Update libsecp256k1 subtree to latest master

39 files changed, 1586 insertions, 947 deletions

diff --git a/src/secp256k1/.travis.yml b/src/secp256k1/.travis.yml
index e1a88c4051..bcc8c210f5 100644
--- a/src/secp256k1/.travis.yml
+++ b/src/secp256k1/.travis.yml
@@ -17,33 +17,29 @@ compiler:
   - gcc
 env:
   global:
-    - WIDEMUL=auto  BIGNUM=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ECMULTGENPRECISION=auto  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  RECOVERY=no SCHNORRSIG=no EXPERIMENTAL=no CTIMETEST=yes BENCH=yes ITERS=2
+    - WIDEMUL=auto  BIGNUM=auto  STATICPRECOMPUTATION=yes  ECMULTGENPRECISION=auto  ASM=no  BUILD=check  WITH_VALGRIND=yes RUN_VALGRIND=no EXTRAFLAGS=  HOST=  ECDH=no  RECOVERY=no SCHNORRSIG=no EXPERIMENTAL=no CTIMETEST=yes BENCH=yes ITERS=2
   matrix:
     - WIDEMUL=int64   RECOVERY=yes
     - WIDEMUL=int64   ECDH=yes  EXPERIMENTAL=yes SCHNORRSIG=yes
-    - WIDEMUL=int64   ENDOMORPHISM=yes
     - WIDEMUL=int128
     - WIDEMUL=int128  RECOVERY=yes EXPERIMENTAL=yes SCHNORRSIG=yes
-    - WIDEMUL=int128  ENDOMORPHISM=yes
-    - WIDEMUL=int128  ENDOMORPHISM=yes  ECDH=yes EXPERIMENTAL=yes SCHNORRSIG=yes
+    - WIDEMUL=int128  ECDH=yes EXPERIMENTAL=yes SCHNORRSIG=yes
     - WIDEMUL=int128                    ASM=x86_64
-    - WIDEMUL=int128  ENDOMORPHISM=yes  ASM=x86_64
     - BIGNUM=no
-    - BIGNUM=no       ENDOMORPHISM=yes RECOVERY=yes EXPERIMENTAL=yes SCHNORRSIG=yes
+    - BIGNUM=no       RECOVERY=yes EXPERIMENTAL=yes SCHNORRSIG=yes
     - BIGNUM=no       STATICPRECOMPUTATION=no
-    - BUILD=distcheck CTIMETEST= BENCH=
+    - BUILD=distcheck WITH_VALGRIND=no CTIMETEST=no BENCH=no
     - CPPFLAGS=-DDETERMINISTIC
-    - CFLAGS=-O0 CTIMETEST=
+    - CFLAGS=-O0 CTIMETEST=no
     - ECMULTGENPRECISION=2
     - ECMULTGENPRECISION=8
-    - VALGRIND=yes ENDOMORPHISM=yes BIGNUM=no ASM=x86_64 EXPERIMENTAL=yes ECDH=yes  RECOVERY=yes EXTRAFLAGS="--disable-openssl-tests" CPPFLAGS=-DVALGRIND BUILD=
-    - VALGRIND=yes                  BIGNUM=no ASM=x86_64 EXPERIMENTAL=yes ECDH=yes  RECOVERY=yes EXTRAFLAGS="--disable-openssl-tests" CPPFLAGS=-DVALGRIND BUILD=
+    - RUN_VALGRIND=yes BIGNUM=no ASM=x86_64 EXPERIMENTAL=yes ECDH=yes  RECOVERY=yes EXTRAFLAGS="--disable-openssl-tests" BUILD=
 matrix:
   fast_finish: true
   include:
     - compiler: clang
       os: linux
-      env: HOST=i686-linux-gnu ENDOMORPHISM=yes
+      env: HOST=i686-linux-gnu
       addons:
         apt:
           packages:
@@ -63,7 +59,7 @@ matrix:
             - libtool-bin
             - libc6-dbg:i386
     - compiler: gcc
-      env: HOST=i686-linux-gnu ENDOMORPHISM=yes
+      env: HOST=i686-linux-gnu
       os: linux
       addons:
         apt:
diff --git a/src/secp256k1/README.md b/src/secp256k1/README.md
index 434178b372..2602475787 100644
--- a/src/secp256k1/README.md
+++ b/src/secp256k1/README.md
@@ -48,7 +48,7 @@ Implementation details
   * Use wNAF notation for point multiplicands.
   * Use a much larger window for multiples of G, using precomputed multiples.
   * Use Shamir's trick to do the multiplication with the public key and the generator simultaneously.
-  * Optionally (off by default) use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones.
+  * Use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones.
 * Point multiplication for signing
   * Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions.
   * Intended to be completely free of timing sidechannels for secret-key operations (on reasonable hardware/toolchains)
diff --git a/src/secp256k1/configure.ac b/src/secp256k1/configure.ac
index 6fe8984f4d..5a078e6c81 100644
--- a/src/secp256k1/configure.ac
+++ b/src/secp256k1/configure.ac
@@ -67,7 +67,7 @@ esac
 
 CFLAGS="-W $CFLAGS"
 
-warn_CFLAGS="-std=c89 -pedantic -Wall -Wextra -Wcast-align -Wnested-externs -Wshadow -Wstrict-prototypes -Wno-unused-function -Wno-long-long -Wno-overlength-strings"
+warn_CFLAGS="-std=c89 -pedantic -Wall -Wextra -Wcast-align -Wnested-externs -Wshadow -Wstrict-prototypes -Wundef -Wno-unused-function -Wno-long-long -Wno-overlength-strings"
 saved_CFLAGS="$CFLAGS"
 CFLAGS="$warn_CFLAGS $CFLAGS"
 AC_MSG_CHECKING([if ${CC} supports ${warn_CFLAGS}])
@@ -116,11 +116,6 @@ AC_ARG_ENABLE(exhaustive_tests,
     [use_exhaustive_tests=$enableval],
     [use_exhaustive_tests=yes])
 
-AC_ARG_ENABLE(endomorphism,
-    AS_HELP_STRING([--enable-endomorphism],[enable endomorphism [default=no]]),
-    [use_endomorphism=$enableval],
-    [use_endomorphism=no])
-
 AC_ARG_ENABLE(ecmult_static_precomputation,
     AS_HELP_STRING([--enable-ecmult-static-precomputation],[enable precomputed ecmult table for signing [default=auto]]),
     [use_ecmult_static_precomputation=$enableval],
@@ -164,8 +159,7 @@ AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto],
 AC_ARG_WITH([ecmult-window], [AS_HELP_STRING([--with-ecmult-window=SIZE|auto],
 [window size for ecmult precomputation for verification, specified as integer in range [2..24].]
 [Larger values result in possibly better performance at the cost of an exponentially larger precomputed table.]
-[The table will store 2^(SIZE-2) * 64 bytes of data but can be larger in memory due to platform-specific padding and alignment.]
-[If the endomorphism optimization is enabled, two tables of this size are used instead of only one.]
+[The table will store 2^(SIZE-1) * 64 bytes of data but can be larger in memory due to platform-specific padding and alignment.]
 ["auto" is a reasonable setting for desktop machines (currently 15). [default=auto]]
 )],
 [req_ecmult_window=$withval], [req_ecmult_window=auto])
@@ -178,7 +172,21 @@ AC_ARG_WITH([ecmult-gen-precision], [AS_HELP_STRING([--with-ecmult-gen-precision
 )],
 [req_ecmult_gen_precision=$withval], [req_ecmult_gen_precision=auto])
 
-AC_CHECK_HEADER([valgrind/memcheck.h], [enable_valgrind=yes], [enable_valgrind=no], [])
+AC_ARG_WITH([valgrind], [AS_HELP_STRING([--with-valgrind=yes|no|auto],
+[Build with extra checks for running inside Valgrind [default=auto]]
+)],
+[req_valgrind=$withval], [req_valgrind=auto])
+
+if test x"$req_valgrind" = x"no"; then
+  enable_valgrind=no
+else
+  AC_CHECK_HEADER([valgrind/memcheck.h], [enable_valgrind=yes], [
+    if test x"$req_valgrind" = x"yes"; then
+      AC_MSG_ERROR([Valgrind support explicitly requested but valgrind/memcheck.h header not available])
+    fi
+    enable_valgrind=no
+  ], [])
+fi
 AM_CONDITIONAL([VALGRIND_ENABLED],[test "$enable_valgrind" = "yes"])
 
 if test x"$enable_coverage" = x"yes"; then
@@ -415,10 +423,6 @@ if test x"$set_bignum" = x"gmp"; then
   SECP_INCLUDES="$SECP_INCLUDES $GMP_CPPFLAGS"
 fi
 
-if test x"$use_endomorphism" = x"yes"; then
-  AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization])
-fi
-
 if test x"$set_precomp" = x"yes"; then
   AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table])
 fi
@@ -500,7 +504,6 @@ AC_OUTPUT
 
 echo
 echo "Build Options:"
-echo "  with endomorphism       = $use_endomorphism"
 echo "  with ecmult precomp     = $set_precomp"
 echo "  with external callbacks = $use_external_default_callbacks"
 echo "  with benchmarks         = $use_benchmark"
diff --git a/src/secp256k1/contrib/travis.sh b/src/secp256k1/contrib/travis.sh
index b0b55b44b8..24cc9315cb 100755
--- a/src/secp256k1/contrib/travis.sh
+++ b/src/secp256k1/contrib/travis.sh
@@ -13,27 +13,28 @@ then
 fi
 
 ./configure \
-    --enable-experimental="$EXPERIMENTAL" --enable-endomorphism="$ENDOMORPHISM" \
+    --enable-experimental="$EXPERIMENTAL" \
     --with-test-override-wide-multiply="$WIDEMUL" --with-bignum="$BIGNUM" --with-asm="$ASM" \
     --enable-ecmult-static-precomputation="$STATICPRECOMPUTATION" --with-ecmult-gen-precision="$ECMULTGENPRECISION" \
     --enable-module-ecdh="$ECDH" --enable-module-recovery="$RECOVERY" \
     --enable-module-schnorrsig="$SCHNORRSIG" \
+    --with-valgrind="$WITH_VALGRIND" \
     --host="$HOST" $EXTRAFLAGS
 
 if [ -n "$BUILD" ]
 then
     make -j2 "$BUILD"
 fi
-if [ -n "$VALGRIND" ]
+if [ "$RUN_VALGRIND" = "yes" ]
 then
     make -j2
     # the `--error-exitcode` is required to make the test fail if valgrind found errors, otherwise it'll return 0 (http://valgrind.org/docs/manual/manual-core.html)
     valgrind --error-exitcode=42 ./tests 16
     valgrind --error-exitcode=42 ./exhaustive_tests
 fi
-if [ -n "$BENCH" ]
+if [ "$BENCH" = "yes" ]
 then
-    if [ -n "$VALGRIND" ]
+    if [ "$RUN_VALGRIND" = "yes" ]
     then
         # Using the local `libtool` because on macOS the system's libtool has nothing to do with GNU libtool
         EXEC='./libtool --mode=execute valgrind --error-exitcode=42'
@@ -56,8 +57,12 @@ then
     then
         $EXEC ./bench_ecdh >> bench.log 2>&1
     fi
+    if [ "$SCHNORRSIG" = "yes" ]
+    then
+        $EXEC ./bench_schnorrsig >> bench.log 2>&1
+    fi
 fi
-if [ -n "$CTIMETEST" ]
+if [ "$CTIMETEST" = "yes" ]
 then
     ./libtool --mode=execute valgrind --error-exitcode=42 ./valgrind_ctime_test > valgrind_ctime_test.log 2>&1
 fi
diff --git a/src/secp256k1/sage/gen_exhaustive_groups.sage b/src/secp256k1/sage/gen_exhaustive_groups.sage
new file mode 100644
index 0000000000..3c3c984811
--- /dev/null
+++ b/src/secp256k1/sage/gen_exhaustive_groups.sage
@@ -0,0 +1,129 @@
+# Define field size and field
+P = 2^256 - 2^32 - 977
+F = GF(P)
+BETA = F(0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee)
+
+assert(BETA != F(1) and BETA^3 == F(1))
+
+orders_done = set()
+results = {}
+first = True
+for b in range(1, P):
+    # There are only 6 curves (up to isomorphism) of the form y^2=x^3+B. Stop once we have tried all.
+    if len(orders_done) == 6:
+        break
+
+    E = EllipticCurve(F, [0, b])
+    print("Analyzing curve y^2 = x^3 + %i" % b)
+    n = E.order()
+    # Skip curves with an order we've already tried
+    if n in orders_done:
+        print("- Isomorphic to earlier curve")
+        continue
+    orders_done.add(n)
+    # Skip curves isomorphic to the real secp256k1
+    if n.is_pseudoprime():
+        print(" - Isomorphic to secp256k1")
+        continue
+
+    print("- Finding subgroups")
+
+    # Find what prime subgroups exist
+    for f, _ in n.factor():
+        print("- Analyzing subgroup of order %i" % f)
+        # Skip subgroups of order >1000
+        if f < 4 or f > 1000:
+            print("  - Bad size")
+            continue
+
+        # Iterate over X coordinates until we find one that is on the curve, has order f,
+        # and for which curve isomorphism exists that maps it to X coordinate 1.
+        for x in range(1, P):
+            # Skip X coordinates not on the curve, and construct the full point otherwise.
+            if not E.is_x_coord(x):
+                continue
+            G = E.lift_x(F(x))
+
+            print("  - Analyzing (multiples of) point with X=%i" % x)
+
+            # Skip points whose order is not a multiple of f. Project the point to have
+            # order f otherwise.
+            if (G.order() % f):
+                print("    - Bad order")
+                continue
+            G = G * (G.order() // f)
+
+            # Find lambda for endomorphism. Skip if none can be found.
+            lam = None
+            for l in Integers(f)(1).nth_root(3, all=True):
+                if int(l)*G == E(BETA*G[0], G[1]):
+                    lam = int(l)
+                    break
+            if lam is None:
+                print("    - No endomorphism for this subgroup")
+                break
+
+            # Now look for an isomorphism of the curve that gives this point an X
+            # coordinate equal to 1.
+            # If (x,y) is on y^2 = x^3 + b, then (a^2*x, a^3*y) is on y^2 = x^3 + a^6*b.
+            # So look for m=a^2=1/x.
+            m = F(1)/G[0]
+            if not m.is_square():
+                print("    - No curve isomorphism maps it to a point with X=1")
+                continue
+            a = m.sqrt()
+            rb = a^6*b
+            RE = EllipticCurve(F, [0, rb])
+
+            # Use as generator twice the image of G under the above isormorphism.
+            # This means that generator*(1/2 mod f) will have X coordinate 1.
+            RG = RE(1, a^3*G[1]) * 2
+            # And even Y coordinate.
+            if int(RG[1]) % 2:
+                RG = -RG
+            assert(RG.order() == f)
+            assert(lam*RG == RE(BETA*RG[0], RG[1]))
+
+            # We have found curve RE:y^2=x^3+rb with generator RG of order f. Remember it
+            results[f] = {"b": rb, "G": RG, "lambda": lam}
+            print("    - Found solution")
+            break
+
+    print("")
+
+print("")
+print("")
+print("/* To be put in src/group_impl.h: */")
+first = True
+for f in sorted(results.keys()):
+    b = results[f]["b"]
+    G = results[f]["G"]
+    print("#  %s EXHAUSTIVE_TEST_ORDER == %i" % ("if" if first else "elif", f))
+    first = False
+    print("static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(")
+    print("    0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(G[0]) >> (32 * (7 - i))) & 0xffffffff for i in range(4)))
+    print("    0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(G[0]) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8)))
+    print("    0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(G[1]) >> (32 * (7 - i))) & 0xffffffff for i in range(4)))
+    print("    0x%08x, 0x%08x, 0x%08x, 0x%08x" % tuple((int(G[1]) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8)))
+    print(");")
+    print("static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(")
+    print("    0x%08x, 0x%08x, 0x%08x, 0x%08x," % tuple((int(b) >> (32 * (7 - i))) & 0xffffffff for i in range(4)))
+    print("    0x%08x, 0x%08x, 0x%08x, 0x%08x" % tuple((int(b) >> (32 * (7 - i))) & 0xffffffff for i in range(4, 8)))
+    print(");")
+print("#  else")
+print("#    error No known generator for the specified exhaustive test group order.")
+print("#  endif")
+
+print("")
+print("")
+print("/* To be put in src/scalar_impl.h: */")
+first = True
+for f in sorted(results.keys()):
+    lam = results[f]["lambda"]
+    print("#  %s EXHAUSTIVE_TEST_ORDER == %i" % ("if" if first else "elif", f))
+    first = False
+    print("#    define EXHAUSTIVE_TEST_LAMBDA %i" % lam)
+print("#  else")
+print("#    error No known lambda for the specified exhaustive test group order.")
+print("#  endif")
+print("")
diff --git a/src/secp256k1/src/assumptions.h b/src/secp256k1/src/assumptions.h
index f9d4e8e793..77204de2b8 100644
--- a/src/secp256k1/src/assumptions.h
+++ b/src/secp256k1/src/assumptions.h
@@ -7,6 +7,8 @@
 #ifndef SECP256K1_ASSUMPTIONS_H
 #define SECP256K1_ASSUMPTIONS_H
 
+#include <limits.h>
+
 #include "util.h"
 
 /* This library, like most software, relies on a number of compiler implementation defined (but not undefined)
@@ -19,7 +21,11 @@ struct secp256k1_assumption_checker {
        allowed. */
     int dummy_array[(
         /* Bytes are 8 bits. */
-        CHAR_BIT == 8 &&
+        (CHAR_BIT == 8) &&
+
+        /* No integer promotion for uint32_t. This ensures that we can multiply uintXX_t values where XX >= 32
+           without signed overflow, which would be undefined behaviour. */
+        (UINT_MAX <= UINT32_MAX) &&
 
         /* Conversions from unsigned to signed outside of the bounds of the signed type are
            implementation-defined. Verify that they function as reinterpreting the lower
diff --git a/src/secp256k1/src/basic-config.h b/src/secp256k1/src/basic-config.h
index 83dbe6f25b..b0d82e89b4 100644
--- a/src/secp256k1/src/basic-config.h
+++ b/src/secp256k1/src/basic-config.h
@@ -11,7 +11,6 @@
 
 #undef USE_ASM_X86_64
 #undef USE_ECMULT_STATIC_PRECOMPUTATION
-#undef USE_ENDOMORPHISM
 #undef USE_EXTERNAL_ASM
 #undef USE_EXTERNAL_DEFAULT_CALLBACKS
 #undef USE_FIELD_INV_BUILTIN
diff --git a/src/secp256k1/src/bench_internal.c b/src/secp256k1/src/bench_internal.c
index 9687fe4482..5f2b7a9759 100644
--- a/src/secp256k1/src/bench_internal.c
+++ b/src/secp256k1/src/bench_internal.c
@@ -117,7 +117,6 @@ void bench_scalar_mul(void* arg, int iters) {
     }
 }
 
