+void random_fe(secp256k1_fe *x) {
+    unsigned char bin[32];
+    do {
+        secp256k1_rand256(bin);
+        if (secp256k1_fe_set_b32(x, bin)) {
+            return;
+        }
+    } while(1);
+}
+/** END stolen from tests.c */
+
+int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32,
+                                      const unsigned char *key32, const unsigned char *algo16,
+                                      void *data, unsigned int attempt) {
+    secp256k1_scalar s;
+    int *idata = data;
+    (void)msg32;
+    (void)key32;
+    (void)algo16;
+    /* Some nonces cannot be used because they'd cause s and/or r to be zero.
+     * The signing function has retry logic here that just re-calls the nonce
+     * function with an increased `attempt`. So if attempt > 0 this means we
+     * need to change the nonce to avoid an infinite loop. */
+    if (attempt > 0) {
+        (*idata)++;
+    }
+    secp256k1_scalar_set_int(&s, *idata);
+    secp256k1_scalar_get_b32(nonce32, &s);
+    return 1;
+}
+
+#ifdef USE_ENDOMORPHISM
+void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) {
+    int i;
+    for (i = 0; i < order; i++) {
+        secp256k1_ge res;
+        secp256k1_ge_mul_lambda(&res, &group[i]);
+        ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res);
+    }
+}
+#endif
+
+void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
+    int i, j;
+
+    /* Sanity-check (and check infinity functions) */
+    CHECK(secp256k1_ge_is_infinity(&group[0]));
+    CHECK(secp256k1_gej_is_infinity(&groupj[0]));
+    for (i = 1; i < order; i++) {
+        CHECK(!secp256k1_ge_is_infinity(&group[i]));
+        CHECK(!secp256k1_gej_is_infinity(&groupj[i]));
+    }
+
+    /* Check all addition formulae */
+    for (j = 0; j < order; j++) {
+        secp256k1_fe fe_inv;
+        secp256k1_fe_inv(&fe_inv, &groupj[j].z);
+        for (i = 0; i < order; i++) {
+            secp256k1_ge zless_gej;
+            secp256k1_gej tmp;
+            /* add_var */
+            secp256k1_gej_add_var(&tmp, &groupj[i], &groupj[j], NULL);
+            ge_equals_gej(&group[(i + j) % order], &tmp);
+            /* add_ge */
+            if (j > 0) {
+                secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]);
+                ge_equals_gej(&group[(i + j) % order], &tmp);
+            }
+            /* add_ge_var */
+            secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL);
+            ge_equals_gej(&group[(i + j) % order], &tmp);
+            /* add_zinv_var */
+            zless_gej.infinity = groupj[j].infinity;
+            zless_gej.x = groupj[j].x;
+            zless_gej.y = groupj[j].y;
+            secp256k1_gej_add_zinv_var(&tmp, &groupj[i], &zless_gej, &fe_inv);
+            ge_equals_gej(&group[(i + j) % order], &tmp);
+        }
+    }
+
+    /* Check doubling */
+    for (i = 0; i < order; i++) {
+        secp256k1_gej tmp;
+        if (i > 0) {
+            secp256k1_gej_double_nonzero(&tmp, &groupj[i], NULL);
+            ge_equals_gej(&group[(2 * i) % order], &tmp);
+        }
+        secp256k1_gej_double_var(&tmp, &groupj[i], NULL);
+        ge_equals_gej(&group[(2 * i) % order], &tmp);
+    }
+
+    /* Check negation */
+    for (i = 1; i < order; i++) {
+        secp256k1_ge tmp;
+        secp256k1_gej tmpj;
+        secp256k1_ge_neg(&tmp, &group[i]);
+        ge_equals_ge(&group[order - i], &tmp);
+        secp256k1_gej_neg(&tmpj, &groupj[i]);
+        ge_equals_gej(&group[order - i], &tmpj);
+    }
+}
+
+void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
+    int i, j, r_log;
+    for (r_log = 1; r_log < order; r_log++) {
+        for (j = 0; j < order; j++) {
+            for (i = 0; i < order; i++) {
+                secp256k1_gej tmp;
+                secp256k1_scalar na, ng;
+                secp256k1_scalar_set_int(&na, i);
+                secp256k1_scalar_set_int(&ng, j);
+
+                secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng);
+                ge_equals_gej(&group[(i * r_log + j) % order], &tmp);
+
+                if (i > 0) {
+                    secp256k1_ecmult_const(&tmp, &group[i], &ng);
+                    ge_equals_gej(&group[(i * j) % order], &tmp);
+                }
+            }
+        }
+    }
+}
+
+void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k) {
+    secp256k1_fe x;
+    unsigned char x_bin[32];
+    k %= EXHAUSTIVE_TEST_ORDER;
+    x = group[k].x;
+    secp256k1_fe_normalize(&x);
+    secp256k1_fe_get_b32(x_bin, &x);
+    secp256k1_scalar_set_b32(r, x_bin, NULL);
+}
+
+void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+    int s, r, msg, key;
+    for (s = 1; s < order; s++) {
+        for (r = 1; r < order; r++) {
+            for (msg = 1; msg < order; msg++) {
+                for (key = 1; key < order; key++) {
+                    secp256k1_ge nonconst_ge;
+                    secp256k1_ecdsa_signature sig;
+                    secp256k1_pubkey pk;
+                    secp256k1_scalar sk_s, msg_s, r_s, s_s;
+                    secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
+                    int k, should_verify;
+                    unsigned char msg32[32];
+
+                    secp256k1_scalar_set_int(&s_s, s);
+                    secp256k1_scalar_set_int(&r_s, r);
+                    secp256k1_scalar_set_int(&msg_s, msg);
+                    secp256k1_scalar_set_int(&sk_s, key);
+
+                    /* Verify by hand */
+                    /* Run through every k value that gives us this r and check that *one* works.