-#ifdef USE_ENDOMORPHISM
 void bench_scalar_split(void* arg, int iters) {
     int i, j = 0;
     bench_inv *data = (bench_inv*)arg;
@@ -128,7 +127,6 @@ void bench_scalar_split(void* arg, int iters) {
     }
     CHECK(j <= iters);
 }
-#endif
 
 void bench_scalar_inverse(void* arg, int iters) {
     int i, j = 0;
@@ -397,9 +395,7 @@ int main(int argc, char **argv) {
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, iters*100);
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "sqr")) run_benchmark("scalar_sqr", bench_scalar_sqr, bench_setup, NULL, &data, 10, iters*10);
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, iters*10);
-#ifdef USE_ENDOMORPHISM
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, iters);
-#endif
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, 2000);
     if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, 2000);
 
diff --git a/src/secp256k1/src/ecmult.h b/src/secp256k1/src/ecmult.h
index c9b198239d..09e8146414 100644
--- a/src/secp256k1/src/ecmult.h
+++ b/src/secp256k1/src/ecmult.h
@@ -15,9 +15,7 @@
 typedef struct {
     /* For accelerating the computation of a*P + b*G: */
     secp256k1_ge_storage (*pre_g)[];    /* odd multiples of the generator */
-#ifdef USE_ENDOMORPHISM
     secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */
-#endif
 } secp256k1_ecmult_context;
 
 static const size_t SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE;
diff --git a/src/secp256k1/src/ecmult_const_impl.h b/src/secp256k1/src/ecmult_const_impl.h
index 55b61e4937..bb9511108b 100644
--- a/src/secp256k1/src/ecmult_const_impl.h
+++ b/src/secp256k1/src/ecmult_const_impl.h
@@ -140,19 +140,16 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
     secp256k1_fe Z;
 
     int skew_1;
-#ifdef USE_ENDOMORPHISM
     secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
     int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
     int skew_lam;
     secp256k1_scalar q_1, q_lam;
-#endif
     int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
 
     int i;
 
     /* build wnaf representation for q. */
     int rsize = size;
-#ifdef USE_ENDOMORPHISM
     if (size > 128) {
         rsize = 128;
         /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
@@ -160,12 +157,9 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
         skew_1   = secp256k1_wnaf_const(wnaf_1,   &q_1,   WINDOW_A - 1, 128);
         skew_lam = secp256k1_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128);
     } else
-#endif
     {
         skew_1   = secp256k1_wnaf_const(wnaf_1, scalar, WINDOW_A - 1, size);
-#ifdef USE_ENDOMORPHISM
         skew_lam = 0;
-#endif
     }
 
     /* Calculate odd multiples of a.
@@ -179,14 +173,12 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
     for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
         secp256k1_fe_normalize_weak(&pre_a[i].y);
     }
-#ifdef USE_ENDOMORPHISM
     if (size > 128) {
         for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
             secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
         }
 
     }
-#endif
 
     /* first loop iteration (separated out so we can directly set r, rather
      * than having it start at infinity, get doubled several times, then have
@@ -195,14 +187,12 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
     VERIFY_CHECK(i != 0);
     ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
     secp256k1_gej_set_ge(r, &tmpa);
-#ifdef USE_ENDOMORPHISM
     if (size > 128) {
         i = wnaf_lam[WNAF_SIZE_BITS(rsize, 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);
     }
-#endif
     /* remaining loop iterations */
     for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) {
         int n;
@@ -215,14 +205,12 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
         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
         if (size > 128) {
             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);
         }
-#endif
     }
 
     secp256k1_fe_mul(&r->z, &r->z, &Z);
@@ -231,43 +219,35 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
         /* 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
         if (size > 128) {
             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
         if (size > 128) {
             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
         if (size > 128) {
             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);
         }
-#endif
     }
 }
 
diff --git a/src/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h
index f03fa9469d..057a69cf73 100644
--- a/src/secp256k1/src/ecmult_impl.h
+++ b/src/secp256k1/src/ecmult_impl.h
@@ -38,8 +38,8 @@
  *      (1 << (WINDOW_G - 2)) * sizeof(secp256k1_ge_storage)  bytes,
  *  where sizeof(secp256k1_ge_storage) is typically 64 bytes but can
  *  be larger due to platform-specific padding and alignment.
- *  If the endomorphism optimization is enabled (USE_ENDOMORMPHSIM)
- *  two tables of this size are used instead of only one.
+ *  Two tables of this size are used (due to the endomorphism
+ *  optimization).
  */
 #  define WINDOW_G ECMULT_WINDOW_SIZE
 #endif
@@ -59,11 +59,7 @@
 #  error Set ECMULT_WINDOW_SIZE to an integer in range [2..24].
 #endif
 
-#ifdef USE_ENDOMORPHISM
-    #define WNAF_BITS 128
-#else
-    #define WNAF_BITS 256
-#endif
+#define WNAF_BITS 128
 #define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w))
 #define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w)
 
@@ -77,17 +73,9 @@
 #define PIPPENGER_MAX_BUCKET_WINDOW 12
 
 /* Minimum number of points for which pippenger_wnaf is faster than strauss wnaf */
-#ifdef USE_ENDOMORPHISM
-    #define ECMULT_PIPPENGER_THRESHOLD 88
-#else
-    #define ECMULT_PIPPENGER_THRESHOLD 160
-#endif
+#define ECMULT_PIPPENGER_THRESHOLD 88
 
-#ifdef USE_ENDOMORPHISM
-    #define ECMULT_MAX_POINTS_PER_BATCH 5000000
-#else
-    #define ECMULT_MAX_POINTS_PER_BATCH 10000000
-#endif
+#define ECMULT_MAX_POINTS_PER_BATCH 5000000
 
 /** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
  *  the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
@@ -313,16 +301,12 @@ static void secp256k1_ecmult_odd_multiples_table_storage_var(const int n, secp25
 
 static const size_t SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE =
     ROUND_TO_ALIGN(sizeof((*((secp256k1_ecmult_context*) NULL)->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G))
-#ifdef USE_ENDOMORPHISM
     + ROUND_TO_ALIGN(sizeof((*((secp256k1_ecmult_context*) NULL)->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G))
-#endif
     ;
 
 static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
     ctx->pre_g = NULL;
-#ifdef USE_ENDOMORPHISM
     ctx->pre_g_128 = NULL;
-#endif
 }
 
 static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, void **prealloc) {
@@ -347,7 +331,6 @@ static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, void *
     /* precompute the tables with odd multiples */
     secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj);
 
-#ifdef USE_ENDOMORPHISM
     {
         secp256k1_gej g_128j;
         int i;
@@ -364,7 +347,6 @@ static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, void *
         }
         secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j);
     }
-#endif
 }
 
 static void secp256k1_ecmult_context_finalize_memcpy(secp256k1_ecmult_context *dst, const secp256k1_ecmult_context *src) {
@@ -372,11 +354,9 @@ static void secp256k1_ecmult_context_finalize_memcpy(secp256k1_ecmult_context *d
         /* We cast to void* first to suppress a -Wcast-align warning. */
         dst->pre_g = (secp256k1_ge_storage (*)[])(void*)((unsigned char*)dst + ((unsigned char*)(src->pre_g) - (unsigned char*)src));
     }
-#ifdef USE_ENDOMORPHISM
     if (src->pre_g_128 != NULL) {
         dst->pre_g_128 = (secp256k1_ge_storage (*)[])(void*)((unsigned char*)dst + ((unsigned char*)(src->pre_g_128) - (unsigned char*)src));
     }
-#endif
 }
 
 static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
@@ -447,16 +427,11 @@ static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a,
 }
 
 struct secp256k1_strauss_point_state {
-#ifdef USE_ENDOMORPHISM
     secp256k1_scalar na_1, na_lam;
-    int wnaf_na_1[130];
-    int wnaf_na_lam[130];
+    int wnaf_na_1[129];
+    int wnaf_na_lam[129];
     int bits_na_1;
     int bits_na_lam;
-#else
-    int wnaf_na[256];
-    int bits_na;
-#endif
     size_t input_pos;
 };
 
@@ -464,26 +439,19 @@ struct secp256k1_strauss_state {
     secp256k1_gej* prej;
     secp256k1_fe* zr;
     secp256k1_ge* pre_a;
-#ifdef USE_ENDOMORPHISM
     secp256k1_ge* pre_a_lam;
-#endif
     struct secp256k1_strauss_point_state* ps;
 };
 
 static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, const struct secp256k1_strauss_state *state, secp256k1_gej *r, int num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
     secp256k1_ge tmpa;
     secp256k1_fe Z;
-#ifdef USE_ENDOMORPHISM
     /* Splitted G factors. */
     secp256k1_scalar ng_1, ng_128;
     int wnaf_ng_1[129];
     int bits_ng_1 = 0;
     int wnaf_ng_128[129];
     int bits_ng_128 = 0;
-#else
-    int wnaf_ng[256];
-    int bits_ng = 0;
-#endif
     int i;
     int bits = 0;
     int np;
@@ -494,28 +462,20 @@ static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, c
             continue;
         }
         state->ps[no].input_pos = np;
-#ifdef USE_ENDOMORPHISM
         /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
         secp256k1_scalar_split_lambda(&state->ps[no].na_1, &state->ps[no].na_lam, &na[np]);
 
         /* build wnaf representation for na_1 and na_lam. */
-        state->ps[no].bits_na_1   = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1,   130, &state->ps[no].na_1,   WINDOW_A);
-        state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 130, &state->ps[no].na_lam, WINDOW_A);
-        VERIFY_CHECK(state->ps[no].bits_na_1 <= 130);
-        VERIFY_CHECK(state->ps[no].bits_na_lam <= 130);
+        state->ps[no].bits_na_1   = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1,   129, &state->ps[no].na_1,   WINDOW_A);
+        state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 129, &state->ps[no].na_lam, WINDOW_A);
+        VERIFY_CHECK(state->ps[no].bits_na_1 <= 129);
+        VERIFY_CHECK(state->ps[no].bits_na_lam <= 129);
         if (state->ps[no].bits_na_1 > bits) {
             bits = state->ps[no].bits_na_1;
         }
         if (state->ps[no].bits_na_lam > bits) {
             bits = state->ps[no].bits_na_lam;
         }
-#else
-        /* build wnaf representation for na. */
-        state->ps[no].bits_na     = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na,     256, &na[np],      WINDOW_A);
-        if (state->ps[no].bits_na > bits) {
-            bits = state->ps[no].bits_na;
-        }
-#endif
         ++no;
     }
 
@@ -547,7 +507,6 @@ static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, c
         secp256k1_fe_set_int(&Z, 1);
     }
 
-#ifdef USE_ENDOMORPHISM
     for (np = 0; np < no; ++np) {
         for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
             secp256k1_ge_mul_lambda(&state->pre_a_lam[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + i]);
@@ -568,21 +527,12 @@ static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, c
             bits = bits_ng_128;
         }
     }
-#else
-    if (ng) {
-        bits_ng     = secp256k1_ecmult_wnaf(wnaf_ng,     256, ng,      WINDOW_G);
-        if (bits_ng > bits) {
-            bits = bits_ng;
-        }
-    }
-#endif
 
     secp256k1_gej_set_infinity(r);
 
     for (i = bits - 1; i >= 0; i--) {
         int n;
         secp256k1_gej_double_var(r, r, NULL);
-#ifdef USE_ENDOMORPHISM
         for (np = 0; np < no; ++np) {
             if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) {
                 ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
@@ -601,18 +551,6 @@ static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, c
             ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
             secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
         }
-#else
-        for (np = 0; np < no; ++np) {
-            if (i < state->ps[np].bits_na && (n = state->ps[np].wnaf_na[i])) {
-                ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
-                secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
-            }
-        }
-        if (i < bits_ng && (n = wnaf_ng[i])) {
-            ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
-            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
-        }
-#endif
     }
 
     if (!r->infinity) {
@@ -625,27 +563,19 @@ static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej
     secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
     secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
     struct secp256k1_strauss_point_state ps[1];
-#ifdef USE_ENDOMORPHISM
     secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
-#endif
     struct secp256k1_strauss_state state;
 
     state.prej = prej;
     state.zr = zr;
     state.pre_a = pre_a;
-#ifdef USE_ENDOMORPHISM
     state.pre_a_lam = pre_a_lam;
-#endif
     state.ps = ps;
     secp256k1_ecmult_strauss_wnaf(ctx, &state, r, 1, a, na, ng);
 }
 
 static size_t secp256k1_strauss_scratch_size(size_t n_points) {
-#ifdef USE_ENDOMORPHISM
     static const size_t point_size = (2 * sizeof(secp256k1_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar);
-#else
-    static const size_t point_size = (sizeof(secp256k1_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar);
-#endif
     return n_points*point_size;
 }
 
@@ -665,12 +595,8 @@ static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callba
     scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_scalar));
     state.prej = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_gej));
     state.zr = (secp256k1_fe*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe));
-#ifdef USE_ENDOMORPHISM
     state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * 2 * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
     state.pre_a_lam = state.pre_a + n_points * ECMULT_TABLE_SIZE(WINDOW_A);
-#else
-    state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
-#endif
     state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(struct secp256k1_strauss_point_state));
 
     if (points == NULL || scalars == NULL || state.prej == NULL || state.zr == NULL || state.pre_a == NULL) {
@@ -868,7 +794,6 @@ static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_wi
  * set of buckets) for a given number of points.
  */
 static int secp256k1_pippenger_bucket_window(size_t n) {
-#ifdef USE_ENDOMORPHISM
     if (n <= 1) {
         return 1;
     } else if (n <= 4) {
@@ -892,33 +817,6 @@ static int secp256k1_pippenger_bucket_window(size_t n) {
     } else {
         return PIPPENGER_MAX_BUCKET_WINDOW;
     }
-#else
-    if (n <= 1) {
-        return 1;
-    } else if (n <= 11) {
-        return 2;
-    } else if (n <= 45) {
-        return 3;
-    } else if (n <= 100) {
-        return 4;
-    } else if (n <= 275) {
-        return 5;
-    } else if (n <= 625) {
-        return 6;
-    } else if (n <= 1850) {
-        return 7;
-    } else if (n <= 3400) {
-        return 8;
-    } else if (n <= 9630) {
-        return 9;
-    } else if (n <= 17900) {
-        return 10;
-    } else if (n <= 32800) {
-        return 11;
-    } else {
-        return PIPPENGER_MAX_BUCKET_WINDOW;
-    }
-#endif
 }
 
 /**
@@ -926,7 +824,6 @@ static int secp256k1_pippenger_bucket_window(size_t n) {
  */
 static size_t secp256k1_pippenger_bucket_window_inv(int bucket_window) {
     switch(bucket_window) {
-#ifdef USE_ENDOMORPHISM
         case 1: return 1;
         case 2: return 4;
         case 3: return 20;
@@ -939,26 +836,11 @@ static size_t secp256k1_pippenger_bucket_window_inv(int bucket_window) {
         case 10: return 7880;
         case 11: return 16050;
         case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX;
-#else
-        case 1: return 1;
-        case 2: return 11;
-        case 3: return 45;
-        case 4: return 100;
-        case 5: return 275;
-        case 6: return 625;
-        case 7: return 1850;
-        case 8: return 3400;
-        case 9: return 9630;
-        case 10: return 17900;
-        case 11: return 32800;
-        case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX;
-#endif
     }
     return 0;
 }
 
 
-#ifdef USE_ENDOMORPHISM
 SECP256K1_INLINE static void secp256k1_ecmult_endo_split(secp256k1_scalar *s1, secp256k1_scalar *s2, secp256k1_ge *p1, secp256k1_ge *p2) {
     secp256k1_scalar tmp = *s1;
     secp256k1_scalar_split_lambda(s1, s2, &tmp);
@@ -973,32 +855,23 @@ SECP256K1_INLINE static void secp256k1_ecmult_endo_split(secp256k1_scalar *s1, s
         secp256k1_ge_neg(p2, p2);
     }
 }
-#endif
 
 /**
  * Returns the scratch size required for a given number of points (excluding
  * base point G) without considering alignment.
  */
 static size_t secp256k1_pippenger_scratch_size(size_t n_points, int bucket_window) {
-#ifdef USE_ENDOMORPHISM
     size_t entries = 2*n_points + 2;
-#else
-    size_t entries = n_points + 1;
-#endif
     size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int);
     return (sizeof(secp256k1_gej) << bucket_window) + sizeof(struct secp256k1_pippenger_state) + entries * entry_size;
 }
 
 static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
     const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch);
-    /* Use 2(n+1) with the endomorphism, n+1 without, when calculating batch
+    /* Use 2(n+1) with the endomorphism, when calculating batch
      * sizes. The reason for +1 is that we add the G scalar to the list of
      * other scalars. */
-#ifdef USE_ENDOMORPHISM
     size_t entries = 2*n_points + 2;
-#else
-    size_t entries = n_points + 1;
-#endif
     secp256k1_ge *points;
     secp256k1_scalar *scalars;
     secp256k1_gej *buckets;
@@ -1035,10 +908,8 @@ static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_call
         scalars[0] = *inp_g_sc;
         points[0] = secp256k1_ge_const_g;
         idx++;
-#ifdef USE_ENDOMORPHISM
         secp256k1_ecmult_endo_split(&scalars[0], &scalars[1], &points[0], &points[1]);
         idx++;
-#endif
     }
 
     while (point_idx < n_points) {
@@ -1047,10 +918,8 @@ static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_call
             return 0;
         }
         idx++;
-#ifdef USE_ENDOMORPHISM
         secp256k1_ecmult_endo_split(&scalars[idx - 1], &scalars[idx], &points[idx - 1], &points[idx]);
         idx++;
-#endif
         point_idx++;
     }
 
@@ -1093,9 +962,7 @@ static size_t secp256k1_pippenger_max_points(const secp256k1_callback* error_cal
         size_t space_overhead;
         size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int);
 
-#ifdef USE_ENDOMORPHISM
         entry_size = 2*entry_size;
-#endif
         space_overhead = (sizeof(secp256k1_gej) << bucket_window) + entry_size + sizeof(struct secp256k1_pippenger_state);
         if (space_overhead > max_alloc) {
             break;
diff --git a/src/secp256k1/src/group.h b/src/secp256k1/src/group.h
index 6185be052d..36e39ecf0f 100644
--- a/src/secp256k1/src/group.h
+++ b/src/secp256k1/src/group.h
@@ -59,6 +59,7 @@ static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
 /** Check whether a group element is valid (i.e., on the curve). */
 static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
 
+/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
 static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
 
 /** Set a group element equal to another which is given in jacobian coordinates */
@@ -115,10 +116,8 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
 /** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
 static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
 
-#ifdef USE_ENDOMORPHISM
 /** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
 static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
-#endif
 
 /** Clear a secp256k1_gej to prevent leaking sensitive information. */
 static void secp256k1_gej_clear(secp256k1_gej *r);
@@ -138,4 +137,15 @@ static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_g
 /** Rescale a jacobian point by b which must be non-zero. Constant-time. */
 static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
 
+/** Determine if a point (which is assumed to be on the curve) is in the correct (sub)group of the curve.
+ *
+ * In normal mode, the used group is secp256k1, which has cofactor=1 meaning that every point on the curve is in the
+ * group, and this function returns always true.
+ *
+ * When compiling in exhaustive test mode, a slightly different curve equation is used, leading to a group with a
+ * (very) small subgroup, and that subgroup is what is used for all cryptographic operations. In that mode, this
+ * function checks whether a point that is on the curve is in fact also in that subgroup.
+ */
+static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge);
+
 #endif /* SECP256K1_GROUP_H */
diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h
index ccd93d3483..a5fbc91a0f 100644
--- a/src/secp256k1/src/group_impl.h
+++ b/src/secp256k1/src/group_impl.h
@@ -11,49 +11,38 @@
 #include "field.h"
 #include "group.h"
 
-/* These points can be generated in sage as follows:
+/* These exhaustive group test orders and generators are chosen such that:
+ * - The field size is equal to that of secp256k1, so field code is the same.
+ * - The curve equation is of the form y^2=x^3+B for some constant B.
+ * - The subgroup has a generator 2*P, where P.x=1.
+ * - The subgroup has size less than 1000 to permit exhaustive testing.
+ * - The subgroup admits an endomorphism of the form lambda*(x,y) == (beta*x,y).
  *
- * 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()
+ * These parameters are generated using sage/gen_exhaustive_groups.sage.
  */
 #if defined(EXHAUSTIVE_TEST_ORDER)
-#  if EXHAUSTIVE_TEST_ORDER == 199
+#  if EXHAUSTIVE_TEST_ORDER == 13
 static 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
+    0xc3459c3d, 0x35326167, 0xcd86cce8, 0x07a2417f,
+    0x5b8bd567, 0xde8538ee, 0x0d507b0c, 0xd128f5bb,
+    0x8e467fec, 0xcd30000a, 0x6cc1184e, 0x25d382c2,
+    0xa2f4494e, 0x2fbe9abc, 0x8b64abac, 0xd005fb24
 );
-
-static const int CURVE_B = 4;
-#  elif EXHAUSTIVE_TEST_ORDER == 13
+static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(
+    0x3d3486b2, 0x159a9ca5, 0xc75638be, 0xb23a69bc,
+    0x946a45ab, 0x24801247, 0xb4ed2b8e, 0x26b6a417
+);
+#  elif EXHAUSTIVE_TEST_ORDER == 199
 static 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
+    0x226e653f, 0xc8df7744, 0x9bacbf12, 0x7d1dcbf9,
+    0x87f05b2a, 0xe7edbd28, 0x1f564575, 0xc48dcf18,
+    0xa13872c2, 0xe933bb17, 0x5d9ffd5b, 0xb5b6e10c,
+    0x57fe3c00, 0xbaaaa15a, 0xe003ec3e, 0x9c269bae
+);
+static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(
+    0x2cca28fa, 0xfc614b80, 0x2a3db42b, 0x00ba00b1,
+    0xbea8d943, 0xdace9ab2, 0x9536daea, 0x0074defb
 );
-static const int CURVE_B = 2;
 #  else
 #    error No known generator for the specified exhaustive test group order.
 #  endif
@@ -68,7 +57,7 @@ static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
     0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
 );
 
-static const int CURVE_B = 7;
+static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 7);
 #endif
 
 static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
@@ -219,14 +208,13 @@ static void secp256k1_ge_clear(secp256k1_ge *r) {
 }
 
 static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) {
-    secp256k1_fe x2, x3, c;
+    secp256k1_fe x2, x3;
     r->x = *x;
     secp256k1_fe_sqr(&x2, x);
     secp256k1_fe_mul(&x3, x, &x2);
     r->infinity = 0;
-    secp256k1_fe_set_int(&c, CURVE_B);
-    secp256k1_fe_add(&c, &x3);
-    return secp256k1_fe_sqrt(&r->y, &c);
+    secp256k1_fe_add(&x3, &secp256k1_fe_const_b);
+    return secp256k1_fe_sqrt(&r->y, &x3);
 }
 
 static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
@@ -269,36 +257,15 @@ static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
     return a->infinity;
 }
 
-static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
-    secp256k1_fe y2, x3, z2, z6;
-    if (a->infinity) {
-        return 0;
-    }
-    /** y^2 = x^3 + 7
-     *  (Y/Z^3)^2 = (X/Z^2)^3 + 7
-     *  Y^2 / Z^6 = X^3 / Z^6 + 7
-     *  Y^2 = X^3 + 7*Z^6
-     */
-    secp256k1_fe_sqr(&y2, &a->y);
-    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, CURVE_B);
-    secp256k1_fe_add(&x3, &z6);
-    secp256k1_fe_normalize_weak(&x3);
-    return secp256k1_fe_equal_var(&y2, &x3);
-}
-
 static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
-    secp256k1_fe y2, x3, c;
+    secp256k1_fe y2, x3;
     if (a->infinity) {
         return 0;
     }
     /* 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, CURVE_B);
-    secp256k1_fe_add(&x3, &c);
+    secp256k1_fe_add(&x3, &secp256k1_fe_const_b);
     secp256k1_fe_normalize_weak(&x3);
     return secp256k1_fe_equal_var(&y2, &x3);
 }
@@ -679,7 +646,6 @@ static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r,
     secp256k1_fe_storage_cmov(&r->y, &a->y, flag);
 }
 
-#ifdef USE_ENDOMORPHISM
 static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
     static const secp256k1_fe beta = SECP256K1_FE_CONST(
         0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
@@ -688,7 +654,6 @@ static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
     *r = *a;
     secp256k1_fe_mul(&r->x, &r->x, &beta);
 }
-#endif
 
 static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a) {
     secp256k1_fe yz;
@@ -704,4 +669,25 @@ static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a) {
     return secp256k1_fe_is_quad_var(&yz);
 }
 
+static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
+#ifdef EXHAUSTIVE_TEST_ORDER
+    secp256k1_gej out;
+    int i;
+
+    /* A very simple EC multiplication ladder that avoids a dependecy on ecmult. */
+    secp256k1_gej_set_infinity(&out);
+    for (i = 0; i < 32; ++i) {
+        secp256k1_gej_double_var(&out, &out, NULL);
+        if ((((uint32_t)EXHAUSTIVE_TEST_ORDER) >> (31 - i)) & 1) {
+            secp256k1_gej_add_ge_var(&out, &out, ge, NULL);
+        }
+    }
+    return secp256k1_gej_is_infinity(&out);
+#else
+    (void)ge;
+    /* The real secp256k1 group has cofactor 1, so the subgroup is the entire curve. */
+    return 1;
+#endif
+}
+
 #endif /* SECP256K1_GROUP_IMPL_H */
diff --git a/src/secp256k1/src/modules/ecdh/tests_impl.h b/src/secp256k1/src/modules/ecdh/tests_impl.h
index fe26e8fb69..e8d2aeab9a 100644
--- a/src/secp256k1/src/modules/ecdh/tests_impl.h
+++ b/src/secp256k1/src/modules/ecdh/tests_impl.h
@@ -80,7 +80,7 @@ void test_ecdh_generator_basepoint(void) {
         /* compute "explicitly" */
         CHECK(secp256k1_ec_pubkey_serialize(ctx, point_ser, &point_ser_len, &point[1], SECP256K1_EC_UNCOMPRESSED) == 1);
         /* compare */
-        CHECK(memcmp(output_ecdh, point_ser, 65) == 0);
+        CHECK(secp256k1_memcmp_var(output_ecdh, point_ser, 65) == 0);
 
         /* compute using ECDH function with default hash function */
         CHECK(secp256k1_ecdh(ctx, output_ecdh, &point[0], s_b32, NULL, NULL) == 1);
@@ -90,7 +90,7 @@ void test_ecdh_generator_basepoint(void) {
         secp256k1_sha256_write(&sha, point_ser, point_ser_len);
         secp256k1_sha256_finalize(&sha, output_ser);
         /* compare */
-        CHECK(memcmp(output_ecdh, output_ser, 32) == 0);
+        CHECK(secp256k1_memcmp_var(output_ecdh, output_ser, 32) == 0);
     }
 }
 
diff --git a/src/secp256k1/src/modules/extrakeys/Makefile.am.include b/src/secp256k1/src/modules/extrakeys/Makefile.am.include
index 8515f92e7a..0d901ec1f4 100644
--- a/src/secp256k1/src/modules/extrakeys/Makefile.am.include
+++ b/src/secp256k1/src/modules/extrakeys/Makefile.am.include
@@ -1,3 +1,4 @@
 include_HEADERS += include/secp256k1_extrakeys.h
 noinst_HEADERS += src/modules/extrakeys/tests_impl.h
+noinst_HEADERS += src/modules/extrakeys/tests_exhaustive_impl.h
 noinst_HEADERS += src/modules/extrakeys/main_impl.h
diff --git a/src/secp256k1/src/modules/extrakeys/main_impl.h b/src/secp256k1/src/modules/extrakeys/main_impl.h
index d319215355..5378d2f301 100644
--- a/src/secp256k1/src/modules/extrakeys/main_impl.h
+++ b/src/secp256k1/src/modules/extrakeys/main_impl.h
@@ -33,6 +33,9 @@ int secp256k1_xonly_pubkey_parse(const secp256k1_context* ctx, secp256k1_xonly_p
     if (!secp256k1_ge_set_xo_var(&pk, &x, 0)) {
         return 0;
     }
+    if (!secp256k1_ge_is_in_correct_subgroup(&pk)) {
+        return 0;
+    }
     secp256k1_xonly_pubkey_save(pubkey, &pk);
     return 1;
 }
@@ -121,7 +124,7 @@ int secp256k1_xonly_pubkey_tweak_add_check(const secp256k1_context* ctx, const u
     secp256k1_fe_normalize_var(&pk.y);
     secp256k1_fe_get_b32(pk_expected32, &pk.x);
 
-    return memcmp(&pk_expected32, tweaked_pubkey32, 32) == 0
+    return secp256k1_memcmp_var(&pk_expected32, tweaked_pubkey32, 32) == 0
             && secp256k1_fe_is_odd(&pk.y) == tweaked_pk_parity;
 }
 
diff --git a/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h b/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h
new file mode 100644
index 0000000000..0e29bc6b09
--- /dev/null
+++ b/src/secp256k1/src/modules/extrakeys/tests_exhaustive_impl.h
@@ -0,0 +1,68 @@
+/**********************************************************************
+ * Copyright (c) 2020 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_EXTRAKEYS_TESTS_EXHAUSTIVE_
+#define _SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_
+
+#include "src/modules/extrakeys/main_impl.h"
+#include "include/secp256k1_extrakeys.h"
+
+static void test_exhaustive_extrakeys(const secp256k1_context *ctx, const secp256k1_ge* group) {
+    secp256k1_keypair keypair[EXHAUSTIVE_TEST_ORDER - 1];
+    secp256k1_pubkey pubkey[EXHAUSTIVE_TEST_ORDER - 1];
+    secp256k1_xonly_pubkey xonly_pubkey[EXHAUSTIVE_TEST_ORDER - 1];
+    int parities[EXHAUSTIVE_TEST_ORDER - 1];
+    unsigned char xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - 1][32];
+    int i;
+
+    for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
+        secp256k1_fe fe;
+        secp256k1_scalar scalar_i;
+        unsigned char buf[33];
+        int parity;
+
+        secp256k1_scalar_set_int(&scalar_i, i);
+        secp256k1_scalar_get_b32(buf, &scalar_i);
+
+        /* Construct pubkey and keypair. */
+        CHECK(secp256k1_keypair_create(ctx, &keypair[i - 1], buf));
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey[i - 1], buf));
+
+        /* Construct serialized xonly_pubkey from keypair. */
+        CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pubkey[i - 1], &parities[i - 1], &keypair[i - 1]));
+        CHECK(secp256k1_xonly_pubkey_serialize(ctx, xonly_pubkey_bytes[i - 1], &xonly_pubkey[i - 1]));
+
+        /* Parse the xonly_pubkey back and verify it matches the previously serialized value. */
+        CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pubkey[i - 1], xonly_pubkey_bytes[i - 1]));
+        CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf, &xonly_pubkey[i - 1]));
+        CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], buf, 32) == 0);
+
+        /* Construct the xonly_pubkey from the pubkey, and verify it matches the same. */
+        CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pubkey[i - 1], &parity, &pubkey[i - 1]));
+        CHECK(parity == parities[i - 1]);
+        CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf, &xonly_pubkey[i - 1]));
+        CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], buf, 32) == 0);
+
+        /* Compare the xonly_pubkey bytes against the precomputed group. */
+        secp256k1_fe_set_b32(&fe, xonly_pubkey_bytes[i - 1]);
+        CHECK(secp256k1_fe_equal_var(&fe, &group[i].x));
+
+        /* Check the parity against the precomputed group. */
+        fe = group[i].y;
+        secp256k1_fe_normalize_var(&fe);
+        CHECK(secp256k1_fe_is_odd(&fe) == parities[i - 1]);
+
+        /* Verify that the higher half is identical to the lower half mirrored. */
+        if (i > EXHAUSTIVE_TEST_ORDER / 2) {
+            CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - i - 1], 32) == 0);
+            CHECK(parities[i - 1] == 1 - parities[EXHAUSTIVE_TEST_ORDER - i - 1]);
+        }
+    }
+
+    /* TODO: keypair/xonly_pubkey tweak tests */
+}
+
+#endif
diff --git a/src/secp256k1/src/modules/extrakeys/tests_impl.h b/src/secp256k1/src/modules/extrakeys/tests_impl.h
index fc9d40eda1..5ee135849e 100644
--- a/src/secp256k1/src/modules/extrakeys/tests_impl.h
+++ b/src/secp256k1/src/modules/extrakeys/tests_impl.h
@@ -35,9 +35,9 @@ void test_xonly_pubkey(void) {
     secp256k1_context *sign = api_test_context(SECP256K1_CONTEXT_SIGN, &ecount);
     secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
 
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(sk);
     memset(ones32, 0xFF, 32);
-    secp256k1_rand256(xy_sk);
+    secp256k1_testrand256(xy_sk);
     CHECK(secp256k1_ec_pubkey_create(sign, &pk, sk) == 1);
     CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, &pk_parity, &pk) == 1);
 
@@ -60,7 +60,7 @@ void test_xonly_pubkey(void) {
     sk[0] = 1;
     CHECK(secp256k1_ec_pubkey_create(ctx, &pk, sk) == 1);
     CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, &pk_parity, &pk) == 1);
-    CHECK(memcmp(&pk, &xonly_pk, sizeof(pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&pk, &xonly_pk, sizeof(pk)) == 0);
     CHECK(pk_parity == 0);
 
     /* Choose a secret key such that pubkey and xonly_pubkey are each others
@@ -68,7 +68,7 @@ void test_xonly_pubkey(void) {
     sk[0] = 2;
     CHECK(secp256k1_ec_pubkey_create(ctx, &pk, sk) == 1);
     CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pk, &pk_parity, &pk) == 1);
-    CHECK(memcmp(&xonly_pk, &pk, sizeof(xonly_pk)) != 0);
+    CHECK(secp256k1_memcmp_var(&xonly_pk, &pk, sizeof(xonly_pk)) != 0);
     CHECK(pk_parity == 1);
     secp256k1_pubkey_load(ctx, &pk1, &pk);
     secp256k1_pubkey_load(ctx, &pk2, (secp256k1_pubkey *) &xonly_pk);
@@ -81,7 +81,7 @@ void test_xonly_pubkey(void) {
     CHECK(secp256k1_xonly_pubkey_serialize(none, NULL, &xonly_pk) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_xonly_pubkey_serialize(none, buf32, NULL) == 0);
-    CHECK(memcmp(buf32, zeros64, 32) == 0);
+    CHECK(secp256k1_memcmp_var(buf32, zeros64, 32) == 0);
     CHECK(ecount == 2);
     {
         /* A pubkey filled with 0s will fail to serialize due to pubkey_load
@@ -104,28 +104,28 @@ void test_xonly_pubkey(void) {
     CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, NULL, &pk) == 1);
     CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf32, &xonly_pk) == 1);
     CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pk_tmp, buf32) == 1);
-    CHECK(memcmp(&xonly_pk, &xonly_pk_tmp, sizeof(xonly_pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&xonly_pk, &xonly_pk_tmp, sizeof(xonly_pk)) == 0);
 
     /* Test parsing invalid field elements */
     memset(&xonly_pk, 1, sizeof(xonly_pk));
     /* Overflowing field element */
     CHECK(secp256k1_xonly_pubkey_parse(none, &xonly_pk, ones32) == 0);
-    CHECK(memcmp(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0);
     memset(&xonly_pk, 1, sizeof(xonly_pk));
     /* There's no point with x-coordinate 0 on secp256k1 */
     CHECK(secp256k1_xonly_pubkey_parse(none, &xonly_pk, zeros64) == 0);
-    CHECK(memcmp(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0);
     /* If a random 32-byte string can not be parsed with ec_pubkey_parse
      * (because interpreted as X coordinate it does not correspond to a point on
      * the curve) then xonly_pubkey_parse should fail as well. */
     for (i = 0; i < count; i++) {
         unsigned char rand33[33];
-        secp256k1_rand256(&rand33[1]);
+        secp256k1_testrand256(&rand33[1]);
         rand33[0] = SECP256K1_TAG_PUBKEY_EVEN;
         if (!secp256k1_ec_pubkey_parse(ctx, &pk, rand33, 33)) {
             memset(&xonly_pk, 1, sizeof(xonly_pk));
             CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pk, &rand33[1]) == 0);
-            CHECK(memcmp(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0);
+            CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0);
         } else {
             CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pk, &rand33[1]) == 1);
         }
@@ -154,8 +154,8 @@ void test_xonly_pubkey_tweak(void) {
     secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
 
     memset(overflows, 0xff, sizeof(overflows));
-    secp256k1_rand256(tweak);
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(tweak);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_ec_pubkey_create(ctx, &internal_pk, sk) == 1);
     CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &internal_xonly_pk, &pk_parity, &internal_pk) == 1);
 
@@ -170,15 +170,15 @@ void test_xonly_pubkey_tweak(void) {
     CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, NULL, tweak) == 0);
     CHECK(ecount == 4);
     /* NULL internal_xonly_pk zeroes the output_pk */
-    CHECK(memcmp(&output_pk, zeros64, sizeof(output_pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0);
     CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, NULL) == 0);
     CHECK(ecount == 5);
     /* NULL tweak zeroes the output_pk */
-    CHECK(memcmp(&output_pk, zeros64, sizeof(output_pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0);
 
     /* Invalid tweak zeroes the output_pk */
     CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, overflows) == 0);
-    CHECK(memcmp(&output_pk, zeros64, sizeof(output_pk))  == 0);
+    CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk))  == 0);
 
     /* A zero tweak is fine */
     CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, zeros64) == 1);
@@ -193,16 +193,16 @@ void test_xonly_pubkey_tweak(void) {
         secp256k1_scalar_get_b32(tweak, &scalar_tweak);
         CHECK((secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, sk) == 0)
               || (secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, tweak) == 0));
-        CHECK(memcmp(&output_pk, zeros64, sizeof(output_pk)) == 0);
+        CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0);
     }
 
     /* Invalid pk with a valid tweak */
     memset(&internal_xonly_pk, 0, sizeof(internal_xonly_pk));
-    secp256k1_rand256(tweak);
+    secp256k1_testrand256(tweak);
     ecount = 0;
     CHECK(secp256k1_xonly_pubkey_tweak_add(verify, &output_pk, &internal_xonly_pk, tweak) == 0);
     CHECK(ecount == 1);
-    CHECK(memcmp(&output_pk, zeros64, sizeof(output_pk))  == 0);
+    CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk))  == 0);
 
     secp256k1_context_destroy(none);
     secp256k1_context_destroy(sign);
@@ -228,8 +228,8 @@ void test_xonly_pubkey_tweak_check(void) {
     secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
 
     memset(overflows, 0xff, sizeof(overflows));
-    secp256k1_rand256(tweak);
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(tweak);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_ec_pubkey_create(ctx, &internal_pk, sk) == 1);
     CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &internal_xonly_pk, &pk_parity, &internal_pk) == 1);
 