+                     * Note there could be none, there could be multiple, ECDSA is weird. */
+                    should_verify = 0;
+                    for (k = 0; k < order; k++) {
+                        secp256k1_scalar check_x_s;
+                        r_from_k(&check_x_s, group, k);
+                        if (r_s == check_x_s) {
+                            secp256k1_scalar_set_int(&s_times_k_s, k);
+                            secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
+                            secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
+                            secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
+                            should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
+                        }
+                    }
+                    /* nb we have a "high s" rule */
+                    should_verify &= !secp256k1_scalar_is_high(&s_s);
+
+                    /* Verify by calling verify */
+                    secp256k1_ecdsa_signature_save(&sig, &r_s, &s_s);
+                    memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
+                    secp256k1_pubkey_save(&pk, &nonconst_ge);
+                    secp256k1_scalar_get_b32(msg32, &msg_s);
+                    CHECK(should_verify ==
+                          secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
+                }
+            }
+        }
+    }
+}
+
+void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+    int i, j, k;
+
+    /* Loop */
+    for (i = 1; i < order; i++) {  /* message */
+        for (j = 1; j < order; j++) {  /* key */
+            for (k = 1; k < order; k++) {  /* nonce */
+                secp256k1_ecdsa_signature sig;
+                secp256k1_scalar sk, msg, r, s, expected_r;
+                unsigned char sk32[32], msg32[32];
+                secp256k1_scalar_set_int(&msg, i);
+                secp256k1_scalar_set_int(&sk, j);
+                secp256k1_scalar_get_b32(sk32, &sk);
+                secp256k1_scalar_get_b32(msg32, &msg);
+
+                secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+
+                secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig);
+                /* Note that we compute expected_r *after* signing -- this is important
+                 * because our nonce-computing function function might change k during
+                 * signing. */
+                r_from_k(&expected_r, group, k);
+                CHECK(r == expected_r);
+                CHECK((k * s) % order == (i + r * j) % order ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+            }
+        }
+    }
+
+    /* We would like to verify zero-knowledge here by counting how often every
+     * possible (s, r) tuple appears, but because the group order is larger
+     * than the field order, when coercing the x-values to scalar values, some
+     * appear more often than others, so we are actually not zero-knowledge.
+     * (This effect also appears in the real code, but the difference is on the
+     * order of 1/2^128th the field order, so the deviation is not useful to a
+     * computationally bounded attacker.)
+     */
+}
+
+int main(void) {
+    int i;
+    secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER];
+    secp256k1_ge group[EXHAUSTIVE_TEST_ORDER];
+
+    /* Build context */
+    secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    /* TODO set z = 1, then do num_tests runs with random z values */
+
+    /* Generate the entire group */
+    secp256k1_gej_set_infinity(&groupj[0]);
+    secp256k1_ge_set_gej(&group[0], &groupj[0]);
+    for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
+        /* Set a different random z-value for each Jacobian point */
+        secp256k1_fe z;
+        random_fe(&z);
+
+        secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g);
+        secp256k1_ge_set_gej(&group[i], &groupj[i]);
+        secp256k1_gej_rescale(&groupj[i], &z);
+
+        /* Verify against ecmult_gen */
+        {
+            secp256k1_scalar scalar_i;
+            secp256k1_gej generatedj;
+            secp256k1_ge generated;
+
+            secp256k1_scalar_set_int(&scalar_i, i);
+            secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &generatedj, &scalar_i);
+            secp256k1_ge_set_gej(&generated, &generatedj);
+
+            CHECK(group[i].infinity == 0);
+            CHECK(generated.infinity == 0);
+            CHECK(secp256k1_fe_equal_var(&generated.x, &group[i].x));
+            CHECK(secp256k1_fe_equal_var(&generated.y, &group[i].y));
+        }
+    }
+
+    /* Run the tests */
+#ifdef USE_ENDOMORPHISM
+    test_exhaustive_endomorphism(group, EXHAUSTIVE_TEST_ORDER);
+#endif
+    test_exhaustive_addition(group, groupj, EXHAUSTIVE_TEST_ORDER);
+    test_exhaustive_ecmult(ctx, group, groupj, EXHAUSTIVE_TEST_ORDER);
+    test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
+    test_exhaustive_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
+
+    return 0;
+}
+