@@ -268,7 +268,7 @@ void test_xonly_pubkey_tweak_check(void) {
     /* Overflowing tweak not allowed */
     CHECK(secp256k1_xonly_pubkey_tweak_add_check(ctx, output_pk32, pk_parity, &internal_xonly_pk, overflows) == 0);
     CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk, &internal_xonly_pk, overflows) == 0);
-    CHECK(memcmp(&output_pk, zeros64, sizeof(output_pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0);
     CHECK(ecount == 5);
 
     secp256k1_context_destroy(none);
@@ -287,7 +287,7 @@ void test_xonly_pubkey_tweak_recursive(void) {
     unsigned char tweak[N_PUBKEYS - 1][32];
     int i;
 
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_ec_pubkey_create(ctx, &pk[0], sk) == 1);
     /* Add tweaks */
     for (i = 0; i < N_PUBKEYS - 1; i++) {
@@ -327,51 +327,51 @@ void test_keypair(void) {
 
     /* Test keypair_create */
     ecount = 0;
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(none, &keypair, sk) == 0);
-    CHECK(memcmp(zeros96, &keypair, sizeof(keypair)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_keypair_create(verify, &keypair, sk) == 0);
-    CHECK(memcmp(zeros96, &keypair, sizeof(keypair)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
     CHECK(ecount == 2);
     CHECK(secp256k1_keypair_create(sign, &keypair, sk) == 1);
     CHECK(secp256k1_keypair_create(sign, NULL, sk) == 0);
     CHECK(ecount == 3);
     CHECK(secp256k1_keypair_create(sign, &keypair, NULL) == 0);
-    CHECK(memcmp(zeros96, &keypair, sizeof(keypair)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
     CHECK(ecount == 4);
 
     /* Invalid secret key */
     CHECK(secp256k1_keypair_create(sign, &keypair, zeros96) == 0);
-    CHECK(memcmp(zeros96, &keypair, sizeof(keypair)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
     CHECK(secp256k1_keypair_create(sign, &keypair, overflows) == 0);
-    CHECK(memcmp(zeros96, &keypair, sizeof(keypair)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0);
 
     /* Test keypair_pub */
     ecount = 0;
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
     CHECK(secp256k1_keypair_pub(none, &pk, &keypair) == 1);
     CHECK(secp256k1_keypair_pub(none, NULL, &keypair) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_keypair_pub(none, &pk, NULL) == 0);
     CHECK(ecount == 2);
-    CHECK(memcmp(zeros96, &pk, sizeof(pk)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &pk, sizeof(pk)) == 0);
 
     /* Using an invalid keypair is fine for keypair_pub */
     memset(&keypair, 0, sizeof(keypair));
     CHECK(secp256k1_keypair_pub(none, &pk, &keypair) == 1);
-    CHECK(memcmp(zeros96, &pk, sizeof(pk)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &pk, sizeof(pk)) == 0);
 
     /* keypair holds the same pubkey as pubkey_create */
     CHECK(secp256k1_ec_pubkey_create(sign, &pk, sk) == 1);
     CHECK(secp256k1_keypair_create(sign, &keypair, sk) == 1);
     CHECK(secp256k1_keypair_pub(none, &pk_tmp, &keypair) == 1);
-    CHECK(memcmp(&pk, &pk_tmp, sizeof(pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&pk, &pk_tmp, sizeof(pk)) == 0);
 
     /** Test keypair_xonly_pub **/
     ecount = 0;
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
     CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, &pk_parity, &keypair) == 1);
     CHECK(secp256k1_keypair_xonly_pub(none, NULL, &pk_parity, &keypair) == 0);
@@ -379,13 +379,13 @@ void test_keypair(void) {
     CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, NULL, &keypair) == 1);
     CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, &pk_parity, NULL) == 0);
     CHECK(ecount == 2);
-    CHECK(memcmp(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0);
     /* Using an invalid keypair will set the xonly_pk to 0 (first reset
      * xonly_pk). */
     CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, &pk_parity, &keypair) == 1);
     memset(&keypair, 0, sizeof(keypair));
     CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk, &pk_parity, &keypair) == 0);
-    CHECK(memcmp(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0);
+    CHECK(secp256k1_memcmp_var(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0);
     CHECK(ecount == 3);
 
     /** keypair holds the same xonly pubkey as pubkey_create **/
@@ -393,7 +393,7 @@ void test_keypair(void) {
     CHECK(secp256k1_xonly_pubkey_from_pubkey(none, &xonly_pk, &pk_parity, &pk) == 1);
     CHECK(secp256k1_keypair_create(sign, &keypair, sk) == 1);
     CHECK(secp256k1_keypair_xonly_pub(none, &xonly_pk_tmp, &pk_parity_tmp, &keypair) == 1);
-    CHECK(memcmp(&xonly_pk, &xonly_pk_tmp, sizeof(pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&xonly_pk, &xonly_pk_tmp, sizeof(pk)) == 0);
     CHECK(pk_parity == pk_parity_tmp);
 
     secp256k1_context_destroy(none);
@@ -414,8 +414,8 @@ void test_keypair_add(void) {
     secp256k1_context *verify = api_test_context(SECP256K1_CONTEXT_VERIFY, &ecount);
 
     CHECK(sizeof(zeros96) == sizeof(keypair));
-    secp256k1_rand256(sk);
-    secp256k1_rand256(tweak);
+    secp256k1_testrand256(sk);
+    secp256k1_testrand256(tweak);
     memset(overflows, 0xFF, 32);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
 
@@ -429,12 +429,12 @@ void test_keypair_add(void) {
     CHECK(secp256k1_keypair_xonly_tweak_add(verify, &keypair, NULL) == 0);
     CHECK(ecount == 4);
     /* This does not set the keypair to zeroes */
-    CHECK(memcmp(&keypair, zeros96, sizeof(keypair)) != 0);
+    CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) != 0);
 
     /* Invalid tweak zeroes the keypair */
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
     CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, overflows) == 0);
-    CHECK(memcmp(&keypair, zeros96, sizeof(keypair))  == 0);
+    CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair))  == 0);
 
     /* A zero tweak is fine */
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
@@ -444,7 +444,7 @@ void test_keypair_add(void) {
     for (i = 0; i < count; i++) {
         secp256k1_scalar scalar_tweak;
         secp256k1_keypair keypair_tmp;
-        secp256k1_rand256(sk);
+        secp256k1_testrand256(sk);
         CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
         memcpy(&keypair_tmp, &keypair, sizeof(keypair));
         /* Because sk may be negated before adding, we need to try with tweak =
@@ -454,17 +454,17 @@ void test_keypair_add(void) {
         secp256k1_scalar_get_b32(tweak, &scalar_tweak);
         CHECK((secp256k1_keypair_xonly_tweak_add(ctx, &keypair, sk) == 0)
               || (secp256k1_keypair_xonly_tweak_add(ctx, &keypair_tmp, tweak) == 0));
-        CHECK(memcmp(&keypair, zeros96, sizeof(keypair)) == 0
-              || memcmp(&keypair_tmp, zeros96, sizeof(keypair_tmp)) == 0);
+        CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) == 0
+              || secp256k1_memcmp_var(&keypair_tmp, zeros96, sizeof(keypair_tmp)) == 0);
     }
 
     /* Invalid keypair with a valid tweak */
     memset(&keypair, 0, sizeof(keypair));
-    secp256k1_rand256(tweak);
+    secp256k1_testrand256(tweak);
     ecount = 0;
     CHECK(secp256k1_keypair_xonly_tweak_add(verify, &keypair, tweak) == 0);
     CHECK(ecount == 1);
-    CHECK(memcmp(&keypair, zeros96, sizeof(keypair))  == 0);
+    CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair))  == 0);
     /* Only seckey part of keypair invalid */
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
     memset(&keypair, 0, 32);
@@ -486,7 +486,7 @@ void test_keypair_add(void) {
         unsigned char pk32[32];
         int pk_parity;
 
-        secp256k1_rand256(tweak);
+        secp256k1_testrand256(tweak);
         CHECK(secp256k1_keypair_xonly_pub(ctx, &internal_pk, NULL, &keypair) == 1);
         CHECK(secp256k1_keypair_xonly_tweak_add(ctx, &keypair, tweak) == 1);
         CHECK(secp256k1_keypair_xonly_pub(ctx, &output_pk, &pk_parity, &keypair) == 1);
@@ -498,11 +498,11 @@ void test_keypair_add(void) {
         /* Check that the resulting pubkey matches xonly_pubkey_tweak_add */
         CHECK(secp256k1_keypair_pub(ctx, &output_pk_xy, &keypair) == 1);
         CHECK(secp256k1_xonly_pubkey_tweak_add(ctx, &output_pk_expected, &internal_pk, tweak) == 1);
-        CHECK(memcmp(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0);
+        CHECK(secp256k1_memcmp_var(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0);
 
         /* Check that the secret key in the keypair is tweaked correctly */
         CHECK(secp256k1_ec_pubkey_create(ctx, &output_pk_expected, &keypair.data[0]) == 1);
-        CHECK(memcmp(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0);
+        CHECK(secp256k1_memcmp_var(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0);
     }
     secp256k1_context_destroy(none);
     secp256k1_context_destroy(sign);
diff --git a/src/secp256k1/src/modules/recovery/Makefile.am.include b/src/secp256k1/src/modules/recovery/Makefile.am.include
index bf23c26e71..e2d3f1248d 100644
--- a/src/secp256k1/src/modules/recovery/Makefile.am.include
+++ b/src/secp256k1/src/modules/recovery/Makefile.am.include
@@ -1,6 +1,7 @@
 include_HEADERS += include/secp256k1_recovery.h
 noinst_HEADERS += src/modules/recovery/main_impl.h
 noinst_HEADERS += src/modules/recovery/tests_impl.h
+noinst_HEADERS += src/modules/recovery/tests_exhaustive_impl.h
 if USE_BENCHMARK
 noinst_PROGRAMS += bench_recover
 bench_recover_SOURCES = src/bench_recover.c
diff --git a/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h b/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h
new file mode 100644
index 0000000000..a2f381d77a
--- /dev/null
+++ b/src/secp256k1/src/modules/recovery/tests_exhaustive_impl.h
@@ -0,0 +1,149 @@
+/**********************************************************************
+ * 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.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODULE_RECOVERY_EXHAUSTIVE_TESTS_H
+#define SECP256K1_MODULE_RECOVERY_EXHAUSTIVE_TESTS_H
+
+#include "src/modules/recovery/main_impl.h"
+#include "include/secp256k1_recovery.h"
+
+void test_exhaustive_recovery_sign(const secp256k1_context *ctx, const secp256k1_ge *group) {
+    int i, j, k;
+    uint64_t iter = 0;
+
+    /* Loop */
+    for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {  /* message */
+        for (j = 1; j < EXHAUSTIVE_TEST_ORDER; j++) {  /* key */
+            if (skip_section(&iter)) continue;
+            for (k = 1; k < EXHAUSTIVE_TEST_ORDER; k++) {  /* nonce */
+                const int starting_k = k;
+                secp256k1_fe r_dot_y_normalized;
+                secp256k1_ecdsa_recoverable_signature rsig;
+                secp256k1_ecdsa_signature sig;
+                secp256k1_scalar sk, msg, r, s, expected_r;
+                unsigned char sk32[32], msg32[32];
+                int expected_recid;
+                int recid;
+                int overflow;
+                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_recoverable(ctx, &rsig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+
+                /* Check directly */
+                secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, &rsig);
+                r_from_k(&expected_r, group, k, &overflow);
+                CHECK(r == expected_r);
+                CHECK((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER);
+                /* The recid's second bit is for conveying overflow (R.x value >= group order).
+                 * In the actual secp256k1 this is an astronomically unlikely event, but in the
+                 * small group used here, it will be the case for all points except the ones where
+                 * R.x=1 (which the group is specifically selected to have).
+                 * Note that this isn't actually useful; full recovery would need to convey
+                 * floor(R.x / group_order), but only one bit is used as that is sufficient
+                 * in the real group. */
+                expected_recid = overflow ? 2 : 0;
+                r_dot_y_normalized = group[k].y;
+                secp256k1_fe_normalize(&r_dot_y_normalized);
+                /* Also the recovery id is flipped depending if we hit the low-s branch */
+                if ((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER) {
+                    expected_recid |= secp256k1_fe_is_odd(&r_dot_y_normalized);
+                } else {
+                    expected_recid |= !secp256k1_fe_is_odd(&r_dot_y_normalized);
+                }
+                CHECK(recid == expected_recid);
+
+                /* Convert to a standard sig then check */
+                secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
+                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, NULL);
+                CHECK(r == expected_r);
+                CHECK((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER);
+
+                /* Overflow means we've tried every possible nonce */
+                if (k < starting_k) {
+                    break;
+                }
+            }
+        }
+    }
+}
+
+void test_exhaustive_recovery_verify(const secp256k1_context *ctx, const secp256k1_ge *group) {
+    /* This is essentially a copy of test_exhaustive_verify, with recovery added */
+    int s, r, msg, key;
+    uint64_t iter = 0;
+    for (s = 1; s < EXHAUSTIVE_TEST_ORDER; s++) {
+        for (r = 1; r < EXHAUSTIVE_TEST_ORDER; r++) {
+            for (msg = 1; msg < EXHAUSTIVE_TEST_ORDER; msg++) {
+                for (key = 1; key < EXHAUSTIVE_TEST_ORDER; key++) {
+                    secp256k1_ge nonconst_ge;
+                    secp256k1_ecdsa_recoverable_signature rsig;
+                    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 recid = 0;
+                    int k, should_verify;
+                    unsigned char msg32[32];
+
+                    if (skip_section(&iter)) continue;
+
+                    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);
+                    secp256k1_scalar_get_b32(msg32, &msg_s);
+
+                    /* 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 < EXHAUSTIVE_TEST_ORDER; k++) {
+                        secp256k1_scalar check_x_s;
+                        r_from_k(&check_x_s, group, k, NULL);
+                        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);
+
+                    /* We would like to try recovering the pubkey and checking that it matches,
+                     * but pubkey recovery is impossible in the exhaustive tests (the reason
+                     * being that there are 12 nonzero r values, 12 nonzero points, and no
+                     * overlap between the sets, so there are no valid signatures). */
+
+                    /* Verify by converting to a standard signature and calling verify */
+                    secp256k1_ecdsa_recoverable_signature_save(&rsig, &r_s, &s_s, recid);
+                    secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
+                    memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
+                    secp256k1_pubkey_save(&pk, &nonconst_ge);
+                    CHECK(should_verify ==
+                          secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
+                }
+            }
+        }
+    }
+}
+
+static void test_exhaustive_recovery(const secp256k1_context *ctx, const secp256k1_ge *group) {
+    test_exhaustive_recovery_sign(ctx, group);
+    test_exhaustive_recovery_verify(ctx, group);
+}
+
+#endif /* SECP256K1_MODULE_RECOVERY_EXHAUSTIVE_TESTS_H */
diff --git a/src/secp256k1/src/modules/recovery/tests_impl.h b/src/secp256k1/src/modules/recovery/tests_impl.h
index 38a533a755..09cae38403 100644
--- a/src/secp256k1/src/modules/recovery/tests_impl.h
+++ b/src/secp256k1/src/modules/recovery/tests_impl.h
@@ -25,7 +25,7 @@ static int recovery_test_nonce_function(unsigned char *nonce32, const unsigned c
     }
     /* On the next run, return a valid nonce, but flip a coin as to whether or not to fail signing. */
     memset(nonce32, 1, 32);
-    return secp256k1_rand_bits(1);
+    return secp256k1_testrand_bits(1);
 }
 
 void test_ecdsa_recovery_api(void) {
@@ -184,7 +184,7 @@ void test_ecdsa_recovery_end_to_end(void) {
     CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[3], message, privkey, NULL, extra) == 1);
     CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
     CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
-    CHECK(memcmp(&signature[4], &signature[0], 64) == 0);
+    CHECK(secp256k1_memcmp_var(&signature[4], &signature[0], 64) == 0);
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1);
     memset(&rsignature[4], 0, sizeof(rsignature[4]));
     CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
@@ -193,16 +193,16 @@ void test_ecdsa_recovery_end_to_end(void) {
     /* Parse compact (with recovery id) and recover. */
     CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
     CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 1);
-    CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
     /* Serialize/destroy/parse signature and verify again. */
     CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1);
-    sig[secp256k1_rand_bits(6)] += 1 + secp256k1_rand_int(255);
+    sig[secp256k1_testrand_bits(6)] += 1 + secp256k1_testrand_int(255);
     CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1);
     CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1);
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 0);
     /* Recover again */
     CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 0 ||
-          memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
+          secp256k1_memcmp_var(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
 }
 
 /* Tests several edge cases. */
diff --git a/src/secp256k1/src/modules/schnorrsig/Makefile.am.include b/src/secp256k1/src/modules/schnorrsig/Makefile.am.include
index a82bafe43f..568bcc3523 100644
--- a/src/secp256k1/src/modules/schnorrsig/Makefile.am.include
+++ b/src/secp256k1/src/modules/schnorrsig/Makefile.am.include
@@ -1,6 +1,7 @@
 include_HEADERS += include/secp256k1_schnorrsig.h
 noinst_HEADERS += src/modules/schnorrsig/main_impl.h
 noinst_HEADERS += src/modules/schnorrsig/tests_impl.h
+noinst_HEADERS += src/modules/schnorrsig/tests_exhaustive_impl.h
 if USE_BENCHMARK
 noinst_PROGRAMS += bench_schnorrsig
 bench_schnorrsig_SOURCES = src/bench_schnorrsig.c
diff --git a/src/secp256k1/src/modules/schnorrsig/main_impl.h b/src/secp256k1/src/modules/schnorrsig/main_impl.h
index a0218f881a..b0d8481f9b 100644
--- a/src/secp256k1/src/modules/schnorrsig/main_impl.h
+++ b/src/secp256k1/src/modules/schnorrsig/main_impl.h
@@ -68,7 +68,7 @@ static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *ms
     /* Tag the hash with algo16 which is important to avoid nonce reuse across
      * algorithms. If this nonce function is used in BIP-340 signing as defined
      * in the spec, an optimized tagging implementation is used. */
-    if (memcmp(algo16, bip340_algo16, 16) == 0) {
+    if (secp256k1_memcmp_var(algo16, bip340_algo16, 16) == 0) {
         secp256k1_nonce_function_bip340_sha256_tagged(&sha);
     } else {
         int algo16_len = 16;
@@ -108,6 +108,22 @@ static void secp256k1_schnorrsig_sha256_tagged(secp256k1_sha256 *sha) {
     sha->bytes = 64;
 }
 
+static void secp256k1_schnorrsig_challenge(secp256k1_scalar* e, const unsigned char *r32, const unsigned char *msg32, const unsigned char *pubkey32)
+{
+    unsigned char buf[32];
+    secp256k1_sha256 sha;
+
+    /* tagged hash(r.x, pk.x, msg32) */
+    secp256k1_schnorrsig_sha256_tagged(&sha);
+    secp256k1_sha256_write(&sha, r32, 32);
+    secp256k1_sha256_write(&sha, pubkey32, 32);
+    secp256k1_sha256_write(&sha, msg32, 32);
+    secp256k1_sha256_finalize(&sha, buf);
+    /* Set scalar e to the challenge hash modulo the curve order as per
+     * BIP340. */
+    secp256k1_scalar_set_b32(e, buf, NULL);
+}
+
 int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const secp256k1_keypair *keypair, secp256k1_nonce_function_hardened noncefp, void *ndata) {
     secp256k1_scalar sk;
     secp256k1_scalar e;
@@ -115,7 +131,6 @@ int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64
     secp256k1_gej rj;
     secp256k1_ge pk;
     secp256k1_ge r;
-    secp256k1_sha256 sha;
     unsigned char buf[32] = { 0 };
     unsigned char pk_buf[32];
     unsigned char seckey[32];
@@ -159,16 +174,7 @@ int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64
     secp256k1_fe_normalize_var(&r.x);
     secp256k1_fe_get_b32(&sig64[0], &r.x);
 
-    /* tagged hash(r.x, pk.x, msg32) */
-    secp256k1_schnorrsig_sha256_tagged(&sha);
-    secp256k1_sha256_write(&sha, &sig64[0], 32);
-    secp256k1_sha256_write(&sha, pk_buf, sizeof(pk_buf));
-    secp256k1_sha256_write(&sha, msg32, 32);
-    secp256k1_sha256_finalize(&sha, buf);
-
-    /* Set scalar e to the challenge hash modulo the curve order as per
-     * BIP340. */
-    secp256k1_scalar_set_b32(&e, buf, NULL);
+    secp256k1_schnorrsig_challenge(&e, &sig64[0], msg32, pk_buf);
     secp256k1_scalar_mul(&e, &e, &sk);
     secp256k1_scalar_add(&e, &e, &k);
     secp256k1_scalar_get_b32(&sig64[32], &e);
@@ -189,7 +195,6 @@ int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned cha
     secp256k1_gej pkj;
     secp256k1_fe rx;
     secp256k1_ge r;
-    secp256k1_sha256 sha;
     unsigned char buf[32];
     int overflow;
 
@@ -212,13 +217,9 @@ int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned cha
         return 0;
     }
 
-    secp256k1_schnorrsig_sha256_tagged(&sha);
-    secp256k1_sha256_write(&sha, &sig64[0], 32);
+    /* Compute e. */
     secp256k1_fe_get_b32(buf, &pk.x);
-    secp256k1_sha256_write(&sha, buf, sizeof(buf));
-    secp256k1_sha256_write(&sha, msg32, 32);
-    secp256k1_sha256_finalize(&sha, buf);
-    secp256k1_scalar_set_b32(&e, buf, NULL);
+    secp256k1_schnorrsig_challenge(&e, &sig64[0], msg32, buf);
 
     /* Compute rj =  s*G + (-e)*pkj */
     secp256k1_scalar_negate(&e, &e);
diff --git a/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h b/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h
new file mode 100644
index 0000000000..4bf0bc1680
--- /dev/null
+++ b/src/secp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h
@@ -0,0 +1,206 @@
+/**********************************************************************
+ * Copyright (c) 2020 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_SCHNORRSIG_TESTS_EXHAUSTIVE_
+#define _SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_
+
+#include "include/secp256k1_schnorrsig.h"
+#include "src/modules/schnorrsig/main_impl.h"
+
+static const unsigned char invalid_pubkey_bytes[][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, 0, 0
+    },
+    /* 2 */
+    {
+        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, 2
+    },
+    /* order */
+    {
+        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 + 0UL) >> 24) & 0xFF,
+        ((EXHAUSTIVE_TEST_ORDER + 0UL) >> 16) & 0xFF,
+        ((EXHAUSTIVE_TEST_ORDER + 0UL) >> 8) & 0xFF,
+        (EXHAUSTIVE_TEST_ORDER + 0UL) & 0xFF
+    },
+    /* order + 1 */
+    {
+        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 + 1UL) >> 24) & 0xFF,
+        ((EXHAUSTIVE_TEST_ORDER + 1UL) >> 16) & 0xFF,
+        ((EXHAUSTIVE_TEST_ORDER + 1UL) >> 8) & 0xFF,
+        (EXHAUSTIVE_TEST_ORDER + 1UL) & 0xFF
+    },
+    /* field size */
+    {
+        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
+    },
+    /* field size + 1 (note that 1 is legal) */
+    {
+        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30
+    },
+    /* 2^256 - 1 */
+    {
+        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+        0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
+    }
+};
+
+#define NUM_INVALID_KEYS (sizeof(invalid_pubkey_bytes) / sizeof(invalid_pubkey_bytes[0]))
+
+static int secp256k1_hardened_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32,
+                                                      const unsigned char *key32, const unsigned char *xonly_pk32,
+                                                      const unsigned char *algo16, void* data) {
+    secp256k1_scalar s;
+    int *idata = data;
+    (void)msg32;
+    (void)key32;
+    (void)xonly_pk32;
+    (void)algo16;
+    secp256k1_scalar_set_int(&s, *idata);
+    secp256k1_scalar_get_b32(nonce32, &s);
+    return 1;
+}
+
+static void test_exhaustive_schnorrsig_verify(const secp256k1_context *ctx, const secp256k1_xonly_pubkey* pubkeys, unsigned char (*xonly_pubkey_bytes)[32], const int* parities) {
+    int d;
+    uint64_t iter = 0;
+    /* Iterate over the possible public keys to verify against (through their corresponding DL d). */
+    for (d = 1; d <= EXHAUSTIVE_TEST_ORDER / 2; ++d) {
+        int actual_d;
+        unsigned k;
+        unsigned char pk32[32];
+        memcpy(pk32, xonly_pubkey_bytes[d - 1], 32);
+        actual_d = parities[d - 1] ? EXHAUSTIVE_TEST_ORDER - d : d;
+        /* Iterate over the possible valid first 32 bytes in the signature, through their corresponding DL k.
+           Values above EXHAUSTIVE_TEST_ORDER/2 refer to the entries in invalid_pubkey_bytes. */
+        for (k = 1; k <= EXHAUSTIVE_TEST_ORDER / 2 + NUM_INVALID_KEYS; ++k) {
+            unsigned char sig64[64];
+            int actual_k = -1;
+            int e_done[EXHAUSTIVE_TEST_ORDER] = {0};
+            int e_count_done = 0;
+            if (skip_section(&iter)) continue;
+            if (k <= EXHAUSTIVE_TEST_ORDER / 2) {
+                memcpy(sig64, xonly_pubkey_bytes[k - 1], 32);
+                actual_k = parities[k - 1] ? EXHAUSTIVE_TEST_ORDER - k : k;
+            } else {
+                memcpy(sig64, invalid_pubkey_bytes[k - 1 - EXHAUSTIVE_TEST_ORDER / 2], 32);
+            }
+            /* Randomly generate messages until all challenges have been hit. */
+            while (e_count_done < EXHAUSTIVE_TEST_ORDER) {
+                secp256k1_scalar e;
+                unsigned char msg32[32];
+                secp256k1_testrand256(msg32);
+                secp256k1_schnorrsig_challenge(&e, sig64, msg32, pk32);
+                /* Only do work if we hit a challenge we haven't tried before. */
+                if (!e_done[e]) {
+                    /* Iterate over the possible valid last 32 bytes in the signature.
+                       0..order=that s value; order+1=random bytes */
+                    int count_valid = 0, s;
+                    for (s = 0; s <= EXHAUSTIVE_TEST_ORDER + 1; ++s) {
+                        int expect_valid, valid;
+                        if (s <= EXHAUSTIVE_TEST_ORDER) {
+                            secp256k1_scalar s_s;
+                            secp256k1_scalar_set_int(&s_s, s);
+                            secp256k1_scalar_get_b32(sig64 + 32, &s_s);
+                            expect_valid = actual_k != -1 && s != EXHAUSTIVE_TEST_ORDER &&
+                                           (s_s == (actual_k + actual_d * e) % EXHAUSTIVE_TEST_ORDER);
+                        } else {
+                            secp256k1_testrand256(sig64 + 32);
+                            expect_valid = 0;
+                        }
+                        valid = secp256k1_schnorrsig_verify(ctx, sig64, msg32, &pubkeys[d - 1]);
+                        CHECK(valid == expect_valid);
+                        count_valid += valid;
+                    }
+                    /* Exactly one s value must verify, unless R is illegal. */
+                    CHECK(count_valid == (actual_k != -1));
+                    /* Don't retry other messages that result in the same challenge. */
+                    e_done[e] = 1;
+                    ++e_count_done;
+                }
+            }
+        }
+    }
+}
+
+static void test_exhaustive_schnorrsig_sign(const secp256k1_context *ctx, unsigned char (*xonly_pubkey_bytes)[32], const secp256k1_keypair* keypairs, const int* parities) {
+    int d, k;
+    uint64_t iter = 0;
+    /* Loop over keys. */
+    for (d = 1; d < EXHAUSTIVE_TEST_ORDER; ++d) {
+        int actual_d = d;
+        if (parities[d - 1]) actual_d = EXHAUSTIVE_TEST_ORDER - d;
+        /* Loop over nonces. */
+        for (k = 1; k < EXHAUSTIVE_TEST_ORDER; ++k) {
+            int e_done[EXHAUSTIVE_TEST_ORDER] = {0};
+            int e_count_done = 0;
+            unsigned char msg32[32];
+            unsigned char sig64[64];
+            int actual_k = k;
+            if (skip_section(&iter)) continue;
+            if (parities[k - 1]) actual_k = EXHAUSTIVE_TEST_ORDER - k;
+            /* Generate random messages until all challenges have been tried. */
+            while (e_count_done < EXHAUSTIVE_TEST_ORDER) {
+                secp256k1_scalar e;
+                secp256k1_testrand256(msg32);
+                secp256k1_schnorrsig_challenge(&e, xonly_pubkey_bytes[k - 1], msg32, xonly_pubkey_bytes[d - 1]);
+                /* Only do work if we hit a challenge we haven't tried before. */
+                if (!e_done[e]) {
+                    secp256k1_scalar expected_s = (actual_k + e * actual_d) % EXHAUSTIVE_TEST_ORDER;
+                    unsigned char expected_s_bytes[32];
+                    secp256k1_scalar_get_b32(expected_s_bytes, &expected_s);
+                    /* Invoke the real function to construct a signature. */
+                    CHECK(secp256k1_schnorrsig_sign(ctx, sig64, msg32, &keypairs[d - 1], secp256k1_hardened_nonce_function_smallint, &k));
+                    /* The first 32 bytes must match the xonly pubkey for the specified k. */
+                    CHECK(secp256k1_memcmp_var(sig64, xonly_pubkey_bytes[k - 1], 32) == 0);
+                    /* The last 32 bytes must match the expected s value. */
+                    CHECK(secp256k1_memcmp_var(sig64 + 32, expected_s_bytes, 32) == 0);
+                    /* Don't retry other messages that result in the same challenge. */
+                    e_done[e] = 1;
+                    ++e_count_done;
+                }
+            }
+        }
+    }
+}
+
+static void test_exhaustive_schnorrsig(const secp256k1_context *ctx) {
+    secp256k1_keypair keypair[EXHAUSTIVE_TEST_ORDER - 1];
+    secp256k1_xonly_pubkey xonly_pubkey[EXHAUSTIVE_TEST_ORDER - 1];
+    int parity[EXHAUSTIVE_TEST_ORDER - 1];
+    unsigned char xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - 1][32];
+    unsigned i;
+
+    /* Verify that all invalid_pubkey_bytes are actually invalid. */
+    for (i = 0; i < NUM_INVALID_KEYS; ++i) {
+        secp256k1_xonly_pubkey pk;
+        CHECK(!secp256k1_xonly_pubkey_parse(ctx, &pk, invalid_pubkey_bytes[i]));
+    }
+
+    /* Construct keypairs and xonly-pubkeys for the entire group. */
+    for (i = 1; i < EXHAUSTIVE_TEST_ORDER; ++i) {
+        secp256k1_scalar scalar_i;
+        unsigned char buf[32];
+        secp256k1_scalar_set_int(&scalar_i, i);
+        secp256k1_scalar_get_b32(buf, &scalar_i);
+        CHECK(secp256k1_keypair_create(ctx, &keypair[i - 1], buf));
+        CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pubkey[i - 1], &parity[i - 1], &keypair[i - 1]));
+        CHECK(secp256k1_xonly_pubkey_serialize(ctx, xonly_pubkey_bytes[i - 1], &xonly_pubkey[i - 1]));
+    }
+
+    test_exhaustive_schnorrsig_sign(ctx, xonly_pubkey_bytes, keypair, parity);
+    test_exhaustive_schnorrsig_verify(ctx, xonly_pubkey, xonly_pubkey_bytes, parity);
+}
+
+#endif
diff --git a/src/secp256k1/src/modules/schnorrsig/tests_impl.h b/src/secp256k1/src/modules/schnorrsig/tests_impl.h
index 88d8f56404..f522fcb320 100644
--- a/src/secp256k1/src/modules/schnorrsig/tests_impl.h
+++ b/src/secp256k1/src/modules/schnorrsig/tests_impl.h
@@ -15,9 +15,9 @@
 void nonce_function_bip340_bitflip(unsigned char **args, size_t n_flip, size_t n_bytes) {
     unsigned char nonces[2][32];
     CHECK(nonce_function_bip340(nonces[0], args[0], args[1], args[2], args[3], args[4]) == 1);
-    secp256k1_rand_flip(args[n_flip], n_bytes);
+    secp256k1_testrand_flip(args[n_flip], n_bytes);
     CHECK(nonce_function_bip340(nonces[1], args[0], args[1], args[2], args[3], args[4]) == 1);
-    CHECK(memcmp(nonces[0], nonces[1], 32) != 0);
+    CHECK(secp256k1_memcmp_var(nonces[0], nonces[1], 32) != 0);
 }
 
 /* Tests for the equality of two sha256 structs. This function only produces a
@@ -28,7 +28,7 @@ void test_sha256_eq(const secp256k1_sha256 *sha1, const secp256k1_sha256 *sha2)
     CHECK((sha1->bytes & 0x3F) == 0);
 
     CHECK(sha1->bytes == sha2->bytes);
-    CHECK(memcmp(sha1->s, sha2->s, sizeof(sha1->s)) == 0);
+    CHECK(secp256k1_memcmp_var(sha1->s, sha2->s, sizeof(sha1->s)) == 0);
 }
 
 void run_nonce_function_bip340_tests(void) {
@@ -59,10 +59,10 @@ void run_nonce_function_bip340_tests(void) {
     secp256k1_nonce_function_bip340_sha256_tagged_aux(&sha_optimized);
     test_sha256_eq(&sha, &sha_optimized);
 
-    secp256k1_rand256(msg);
-    secp256k1_rand256(key);
-    secp256k1_rand256(pk);
-    secp256k1_rand256(aux_rand);
+    secp256k1_testrand256(msg);
+    secp256k1_testrand256(key);
+    secp256k1_testrand256(pk);
+    secp256k1_testrand256(aux_rand);
 
     /* Check that a bitflip in an argument results in different nonces. */
     args[0] = msg;
@@ -124,10 +124,10 @@ void test_schnorrsig_api(void) {
     secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
     secp256k1_context_set_illegal_callback(both, counting_illegal_callback_fn, &ecount);
 
-    secp256k1_rand256(sk1);
-    secp256k1_rand256(sk2);
-    secp256k1_rand256(sk3);
-    secp256k1_rand256(msg);
+    secp256k1_testrand256(sk1);
+    secp256k1_testrand256(sk2);
+    secp256k1_testrand256(sk3);
+    secp256k1_testrand256(msg);
     CHECK(secp256k1_keypair_create(ctx, &keypairs[0], sk1) == 1);
     CHECK(secp256k1_keypair_create(ctx, &keypairs[1], sk2) == 1);
     CHECK(secp256k1_keypair_create(ctx, &keypairs[2], sk3) == 1);
@@ -197,11 +197,11 @@ void test_schnorrsig_bip_vectors_check_signing(const unsigned char *sk, const un
 
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk));
     CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, NULL, aux_rand));
-    CHECK(memcmp(sig, expected_sig, 64) == 0);
+    CHECK(secp256k1_memcmp_var(sig, expected_sig, 64) == 0);
 
     CHECK(secp256k1_xonly_pubkey_parse(ctx, &pk_expected, pk_serialized));
     CHECK(secp256k1_keypair_xonly_pub(ctx, &pk, NULL, &keypair));
-    CHECK(memcmp(&pk, &pk_expected, sizeof(pk)) == 0);
+    CHECK(secp256k1_memcmp_var(&pk, &pk_expected, sizeof(pk)) == 0);
     CHECK(secp256k1_schnorrsig_verify(ctx, sig, msg, &pk));
 }
 
@@ -675,19 +675,19 @@ void test_schnorrsig_sign(void) {
     unsigned char sig[64];
     unsigned char zeros64[64] = { 0 };
 
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk));
     CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, NULL, NULL) == 1);
 
     /* Test different nonce functions */
     memset(sig, 1, sizeof(sig));
     CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, nonce_function_failing, NULL) == 0);
-    CHECK(memcmp(sig, zeros64, sizeof(sig)) == 0);
+    CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) == 0);
     memset(&sig, 1, sizeof(sig));
     CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, nonce_function_0, NULL) == 0);
-    CHECK(memcmp(sig, zeros64, sizeof(sig)) == 0);
+    CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) == 0);
     CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, nonce_function_overflowing, NULL) == 1);
-    CHECK(memcmp(sig, zeros64, sizeof(sig)) != 0);
+    CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) != 0);
 }
 
 #define N_SIGS 3
@@ -703,12 +703,12 @@ void test_schnorrsig_sign_verify(void) {
     secp256k1_xonly_pubkey pk;
     secp256k1_scalar s;
 
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk));
     CHECK(secp256k1_keypair_xonly_pub(ctx, &pk, NULL, &keypair));
 
     for (i = 0; i < N_SIGS; i++) {
-        secp256k1_rand256(msg[i]);
+        secp256k1_testrand256(msg[i]);
         CHECK(secp256k1_schnorrsig_sign(ctx, sig[i], msg[i], &keypair, NULL, NULL));
         CHECK(secp256k1_schnorrsig_verify(ctx, sig[i], msg[i], &pk));
     }
@@ -716,19 +716,19 @@ void test_schnorrsig_sign_verify(void) {
     {
         /* Flip a few bits in the signature and in the message and check that
          * verify and verify_batch (TODO) fail */
-        size_t sig_idx = secp256k1_rand_int(N_SIGS);
-        size_t byte_idx = secp256k1_rand_int(32);
-        unsigned char xorbyte = secp256k1_rand_int(254)+1;
+        size_t sig_idx = secp256k1_testrand_int(N_SIGS);
+        size_t byte_idx = secp256k1_testrand_int(32);
+        unsigned char xorbyte = secp256k1_testrand_int(254)+1;
         sig[sig_idx][byte_idx] ^= xorbyte;
         CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], &pk));
         sig[sig_idx][byte_idx] ^= xorbyte;
 
-        byte_idx = secp256k1_rand_int(32);
+        byte_idx = secp256k1_testrand_int(32);
         sig[sig_idx][32+byte_idx] ^= xorbyte;
         CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], &pk));
         sig[sig_idx][32+byte_idx] ^= xorbyte;
 
-        byte_idx = secp256k1_rand_int(32);
+        byte_idx = secp256k1_testrand_int(32);
         msg[sig_idx][byte_idx] ^= xorbyte;
         CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], &pk));
         msg[sig_idx][byte_idx] ^= xorbyte;
@@ -766,7 +766,7 @@ void test_schnorrsig_taproot(void) {
     unsigned char sig[64];
 
     /* Create output key */
-    secp256k1_rand256(sk);
+    secp256k1_testrand256(sk);
     CHECK(secp256k1_keypair_create(ctx, &keypair, sk) == 1);
     CHECK(secp256k1_keypair_xonly_pub(ctx, &internal_pk, NULL, &keypair) == 1);
     /* In actual taproot the tweak would be hash of internal_pk */
@@ -776,7 +776,7 @@ void test_schnorrsig_taproot(void) {
     CHECK(secp256k1_xonly_pubkey_serialize(ctx, output_pk_bytes, &output_pk) == 1);
 
     /* Key spend */
-    secp256k1_rand256(msg);
+    secp256k1_testrand256(msg);
     CHECK(secp256k1_schnorrsig_sign(ctx, sig, msg, &keypair, NULL, NULL) == 1);
     /* Verify key spend */
     CHECK(secp256k1_xonly_pubkey_parse(ctx, &output_pk, output_pk_bytes) == 1);
diff --git a/src/secp256k1/src/scalar.h b/src/secp256k1/src/scalar.h
index 95d3e326c9..fb3fb187ce 100644
--- a/src/secp256k1/src/scalar.h
+++ b/src/secp256k1/src/scalar.h
@@ -102,12 +102,11 @@ static void secp256k1_scalar_order_get_num(secp256k1_num *r);
 /** Compare two scalars. */
 static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b);
 
-#ifdef USE_ENDOMORPHISM
-/** Find r1 and r2 such that r1+r2*2^128 = a. */
-static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
-/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
-static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
-#endif
+/** Find r1 and r2 such that r1+r2*2^128 = k. */
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k);
+/** Find r1 and r2 such that r1+r2*lambda = k,
+ * where r1 and r2 or their negations are maximum 128 bits long (see secp256k1_ge_mul_lambda). */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k);
 
 /** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
 static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
diff --git a/src/secp256k1/src/scalar_4x64_impl.h b/src/secp256k1/src/scalar_4x64_impl.h
index 7f39927861..73cbd5e18a 100644
--- a/src/secp256k1/src/scalar_4x64_impl.h
+++ b/src/secp256k1/src/scalar_4x64_impl.h
@@ -912,18 +912,16 @@ static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a)
     secp256k1_scalar_reduce_512(r, l);
 }
 
-#ifdef USE_ENDOMORPHISM
-static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
-    r1->d[0] = a->d[0];
-    r1->d[1] = a->d[1];
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) {
+    r1->d[0] = k->d[0];
+    r1->d[1] = k->d[1];
     r1->d[2] = 0;
     r1->d[3] = 0;
-    r2->d[0] = a->d[2];
-    r2->d[1] = a->d[3];
+    r2->d[0] = k->d[2];
+    r2->d[1] = k->d[3];
     r2->d[2] = 0;
     r2->d[3] = 0;
 }
-#endif
 
 SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
     return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0;
diff --git a/src/secp256k1/src/scalar_8x32_impl.h b/src/secp256k1/src/scalar_8x32_impl.h
index f8c7fa7efa..6853f79ecc 100644
--- a/src/secp256k1/src/scalar_8x32_impl.h
+++ b/src/secp256k1/src/scalar_8x32_impl.h
@@ -672,26 +672,24 @@ static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a)
     secp256k1_scalar_reduce_512(r, l);
 }
 
-#ifdef USE_ENDOMORPHISM
-static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
-    r1->d[0] = a->d[0];
-    r1->d[1] = a->d[1];
-    r1->d[2] = a->d[2];
-    r1->d[3] = a->d[3];
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) {
+    r1->d[0] = k->d[0];
+    r1->d[1] = k->d[1];
+    r1->d[2] = k->d[2];
+    r1->d[3] = k->d[3];
     r1->d[4] = 0;
     r1->d[5] = 0;
     r1->d[6] = 0;
     r1->d[7] = 0;
-    r2->d[0] = a->d[4];
-    r2->d[1] = a->d[5];
-    r2->d[2] = a->d[6];
-    r2->d[3] = a->d[7];
+    r2->d[0] = k->d[4];
+    r2->d[1] = k->d[5];
+    r2->d[2] = k->d[6];
+    r2->d[3] = k->d[7];
     r2->d[4] = 0;
     r2->d[5] = 0;
     r2->d[6] = 0;
     r2->d[7] = 0;
 }
-#endif
 
 SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
     return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
diff --git a/src/secp256k1/src/scalar_impl.h b/src/secp256k1/src/scalar_impl.h
index 2ec04b1ae9..fc75891818 100644
--- a/src/secp256k1/src/scalar_impl.h
+++ b/src/secp256k1/src/scalar_impl.h
@@ -7,6 +7,10 @@
 #ifndef SECP256K1_SCALAR_IMPL_H
 #define SECP256K1_SCALAR_IMPL_H
 
+#ifdef VERIFY
+#include <string.h>
+#endif
+
 #include "scalar.h"
 #include "util.h"
 
@@ -252,37 +256,65 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_sc
 #endif
 }
 
-#ifdef USE_ENDOMORPHISM
+/* These parameters are generated using sage/gen_exhaustive_groups.sage. */
 #if defined(EXHAUSTIVE_TEST_ORDER)
+#  if EXHAUSTIVE_TEST_ORDER == 13
+#    define EXHAUSTIVE_TEST_LAMBDA 9
+#  elif EXHAUSTIVE_TEST_ORDER == 199
+#    define EXHAUSTIVE_TEST_LAMBDA 92
+#  else
+#    error No known lambda for the specified exhaustive test group order.
+#  endif
+
 /**
- * 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
+ * Find r1 and r2 given k, such that r1 + r2 * lambda == k mod n; unlike in the
+ * full case we don't bother making r1 and r2 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.
+ * (arbitrarily) set r2 = k + 5 (mod n) and r1 = k - r2 * lambda (mod n).
  */
-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;
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) {
+    *r2 = (*k + 5) % EXHAUSTIVE_TEST_ORDER;
+    *r1 = (*k + (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,
- *            0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72}
+ * lambda is: */
+static const secp256k1_scalar secp256k1_const_lambda = SECP256K1_SCALAR_CONST(
+    0x5363AD4CUL, 0xC05C30E0UL, 0xA5261C02UL, 0x8812645AUL,
+    0x122E22EAUL, 0x20816678UL, 0xDF02967CUL, 0x1B23BD72UL
+);
+
+#ifdef VERIFY
+static void secp256k1_scalar_split_lambda_verify(const secp256k1_scalar *r1, const secp256k1_scalar *r2, const secp256k1_scalar *k);
+#endif
+
+/*
+ * Both lambda and beta are primitive cube roots of unity.  That is lamba^3 == 1 mod n and
+ * beta^3 == 1 mod p, where n is the curve order and p is the field order.
  *
- * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
- * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
- * and k2 have a small size.
- * It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
+ * Futhermore, because (X^3 - 1) = (X - 1)(X^2 + X + 1), the primitive cube roots of unity are
+ * roots of X^2 + X + 1.  Therefore lambda^2 + lamba == -1 mod n and beta^2 + beta == -1 mod p.
+ * (The other primitive cube roots of unity are lambda^2 and beta^2 respectively.)
+ *
+ * Let l = -1/2 + i*sqrt(3)/2, the complex root of X^2 + X + 1. We can define a ring
+ * homomorphism phi : Z[l] -> Z_n where phi(a + b*l) == a + b*lambda mod n. The kernel of phi
+ * is a lattice over Z[l] (considering Z[l] as a Z-module). This lattice is generated by a
+ * reduced basis {a1 + b1*l, a2 + b2*l} where
  *
  * - a1 =      {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
  * - b1 =     -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
  * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
  * - b2 =      {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
  *
- * The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
+ * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
+ * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
+ * and k2 are small in absolute value.
+ *
+ * The algorithm computes c1 = round(b2 * k / n) and c2 = round((-b1) * k / n), and gives
  * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
- * compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
+ * compute r2 = k2 mod n, and r1 = k1 mod n = (k - r2 * lambda) mod n, avoiding the need for
+ * the constants a1 and a2.
  *
  * g1, g2 are precomputed constants used to replace division with a rounded multiplication
  * when decomposing the scalar for an endomorphism-based point multiplication.
@@ -294,21 +326,21 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar
  * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
  * Section 4.3 (here we use a somewhat higher-precision estimate):
  * d = a1*b2 - b1*a2
- * g1 = round((2^272)*b2/d)
- * g2 = round((2^272)*b1/d)
+ * g1 = round(2^384 * b2/d)
+ * g2 = round(2^384 * (-b1)/d)
  *
- * (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
- * as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
+ * (Note that d is also equal to the curve order, n, here because [a1,b1] and [a2,b2]
+ * can be found as outputs of the Extended Euclidean Algorithm on inputs n and lambda).
  *
- * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
+ * The function below splits k into r1 and r2, such that
+ * - r1 + lambda * r2 == k (mod n)
+ * - either r1 < 2^128 or -r1 mod n < 2^128
+ * - either r2 < 2^128 or -r2 mod n < 2^128
+ *
+ * See proof below.
  */
-
-static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) {
     secp256k1_scalar c1, c2;
-    static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST(
-        0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
-        0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
-    );
     static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST(
         0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
         0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
@@ -318,25 +350,167 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar
         0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
     );
     static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST(
-        0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
-        0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
+        0x3086D221UL, 0xA7D46BCDUL, 0xE86C90E4UL, 0x9284EB15UL,
+        0x3DAA8A14UL, 0x71E8CA7FUL, 0xE893209AUL, 0x45DBB031UL
     );
     static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST(
-        0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
-        0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
+        0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C4UL,
+        0x221208ACUL, 0x9DF506C6UL, 0x1571B4AEUL, 0x8AC47F71UL
     );
-    VERIFY_CHECK(r1 != a);
-    VERIFY_CHECK(r2 != a);
+    VERIFY_CHECK(r1 != k);
+    VERIFY_CHECK(r2 != k);
     /* these _var calls are constant time since the shift amount is constant */
-    secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
-    secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
+    secp256k1_scalar_mul_shift_var(&c1, k, &g1, 384);
+    secp256k1_scalar_mul_shift_var(&c2, k, &g2, 384);
     secp256k1_scalar_mul(&c1, &c1, &minus_b1);
     secp256k1_scalar_mul(&c2, &c2, &minus_b2);
     secp256k1_scalar_add(r2, &c1, &c2);
-    secp256k1_scalar_mul(r1, r2, &minus_lambda);
-    secp256k1_scalar_add(r1, r1, a);
-}
-#endif
+    secp256k1_scalar_mul(r1, r2, &secp256k1_const_lambda);
+    secp256k1_scalar_negate(r1, r1);
+    secp256k1_scalar_add(r1, r1, k);
+
+#ifdef VERIFY
+    secp256k1_scalar_split_lambda_verify(r1, r2, k);
 #endif
+}
+
+#ifdef VERIFY
+/*
+ * Proof for secp256k1_scalar_split_lambda's bounds.
+ *
+ * Let
+ *  - epsilon1 = 2^256 * |g1/2^384 - b2/d|
+ *  - epsilon2 = 2^256 * |g2/2^384 - (-b1)/d|
+ *  - c1 = round(k*g1/2^384)
+ *  - c2 = round(k*g2/2^384)
+ *
+ * Lemma 1: |c1 - k*b2/d| < 2^-1 + epsilon1
+ *
+ *    |c1 - k*b2/d|
+ *  =
+ *    |c1 - k*g1/2^384 + k*g1/2^384 - k*b2/d|
+ * <=   {triangle inequality}
+ *    |c1 - k*g1/2^384| + |k*g1/2^384 - k*b2/d|
+ *  =
+ *    |c1 - k*g1/2^384| + k*|g1/2^384 - b2/d|
+ * <    {rounding in c1 and 0 <= k < 2^256}
+ *    2^-1 + 2^256 * |g1/2^384 - b2/d|
+ *  =   {definition of epsilon1}
+ *    2^-1 + epsilon1
+ *
+ * Lemma 2: |c2 - k*(-b1)/d| < 2^-1 + epsilon2
+ *
+ *    |c2 - k*(-b1)/d|
+ *  =
+ *    |c2 - k*g2/2^384 + k*g2/2^384 - k*(-b1)/d|
+ * <=   {triangle inequality}
+ *    |c2 - k*g2/2^384| + |k*g2/2^384 - k*(-b1)/d|
+ *  =
+ *    |c2 - k*g2/2^384| + k*|g2/2^384 - (-b1)/d|
+ * <    {rounding in c2 and 0 <= k < 2^256}
+ *    2^-1 + 2^256 * |g2/2^384 - (-b1)/d|
+ *  =   {definition of epsilon2}
+ *    2^-1 + epsilon2
+ *
+ * Let
+ *  - k1 = k - c1*a1 - c2*a2
+ *  - k2 = - c1*b1 - c2*b2
+ *
+ * Lemma 3: |k1| < (a1 + a2 + 1)/2 < 2^128
+ *
+ *    |k1|
+ *  =   {definition of k1}
+ *    |k - c1*a1 - c2*a2|
+ *  =   {(a1*b2 - b1*a2)/n = 1}
+ *    |k*(a1*b2 - b1*a2)/n - c1*a1 - c2*a2|
+ *  =
+ *    |a1*(k*b2/n - c1) + a2*(k*(-b1)/n - c2)|
+ * <=   {triangle inequality}
+ *    a1*|k*b2/n - c1| + a2*|k*(-b1)/n - c2|
+ * <    {Lemma 1 and Lemma 2}
+ *    a1*(2^-1 + epslion1) + a2*(2^-1 + epsilon2)
+ * <    {rounding up to an integer}
+ *    (a1 + a2 + 1)/2
+ * <    {rounding up to a power of 2}
+ *    2^128
+ *
+ * Lemma 4: |k2| < (-b1 + b2)/2 + 1 < 2^128
+ *
+ *    |k2|
+ *  =   {definition of k2}
+ *    |- c1*a1 - c2*a2|
+ *  =   {(b1*b2 - b1*b2)/n = 0}
+ *    |k*(b1*b2 - b1*b2)/n - c1*b1 - c2*b2|
+ *  =
+ *    |b1*(k*b2/n - c1) + b2*(k*(-b1)/n - c2)|
+ * <=   {triangle inequality}
+ *    (-b1)*|k*b2/n - c1| + b2*|k*(-b1)/n - c2|
+ * <    {Lemma 1 and Lemma 2}
+ *    (-b1)*(2^-1 + epslion1) + b2*(2^-1 + epsilon2)
+ * <    {rounding up to an integer}
+ *    (-b1 + b2)/2 + 1
+ * <    {rounding up to a power of 2}
+ *    2^128
+ *
+ * Let
+ *  - r2 = k2 mod n
+ *  - r1 = k - r2*lambda mod n.
+ *
+ * Notice that r1 is defined such that r1 + r2 * lambda == k (mod n).
+ *
+ * Lemma 5: r1 == k1 mod n.
+ *
+ *    r1
+ * ==   {definition of r1 and r2}
+ *    k - k2*lambda
+ * ==   {definition of k2}
+ *    k - (- c1*b1 - c2*b2)*lambda
+ * ==
+ *    k + c1*b1*lambda + c2*b2*lambda
+ * ==  {a1 + b1*lambda == 0 mod n and a2 + b2*lambda == 0 mod n}
+ *    k - c1*a1 - c2*a2
+ * ==  {definition of k1}
+ *    k1
+ *
+ * From Lemma 3, Lemma 4, Lemma 5 and the definition of r2, we can conclude that
+ *
+ *  - either r1 < 2^128 or -r1 mod n < 2^128
+ *  - either r2 < 2^128 or -r2 mod n < 2^128.
+ *
+ * Q.E.D.
+ */
+static void secp256k1_scalar_split_lambda_verify(const secp256k1_scalar *r1, const secp256k1_scalar *r2, const secp256k1_scalar *k) {
+    secp256k1_scalar s;
+    unsigned char buf1[32];
+    unsigned char buf2[32];
+
+    /* (a1 + a2 + 1)/2 is 0xa2a8918ca85bafe22016d0b917e4dd77 */
+    static const unsigned char k1_bound[32] = {
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0xa2, 0xa8, 0x91, 0x8c, 0xa8, 0x5b, 0xaf, 0xe2, 0x20, 0x16, 0xd0, 0xb9, 0x17, 0xe4, 0xdd, 0x77
+    };
+
+    /* (-b1 + b2)/2 + 1 is 0x8a65287bd47179fb2be08846cea267ed */
+    static const unsigned char k2_bound[32] = {
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+        0x8a, 0x65, 0x28, 0x7b, 0xd4, 0x71, 0x79, 0xfb, 0x2b, 0xe0, 0x88, 0x46, 0xce, 0xa2, 0x67, 0xed
+    };
+
+    secp256k1_scalar_mul(&s, &secp256k1_const_lambda, r2);
+    secp256k1_scalar_add(&s, &s, r1);
+    VERIFY_CHECK(secp256k1_scalar_eq(&s, k));
+
+    secp256k1_scalar_negate(&s, r1);
+    secp256k1_scalar_get_b32(buf1, r1);
+    secp256k1_scalar_get_b32(buf2, &s);
+    VERIFY_CHECK(secp256k1_memcmp_var(buf1, k1_bound, 32) < 0 || secp256k1_memcmp_var(buf2, k1_bound, 32) < 0);
+
+    secp256k1_scalar_negate(&s, r2);
+    secp256k1_scalar_get_b32(buf1, r2);
+    secp256k1_scalar_get_b32(buf2, &s);
+    VERIFY_CHECK(secp256k1_memcmp_var(buf1, k2_bound, 32) < 0 || secp256k1_memcmp_var(buf2, k2_bound, 32) < 0);
+}
+#endif /* VERIFY */
+#endif /* !defined(EXHAUSTIVE_TEST_ORDER) */
 
 #endif /* SECP256K1_SCALAR_IMPL_H */
diff --git a/src/secp256k1/src/scalar_low_impl.h b/src/secp256k1/src/scalar_low_impl.h
index b79cf1ff6c..a615ec074b 100644
--- a/src/secp256k1/src/scalar_low_impl.h
+++ b/src/secp256k1/src/scalar_low_impl.h
@@ -48,14 +48,17 @@ static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int
 }
 
 static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
-    const int base = 0x100 % EXHAUSTIVE_TEST_ORDER;
     int i;
+    int over = 0;
     *r = 0;
     for (i = 0; i < 32; i++) {
-       *r = ((*r * base) + b32[i]) % EXHAUSTIVE_TEST_ORDER;
+        *r = (*r * 0x100) + b32[i];
+        if (*r >= EXHAUSTIVE_TEST_ORDER) {
+            over = 1;
+            *r %= EXHAUSTIVE_TEST_ORDER;
+        }
     }
-    /* just deny overflow, it basically always happens */
-    if (overflow) *overflow = 0;
+    if (overflow) *overflow = over;
 }
 
 static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
diff --git a/src/secp256k1/src/scratch_impl.h b/src/secp256k1/src/scratch_impl.h
index b205620224..f381e2e322 100644
--- a/src/secp256k1/src/scratch_impl.h
+++ b/src/secp256k1/src/scratch_impl.h
@@ -26,7 +26,7 @@ static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* err
 static void secp256k1_scratch_destroy(const secp256k1_callback* error_callback, secp256k1_scratch* scratch) {
     if (scratch != NULL) {
         VERIFY_CHECK(scratch->alloc_size == 0); /* all checkpoints should be applied */
-        if (memcmp(scratch->magic, "scratch", 8) != 0) {
+        if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) {
             secp256k1_callback_call(error_callback, "invalid scratch space");
             return;
         }
@@ -36,7 +36,7 @@ static void secp256k1_scratch_destroy(const secp256k1_callback* error_callback,
 }
 
 static size_t secp256k1_scratch_checkpoint(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch) {
-    if (memcmp(scratch->magic, "scratch", 8) != 0) {
+    if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) {
         secp256k1_callback_call(error_callback, "invalid scratch space");
         return 0;
     }
@@ -44,7 +44,7 @@ static size_t secp256k1_scratch_checkpoint(const secp256k1_callback* error_callb
 }
 
 static void secp256k1_scratch_apply_checkpoint(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t checkpoint) {
-    if (memcmp(scratch->magic, "scratch", 8) != 0) {
+    if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) {
         secp256k1_callback_call(error_callback, "invalid scratch space");
         return;
     }
@@ -56,7 +56,7 @@ static void secp256k1_scratch_apply_checkpoint(const secp256k1_callback* error_c
 }
 
 static size_t secp256k1_scratch_max_allocation(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch, size_t objects) {
-    if (memcmp(scratch->magic, "scratch", 8) != 0) {
+    if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) {
         secp256k1_callback_call(error_callback, "invalid scratch space");
         return 0;
     }
@@ -81,7 +81,7 @@ static void *secp256k1_scratch_alloc(const secp256k1_callback* error_callback, s
     }
     size = rounded_size;
 
-    if (memcmp(scratch->magic, "scratch", 8) != 0) {
+    if (secp256k1_memcmp_var(scratch->magic, "scratch", 8) != 0) {
         secp256k1_callback_call(error_callback, "invalid scratch space");
         return NULL;
     }
diff --git a/src/secp256k1/src/secp256k1.c b/src/secp256k1/src/secp256k1.c
index eaafb3a21d..dae506d08c 100644
--- a/src/secp256k1/src/secp256k1.c
+++ b/src/secp256k1/src/secp256k1.c
@@ -284,6 +284,9 @@ int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pu
     if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) {
         return 0;
     }
+    if (!secp256k1_ge_is_in_correct_subgroup(&Q)) {
+        return 0;
+    }
     secp256k1_pubkey_save(pubkey, &Q);
     secp256k1_ge_clear(&Q);
     return 1;
diff --git a/src/secp256k1/src/selftest.h b/src/secp256k1/src/selftest.h
index 885983aa20..0e37510c1e 100644
--- a/src/secp256k1/src/selftest.h
+++ b/src/secp256k1/src/selftest.h
@@ -22,7 +22,7 @@ static int secp256k1_selftest_sha256(void) {
     secp256k1_sha256_initialize(&hasher);
     secp256k1_sha256_write(&hasher, (const unsigned char*)input63, 63);
     secp256k1_sha256_finalize(&hasher, out);
-    return memcmp(out, output32, 32) == 0;
+    return secp256k1_memcmp_var(out, output32, 32) == 0;
 }
 
 static int secp256k1_selftest(void) {
diff --git a/src/secp256k1/src/testrand.h b/src/secp256k1/src/testrand.h
index bcbe15a6f1..a76003d5b8 100644
--- a/src/secp256k1/src/testrand.h
+++ b/src/secp256k1/src/testrand.h
@@ -14,28 +14,34 @@
 /* A non-cryptographic RNG used only for test infrastructure. */
 
 /** Seed the pseudorandom number generator for testing. */
-SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16);
+SECP256K1_INLINE static void secp256k1_testrand_seed(const unsigned char *seed16);
 
 /** Generate a pseudorandom number in the range [0..2**32-1]. */
-static uint32_t secp256k1_rand32(void);
+static uint32_t secp256k1_testrand32(void);
 
 /** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or
  *  more. */
-static uint32_t secp256k1_rand_bits(int bits);
+static uint32_t secp256k1_testrand_bits(int bits);
 
 /** Generate a pseudorandom number in the range [0..range-1]. */
-static uint32_t secp256k1_rand_int(uint32_t range);
+static uint32_t secp256k1_testrand_int(uint32_t range);
 
 /** Generate a pseudorandom 32-byte array. */
-static void secp256k1_rand256(unsigned char *b32);
+static void secp256k1_testrand256(unsigned char *b32);
 
 /** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */
-static void secp256k1_rand256_test(unsigned char *b32);
+static void secp256k1_testrand256_test(unsigned char *b32);
 
 /** Generate pseudorandom bytes with long sequences of zero and one bits. */
-static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len);
+static void secp256k1_testrand_bytes_test(unsigned char *bytes, size_t len);
 
 /** Flip a single random bit in a byte array */
-static void secp256k1_rand_flip(unsigned char *b, size_t len);
+static void secp256k1_testrand_flip(unsigned char *b, size_t len);
+
+/** Initialize the test RNG using (hex encoded) array up to 16 bytes, or randomly if hexseed is NULL. */
+static void secp256k1_testrand_init(const char* hexseed);
+
+/** Print final test information. */
+static void secp256k1_testrand_finish(void);
 
 #endif /* SECP256K1_TESTRAND_H */
diff --git a/src/secp256k1/src/testrand_impl.h b/src/secp256k1/src/testrand_impl.h
index dfb658d9c6..3392566329 100644
--- a/src/secp256k1/src/testrand_impl.h
+++ b/src/secp256k1/src/testrand_impl.h
@@ -8,6 +8,7 @@
 #define SECP256K1_TESTRAND_IMPL_H
 
 #include <stdint.h>
+#include <stdio.h>
 #include <string.h>
 
 #include "testrand.h"
@@ -19,11 +20,11 @@ static int secp256k1_test_rng_precomputed_used = 8;
 static uint64_t secp256k1_test_rng_integer;
 static int secp256k1_test_rng_integer_bits_left = 0;
 
-SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) {
+SECP256K1_INLINE static void secp256k1_testrand_seed(const unsigned char *seed16) {
     secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16);
 }
 
-SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {
+SECP256K1_INLINE static uint32_t secp256k1_testrand32(void) {
     if (secp256k1_test_rng_precomputed_used == 8) {
         secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed));
         secp256k1_test_rng_precomputed_used = 0;
@@ -31,10 +32,10 @@ SECP256K1_INLINE static uint32_t secp256k1_rand32(void) {
     return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++];
 }
 
-static uint32_t secp256k1_rand_bits(int bits) {
+static uint32_t secp256k1_testrand_bits(int bits) {
     uint32_t ret;
     if (secp256k1_test_rng_integer_bits_left < bits) {
-        secp256k1_test_rng_integer |= (((uint64_t)secp256k1_rand32()) << secp256k1_test_rng_integer_bits_left);
+        secp256k1_test_rng_integer |= (((uint64_t)secp256k1_testrand32()) << secp256k1_test_rng_integer_bits_left);
         secp256k1_test_rng_integer_bits_left += 32;
     }
     ret = secp256k1_test_rng_integer;
@@ -44,7 +45,7 @@ static uint32_t secp256k1_rand_bits(int bits) {
     return ret;
 }
 
-static uint32_t secp256k1_rand_int(uint32_t range) {
+static uint32_t secp256k1_testrand_int(uint32_t range) {
     /* We want a uniform integer between 0 and range-1, inclusive.
      * B is the smallest number such that range <= 2**B.
      * two mechanisms implemented here:
@@ -76,25 +77,25 @@ static uint32_t secp256k1_rand_int(uint32_t range) {
         mult = 1;
     }
     while(1) {
-        uint32_t x = secp256k1_rand_bits(bits);
+        uint32_t x = secp256k1_testrand_bits(bits);
         if (x < trange) {
             return (mult == 1) ? x : (x % range);
         }
     }
 }
 
-static void secp256k1_rand256(unsigned char *b32) {
+static void secp256k1_testrand256(unsigned char *b32) {
     secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32);
 }
 
-static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len) {
+static void secp256k1_testrand_bytes_test(unsigned char *bytes, size_t len) {
     size_t bits = 0;
     memset(bytes, 0, len);
     while (bits < len * 8) {
         int now;
         uint32_t val;
-        now = 1 + (secp256k1_rand_bits(6) * secp256k1_rand_bits(5) + 16) / 31;
-        val = secp256k1_rand_bits(1);
+        now = 1 + (secp256k1_testrand_bits(6) * secp256k1_testrand_bits(5) + 16) / 31;
+        val = secp256k1_testrand_bits(1);
         while (now > 0 && bits < len * 8) {
             bytes[bits / 8] |= val << (bits % 8);
             now--;
@@ -103,12 +104,55 @@ static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len) {
     }
 }
 
-static void secp256k1_rand256_test(unsigned char *b32) {
-    secp256k1_rand_bytes_test(b32, 32);
+static void secp256k1_testrand256_test(unsigned char *b32) {
+    secp256k1_testrand_bytes_test(b32, 32);
 }
 
-static void secp256k1_rand_flip(unsigned char *b, size_t len) {
-    b[secp256k1_rand_int(len)] ^= (1 << secp256k1_rand_int(8));
+static void secp256k1_testrand_flip(unsigned char *b, size_t len) {
+    b[secp256k1_testrand_int(len)] ^= (1 << secp256k1_testrand_int(8));
+}
+
+static void secp256k1_testrand_init(const char* hexseed) {
+    unsigned char seed16[16] = {0};
+    if (hexseed && strlen(hexseed) != 0) {
+        int pos = 0;
+        while (pos < 16 && hexseed[0] != 0 && hexseed[1] != 0) {
+            unsigned short sh;
+            if ((sscanf(hexseed, "%2hx", &sh)) == 1) {
+                seed16[pos] = sh;
+            } else {
+                break;
+            }
+            hexseed += 2;
+            pos++;
+        }
+    } else {
+        FILE *frand = fopen("/dev/urandom", "r");
+        if ((frand == NULL) || fread(&seed16, 1, sizeof(seed16), frand) != sizeof(seed16)) {
+            uint64_t t = time(NULL) * (uint64_t)1337;
+            fprintf(stderr, "WARNING: could not read 16 bytes from /dev/urandom; falling back to insecure PRNG\n");
+            seed16[0] ^= t;
+            seed16[1] ^= t >> 8;
+            seed16[2] ^= t >> 16;
+            seed16[3] ^= t >> 24;
+            seed16[4] ^= t >> 32;
+            seed16[5] ^= t >> 40;
+            seed16[6] ^= t >> 48;
+            seed16[7] ^= t >> 56;
+        }
+        if (frand) {
+            fclose(frand);
+        }
+    }
+
+    printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]);
+    secp256k1_testrand_seed(seed16);
+}
+
+static void secp256k1_testrand_finish(void) {
+    unsigned char run32[32];
+    secp256k1_testrand256(run32);
+    printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]);
 }
 
 #endif /* SECP256K1_TESTRAND_IMPL_H */
diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
index 4780e9319b..bb4b5b4c07 100644
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/src/tests.c
@@ -54,7 +54,7 @@ static void uncounting_illegal_callback_fn(const char* str, void* data) {
 void random_field_element_test(secp256k1_fe *fe) {
     do {
         unsigned char b32[32];
-        secp256k1_rand256_test(b32);
+        secp256k1_testrand256_test(b32);
         if (secp256k1_fe_set_b32(fe, b32)) {
             break;
         }
@@ -63,7 +63,7 @@ void random_field_element_test(secp256k1_fe *fe) {
 
 void random_field_element_magnitude(secp256k1_fe *fe) {
     secp256k1_fe zero;
-    int n = secp256k1_rand_int(9);
+    int n = secp256k1_testrand_int(9);
     secp256k1_fe_normalize(fe);
     if (n == 0) {
         return;
@@ -81,11 +81,12 @@ void random_group_element_test(secp256k1_ge *ge) {
     secp256k1_fe fe;
     do {
         random_field_element_test(&fe);
-        if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) {
+        if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_testrand_bits(1))) {
             secp256k1_fe_normalize(&ge->y);
             break;
         }
     } while(1);
+    ge->infinity = 0;
 }
 
 void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) {
@@ -107,7 +108,7 @@ void random_scalar_order_test(secp256k1_scalar *num) {
     do {
         unsigned char b32[32];
         int overflow = 0;
-        secp256k1_rand256_test(b32);
+        secp256k1_testrand256_test(b32);
         secp256k1_scalar_set_b32(num, b32, &overflow);
         if (overflow || secp256k1_scalar_is_zero(num)) {
             continue;
@@ -120,7 +121,7 @@ void random_scalar_order(secp256k1_scalar *num) {
     do {
         unsigned char b32[32];
         int overflow = 0;
-        secp256k1_rand256(b32);
+        secp256k1_testrand256(b32);
         secp256k1_scalar_set_b32(num, b32, &overflow);
         if (overflow || secp256k1_scalar_is_zero(num)) {
             continue;
@@ -441,14 +442,14 @@ void run_sha256_tests(void) {
         secp256k1_sha256_initialize(&hasher);
         secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
         secp256k1_sha256_finalize(&hasher, out);
-        CHECK(memcmp(out, outputs[i], 32) == 0);
+        CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         if (strlen(inputs[i]) > 0) {
-            int split = secp256k1_rand_int(strlen(inputs[i]));
+            int split = secp256k1_testrand_int(strlen(inputs[i]));
             secp256k1_sha256_initialize(&hasher);
             secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
             secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
             secp256k1_sha256_finalize(&hasher, out);
-            CHECK(memcmp(out, outputs[i], 32) == 0);
+            CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         }
     }
 }
@@ -485,14 +486,14 @@ void run_hmac_sha256_tests(void) {
         secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
         secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
         secp256k1_hmac_sha256_finalize(&hasher, out);
-        CHECK(memcmp(out, outputs[i], 32) == 0);
+        CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         if (strlen(inputs[i]) > 0) {
-            int split = secp256k1_rand_int(strlen(inputs[i]));
+            int split = secp256k1_testrand_int(strlen(inputs[i]));
             secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
             secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
             secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
             secp256k1_hmac_sha256_finalize(&hasher, out);
-            CHECK(memcmp(out, outputs[i], 32) == 0);
+            CHECK(secp256k1_memcmp_var(out, outputs[i], 32) == 0);
         }
     }
 }
@@ -519,21 +520,21 @@ void run_rfc6979_hmac_sha256_tests(void) {
     secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
-        CHECK(memcmp(out, out1[i], 32) == 0);
+        CHECK(secp256k1_memcmp_var(out, out1[i], 32) == 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
     secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
-        CHECK(memcmp(out, out1[i], 32) != 0);
+        CHECK(secp256k1_memcmp_var(out, out1[i], 32) != 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 
     secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
     for (i = 0; i < 3; i++) {
         secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
-        CHECK(memcmp(out, out2[i], 32) == 0);
+        CHECK(secp256k1_memcmp_var(out, out2[i], 32) == 0);
     }
     secp256k1_rfc6979_hmac_sha256_finalize(&rng);
 }
@@ -557,7 +558,7 @@ void test_rand_bits(int rand32, int bits) {
     /* Multiply the output of all rand calls with the odd number m, which
        should not change the uniformity of its distribution. */
     for (i = 0; i < rounds[usebits]; i++) {
-        uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits));
+        uint32_t r = (rand32 ? secp256k1_testrand32() : secp256k1_testrand_bits(bits));
         CHECK((((uint64_t)r) >> bits) == 0);
         for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
             uint32_t rm = r * mults[m];
@@ -582,7 +583,7 @@ void test_rand_int(uint32_t range, uint32_t subrange) {
     uint64_t x = 0;
     CHECK((range % subrange) == 0);
     for (i = 0; i < rounds; i++) {
-        uint32_t r = secp256k1_rand_int(range);
+        uint32_t r = secp256k1_testrand_int(range);
         CHECK(r < range);
         r = r % subrange;
         x |= (((uint64_t)1) << r);
@@ -614,7 +615,7 @@ void run_rand_int(void) {
 
 #ifndef USE_NUM_NONE
 void random_num_negate(secp256k1_num *num) {
-    if (secp256k1_rand_bits(1)) {
+    if (secp256k1_testrand_bits(1)) {
         secp256k1_num_negate(num);
     }
 }
@@ -658,11 +659,11 @@ void test_num_add_sub(void) {
     secp256k1_num n2;
     secp256k1_num n1p2, n2p1, n1m2, n2m1;
     random_num_order_test(&n1); /* n1 = R1 */
-    if (secp256k1_rand_bits(1)) {
+    if (secp256k1_testrand_bits(1)) {
         random_num_negate(&n1);
     }
     random_num_order_test(&n2); /* n2 = R2 */
-    if (secp256k1_rand_bits(1)) {
+    if (secp256k1_testrand_bits(1)) {
         random_num_negate(&n2);
     }
     secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */
@@ -853,7 +854,7 @@ void scalar_test(void) {
         while (i < 256) {
             secp256k1_scalar t;
             int j;
-            int now = secp256k1_rand_int(15) + 1;
+            int now = secp256k1_testrand_int(15) + 1;
             if (now + i > 256) {
                 now = 256 - i;
             }
@@ -930,7 +931,7 @@ void scalar_test(void) {
         secp256k1_num rnum;
         secp256k1_num rnum2;
         unsigned char cone[1] = {0x01};
-        unsigned int shift = 256 + secp256k1_rand_int(257);
+        unsigned int shift = 256 + secp256k1_testrand_int(257);
         secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
         secp256k1_num_mul(&rnum, &s1num, &s2num);
         secp256k1_num_shift(&rnum, shift - 1);
@@ -948,7 +949,7 @@ void scalar_test(void) {
         random_scalar_order_test(&r);
         for (i = 0; i < 100; ++i) {
             int low;
-            int shift = 1 + secp256k1_rand_int(15);
+            int shift = 1 + secp256k1_testrand_int(15);
             int expected = r.d[0] % (1 << shift);
             low = secp256k1_scalar_shr_int(&r, shift);
             CHECK(expected == low);
@@ -996,7 +997,7 @@ void scalar_test(void) {
         secp256k1_scalar b;
         int i;
         /* Test add_bit. */
-        int bit = secp256k1_rand_bits(8);
+        int bit = secp256k1_testrand_bits(8);
         secp256k1_scalar_set_int(&b, 1);
         CHECK(secp256k1_scalar_is_one(&b));
         for (i = 0; i < bit; i++) {
@@ -1157,7 +1158,7 @@ void run_scalar_tests(void) {
         secp256k1_scalar_set_b32(&scalar, bin, &overflow);
         CHECK(overflow == 0);
         secp256k1_scalar_get_b32(bin_tmp, &scalar);
-        CHECK(memcmp(bin, bin_tmp, 32) == 0);
+        CHECK(secp256k1_memcmp_var(bin, bin_tmp, 32) == 0);
 
         /* A scalar set to all 1s should overflow. */
         memset(bin, 0xFF, 32);
@@ -1767,7 +1768,7 @@ void run_scalar_tests(void) {
 void random_fe(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
-        secp256k1_rand256(bin);
+        secp256k1_testrand256(bin);
         if (secp256k1_fe_set_b32(x, bin)) {
             return;
         }
@@ -1777,7 +1778,7 @@ void random_fe(secp256k1_fe *x) {
 void random_fe_test(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
-        secp256k1_rand256_test(bin);
+        secp256k1_testrand256_test(bin);
         if (secp256k1_fe_set_b32(x, bin)) {
             return;
         }
@@ -1845,18 +1846,18 @@ void run_field_convert(void) {
     CHECK(secp256k1_fe_equal_var(&fe, &fe2));
     /* Check conversion from fe. */
     secp256k1_fe_get_b32(b322, &fe);
-    CHECK(memcmp(b322, b32, 32) == 0);
+    CHECK(secp256k1_memcmp_var(b322, b32, 32) == 0);
     secp256k1_fe_to_storage(&fes2, &fe);
-    CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0);
+    CHECK(secp256k1_memcmp_var(&fes2, &fes, sizeof(fes)) == 0);
 }
 
-int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) {
+int fe_secp256k1_memcmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     secp256k1_fe t = *b;
 #ifdef VERIFY
     t.magnitude = a->magnitude;
     t.normalized = a->normalized;
 #endif
-    return memcmp(a, &t, sizeof(secp256k1_fe));
+    return secp256k1_memcmp_var(a, &t, sizeof(secp256k1_fe));
 }
 
 void run_field_misc(void) {
@@ -1882,13 +1883,13 @@ void run_field_misc(void) {
         CHECK(x.normalized && x.magnitude == 1);
 #endif
         secp256k1_fe_cmov(&x, &x, 1);
-        CHECK(fe_memcmp(&x, &z) != 0);
-        CHECK(fe_memcmp(&x, &q) == 0);
+        CHECK(fe_secp256k1_memcmp_var(&x, &z) != 0);
+        CHECK(fe_secp256k1_memcmp_var(&x, &q) == 0);
         secp256k1_fe_cmov(&q, &z, 1);
 #ifdef VERIFY
         CHECK(!q.normalized && q.magnitude == z.magnitude);
 #endif
-        CHECK(fe_memcmp(&q, &z) == 0);
+        CHECK(fe_secp256k1_memcmp_var(&q, &z) == 0);
         secp256k1_fe_normalize_var(&x);
         secp256k1_fe_normalize_var(&z);
         CHECK(!secp256k1_fe_equal_var(&x, &z));
@@ -1912,9 +1913,9 @@ void run_field_misc(void) {
         secp256k1_fe_to_storage(&zs, &z);
         secp256k1_fe_storage_cmov(&zs, &xs, 0);
         secp256k1_fe_storage_cmov(&zs, &zs, 1);
-        CHECK(memcmp(&xs, &zs, sizeof(xs)) != 0);
+        CHECK(secp256k1_memcmp_var(&xs, &zs, sizeof(xs)) != 0);
         secp256k1_fe_storage_cmov(&ys, &xs, 1);
-        CHECK(memcmp(&xs, &ys, sizeof(xs)) == 0);
+        CHECK(secp256k1_memcmp_var(&xs, &ys, sizeof(xs)) == 0);
         secp256k1_fe_from_storage(&x, &xs);
         secp256k1_fe_from_storage(&y, &ys);
         secp256k1_fe_from_storage(&z, &zs);
@@ -1970,7 +1971,7 @@ void run_field_inv_all_var(void) {
     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;
+        size_t len = secp256k1_testrand_int(15) + 1;
         for (j = 0; j < len; j++) {
             random_fe_non_zero(&x[j]);
         }
@@ -2101,17 +2102,12 @@ void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
 
 void test_ge(void) {
     int i, i1;
-#ifdef USE_ENDOMORPHISM
     int runs = 6;
-#else
-    int runs = 4;
-#endif
-    /* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4).
-     * The second in each pair of identical points uses a random Z coordinate in the Jacobian form.
-     * All magnitudes are randomized.
-     * All 17*17 combinations of points are added to each other, using all applicable methods.
-     *
-     * When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
+    /* 25 points are used:
+     * - infinity
+     * - for each of four random points p1 p2 p3 p4, we add the point, its
+     *   negation, and then those two again but with randomized Z coordinate.
+     * - The same is then done for lambda*p1 and lambda^2*p1.
      */
     secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs));
     secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_gej) * (1 + 4 * runs));
@@ -2126,14 +2122,12 @@ void test_ge(void) {
         int j;
         secp256k1_ge g;
         random_group_element_test(&g);
-#ifdef USE_ENDOMORPHISM
         if (i >= runs - 2) {
             secp256k1_ge_mul_lambda(&g, &ge[1]);
         }
         if (i >= runs - 1) {
             secp256k1_ge_mul_lambda(&g, &g);
         }
-#endif
         ge[1 + 4 * i] = g;
         ge[2 + 4 * i] = g;
         secp256k1_ge_neg(&ge[3 + 4 * i], &g);
@@ -2262,7 +2256,7 @@ void test_ge(void) {
             gej_shuffled[i] = gej[i];
         }
         for (i = 0; i < 4 * runs + 1; i++) {
-            int swap = i + secp256k1_rand_int(4 * runs + 1 - i);
+            int swap = i + secp256k1_testrand_int(4 * runs + 1 - i);
             if (swap != i) {
                 secp256k1_gej t = gej_shuffled[i];
                 gej_shuffled[i] = gej_shuffled[swap];
@@ -2448,7 +2442,7 @@ void test_ec_combine(void) {
         secp256k1_ge_set_gej(&Q, &Qj);
         secp256k1_pubkey_save(&sd, &Q);
         CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1);
-        CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0);
+        CHECK(secp256k1_memcmp_var(&sd, &sd2, sizeof(sd)) == 0);
     }
 }
 
@@ -2614,7 +2608,6 @@ void test_point_times_order(const secp256k1_gej *point) {
     secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
     secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
     CHECK(secp256k1_gej_is_infinity(&res1));
-    CHECK(secp256k1_gej_is_valid_var(&res1) == 0);
     secp256k1_ge_set_gej(&res3, &res1);
     CHECK(secp256k1_ge_is_infinity(&res3));
     CHECK(secp256k1_ge_is_valid_var(&res3) == 0);
@@ -2633,6 +2626,87 @@ void test_point_times_order(const secp256k1_gej *point) {
     ge_equals_ge(&res3, &secp256k1_ge_const_g);
 }
 
+/* These scalars reach large (in absolute value) outputs when fed to secp256k1_scalar_split_lambda.
+ *
+ * They are computed as:
+ * - For a in [-2, -1, 0, 1, 2]:
+ *   - For b in [-3, -1, 1, 3]:
+ *     - Output (a*LAMBDA + (ORDER+b)/2) % ORDER
+ */
+static const secp256k1_scalar scalars_near_split_bounds[20] = {
+    SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fc),
+    SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fd),
+    SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6fe),
+    SECP256K1_SCALAR_CONST(0xd938a566, 0x7f479e3e, 0xb5b3c7fa, 0xefdb3749, 0x3aa0585c, 0xc5ea2367, 0xe1b660db, 0x0209e6ff),
+    SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632d),
+    SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632e),
+    SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf7632f),
+    SECP256K1_SCALAR_CONST(0x2c9c52b3, 0x3fa3cf1f, 0x5ad9e3fd, 0x77ed9ba5, 0xb294b893, 0x3722e9a5, 0x00e698ca, 0x4cf76330),
+    SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b209f),
+    SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a0),
+    SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a1),
+    SECP256K1_SCALAR_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xd576e735, 0x57a4501d, 0xdfe92f46, 0x681b20a2),
+    SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede11),
+    SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede12),
+    SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede13),
+    SECP256K1_SCALAR_CONST(0xd363ad4c, 0xc05c30e0, 0xa5261c02, 0x88126459, 0xf85915d7, 0x7825b696, 0xbeebc5c2, 0x833ede14),
+    SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a42),
+    SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a43),
+    SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a44),
+    SECP256K1_SCALAR_CONST(0x26c75a99, 0x80b861c1, 0x4a4c3805, 0x1024c8b4, 0x704d760e, 0xe95e7cd3, 0xde1bfdb1, 0xce2c5a45)
+};
+
+void test_ecmult_target(const secp256k1_scalar* target, int mode) {
+    /* Mode: 0=ecmult_gen, 1=ecmult, 2=ecmult_const */
+    secp256k1_scalar n1, n2;
+    secp256k1_ge p;
+    secp256k1_gej pj, p1j, p2j, ptj;
+    static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
+
+    /* Generate random n1,n2 such that n1+n2 = -target. */
+    random_scalar_order_test(&n1);
+    secp256k1_scalar_add(&n2, &n1, target);
+    secp256k1_scalar_negate(&n2, &n2);
+
+    /* Generate a random input point. */
+    if (mode != 0) {
+        random_group_element_test(&p);
+        secp256k1_gej_set_ge(&pj, &p);
+    }
+
+    /* EC multiplications */
+    if (mode == 0) {
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &p1j, &n1);
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &p2j, &n2);
+        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &ptj, target);
+    } else if (mode == 1) {
+        secp256k1_ecmult(&ctx->ecmult_ctx, &p1j, &pj, &n1, &zero);
+        secp256k1_ecmult(&ctx->ecmult_ctx, &p2j, &pj, &n2, &zero);
+        secp256k1_ecmult(&ctx->ecmult_ctx, &ptj, &pj, target, &zero);
+    } else {
+        secp256k1_ecmult_const(&p1j, &p, &n1, 256);
+        secp256k1_ecmult_const(&p2j, &p, &n2, 256);
+        secp256k1_ecmult_const(&ptj, &p, target, 256);
+    }
+
+    /* Add them all up: n1*P + n2*P + target*P = (n1+n2+target)*P = (n1+n1-n1-n2)*P = 0. */
+    secp256k1_gej_add_var(&ptj, &ptj, &p1j, NULL);
+    secp256k1_gej_add_var(&ptj, &ptj, &p2j, NULL);
+    CHECK(secp256k1_gej_is_infinity(&ptj));
+}
+
+void run_ecmult_near_split_bound(void) {
+    int i;
+    unsigned j;
+    for (i = 0; i < 4*count; ++i) {
+        for (j = 0; j < sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]); ++j) {
+            test_ecmult_target(&scalars_near_split_bounds[j], 0);
+            test_ecmult_target(&scalars_near_split_bounds[j], 1);
+            test_ecmult_target(&scalars_near_split_bounds[j], 2);
+        }
+    }
+}
+
 void run_point_times_order(void) {
     int i;
     secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
@@ -2646,7 +2720,6 @@ void run_point_times_order(void) {
             secp256k1_gej j;
             CHECK(secp256k1_ge_is_valid_var(&p));
             secp256k1_gej_set_ge(&j, &p);
-            CHECK(secp256k1_gej_is_valid_var(&j));
             test_point_times_order(&j);
         }
         secp256k1_fe_sqr(&x, &x);
@@ -3042,12 +3115,10 @@ void test_secp256k1_pippenger_bucket_window_inv(void) {
 
     CHECK(secp256k1_pippenger_bucket_window_inv(0) == 0);
     for(i = 1; i <= PIPPENGER_MAX_BUCKET_WINDOW; i++) {
-#ifdef USE_ENDOMORPHISM
         /* Bucket_window of 8 is not used with endo */
         if (i == 8) {
             continue;
         }
-#endif
         CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)) == i);
         if (i != PIPPENGER_MAX_BUCKET_WINDOW) {
             CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)+1) > i);
@@ -3060,7 +3131,7 @@ void test_secp256k1_pippenger_bucket_window_inv(void) {
  * for a given scratch space.
  */
 void test_ecmult_multi_pippenger_max_points(void) {
-    size_t scratch_size = secp256k1_rand_int(256);
+    size_t scratch_size = secp256k1_testrand_int(256);
     size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12);
     secp256k1_scratch *scratch;
     size_t n_points_supported;
@@ -3290,13 +3361,10 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) {
 
     secp256k1_scalar_set_int(&x, 0);
     secp256k1_scalar_set_int(&shift, 1 << w);
-    /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
-#ifdef USE_ENDOMORPHISM
     for (i = 0; i < 16; ++i) {
         secp256k1_scalar_shr_int(&num, 8);
     }
     bits = 128;
-#endif
     skew = secp256k1_wnaf_const(wnaf, &num, w, bits);
 
     for (i = WNAF_SIZE_BITS(bits, w); i >= 0; --i) {
@@ -3331,12 +3399,9 @@ void test_fixed_wnaf(const secp256k1_scalar *number, int w) {
 
     secp256k1_scalar_set_int(&x, 0);
     secp256k1_scalar_set_int(&shift, 1 << w);
-    /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
-#ifdef USE_ENDOMORPHISM
     for (i = 0; i < 16; ++i) {
         secp256k1_scalar_shr_int(&num, 8);
     }
-#endif
     skew = secp256k1_wnaf_fixed(wnaf, &num, w);
 
     for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
@@ -3520,7 +3585,7 @@ void test_ecmult_gen_blind(void) {
     secp256k1_ge pge;
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key);
-    secp256k1_rand256(seed32);
+    secp256k1_testrand256(seed32);
     b = ctx->ecmult_gen_ctx.blind;
     i = ctx->ecmult_gen_ctx.initial;
     secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
@@ -3552,16 +3617,18 @@ void run_ecmult_gen_blind(void) {
     }
 }
 
-#ifdef USE_ENDOMORPHISM
 /***** ENDOMORPHISH TESTS *****/
-void test_scalar_split(void) {
-    secp256k1_scalar full;
-    secp256k1_scalar s1, slam;
+void test_scalar_split(const secp256k1_scalar* full) {
+    secp256k1_scalar s, s1, slam;
     const unsigned char zero[32] = {0};
     unsigned char tmp[32];
 
-    random_scalar_order_test(&full);
-    secp256k1_scalar_split_lambda(&s1, &slam, &full);
+    secp256k1_scalar_split_lambda(&s1, &slam, full);
+
+    /* check slam*lambda + s1 == full */
+    secp256k1_scalar_mul(&s, &secp256k1_const_lambda, &slam);
+    secp256k1_scalar_add(&s, &s, &s1);
+    CHECK(secp256k1_scalar_eq(&s, full));
 
     /* check that both are <= 128 bits in size */
     if (secp256k1_scalar_is_high(&s1)) {
@@ -3572,15 +3639,32 @@ void test_scalar_split(void) {
     }
 
     secp256k1_scalar_get_b32(tmp, &s1);
-    CHECK(memcmp(zero, tmp, 16) == 0);
+    CHECK(secp256k1_memcmp_var(zero, tmp, 16) == 0);
     secp256k1_scalar_get_b32(tmp, &slam);
-    CHECK(memcmp(zero, tmp, 16) == 0);
+    CHECK(secp256k1_memcmp_var(zero, tmp, 16) == 0);
 }
 
+
 void run_endomorphism_tests(void) {
-    test_scalar_split();
+    unsigned i;
+    static secp256k1_scalar s;
+    test_scalar_split(&secp256k1_scalar_zero);
+    test_scalar_split(&secp256k1_scalar_one);
+    secp256k1_scalar_negate(&s,&secp256k1_scalar_one);
+    test_scalar_split(&s);
+    test_scalar_split(&secp256k1_const_lambda);
+    secp256k1_scalar_add(&s, &secp256k1_const_lambda, &secp256k1_scalar_one);
+    test_scalar_split(&s);
+
+    for (i = 0; i < 100U * count; ++i) {
+        secp256k1_scalar full;
+        random_scalar_order_test(&full);
+        test_scalar_split(&full);
+    }
+    for (i = 0; i < sizeof(scalars_near_split_bounds) / sizeof(scalars_near_split_bounds[0]); ++i) {
+        test_scalar_split(&scalars_near_split_bounds[i]);
+    }
 }
-#endif
 
 void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) {
     unsigned char pubkeyc[65];
@@ -3622,7 +3706,7 @@ void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvali
                 CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
                 VG_CHECK(pubkeyo, outl);
                 CHECK(outl == 33);
-                CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0);
+                CHECK(secp256k1_memcmp_var(&pubkeyo[1], &pubkeyc[1], 32) == 0);
                 CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
                 if (ypass) {
                     /* This test isn't always done because we decode with alternative signs, so the y won't match. */
@@ -3638,7 +3722,7 @@ void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvali
                     VG_CHECK(pubkeyo, outl);
                     CHECK(outl == 65);
                     CHECK(pubkeyo[0] == 4);
-                    CHECK(memcmp(&pubkeyo[1], input, 64) == 0);
+                    CHECK(secp256k1_memcmp_var(&pubkeyo[1], input, 64) == 0);
                 }
                 CHECK(ecount == 0);
             } else {
@@ -4007,7 +4091,7 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* Maximum value is too large, reject. */
     memset(ctmp, 255, 32);
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
@@ -4015,7 +4099,7 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* Zero is too small, reject. */
     memset(ctmp, 0, 32);
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
@@ -4023,7 +4107,7 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* One must be accepted. */
     ctmp[31] = 0x01;
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
@@ -4031,7 +4115,7 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
     VG_CHECK(&pubkey, sizeof(pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     pubkey_one = pubkey;
     /* Group order + 1 is too large, reject. */
     memcpy(ctmp, orderc, 32);
@@ -4041,7 +4125,7 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
     VG_CHECK(&pubkey, sizeof(pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* -1 must be accepted. */
     ctmp[31] = 0x40;
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
@@ -4049,20 +4133,20 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
     VG_CHECK(&pubkey, sizeof(pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     pubkey_negone = pubkey;
     /* Tweak of zero leaves the value unchanged. */
     memset(ctmp2, 0, 32);
     CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, ctmp2) == 1);
-    CHECK(memcmp(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
+    CHECK(secp256k1_memcmp_var(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
     memcpy(&pubkey2, &pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
-    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     /* Multiply tweak of zero zeroizes the output. */
     CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, ctmp2) == 0);
-    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0);
-    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     /* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing
     seckey, the seckey is zeroized. */
@@ -4072,29 +4156,29 @@ void run_eckey_edge_case_test(void) {
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp2) == 1);
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
     CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, ctmp2) == 0);
-    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
     memcpy(ctmp, orderc, 32);
     CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, ctmp2) == 0);
-    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
     /* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing
     tweak, the seckey is zeroized. */
     memcpy(ctmp, orderc, 32);
     ctmp[31] = 0x40;
     CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, orderc) == 0);
-    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
     memcpy(ctmp, orderc, 32);
     ctmp[31] = 0x40;
     CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, orderc) == 0);
-    CHECK(memcmp(zeros, ctmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(zeros, ctmp, 32) == 0);
     memcpy(ctmp, orderc, 32);
     ctmp[31] = 0x40;
     /* If pubkey_tweak_add or pubkey_tweak_mul are called with an overflowing
     tweak, the pubkey is zeroized. */
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0);
-    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0);
-    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     /* If the resulting key in secp256k1_ec_seckey_tweak_add and
      * secp256k1_ec_pubkey_tweak_add is 0 the functions fail and in the latter
@@ -4104,25 +4188,25 @@ void run_eckey_edge_case_test(void) {
     memset(ctmp2, 0, 32);
     ctmp2[31] = 1;
     CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp2, ctmp) == 0);
-    CHECK(memcmp(zeros, ctmp2, 32) == 0);
+    CHECK(secp256k1_memcmp_var(zeros, ctmp2, 32) == 0);
     ctmp2[31] = 1;
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
-    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     /* Tweak computation wraps and results in a key of 1. */
     ctmp2[31] = 2;
     CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp2, ctmp) == 1);
-    CHECK(memcmp(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
+    CHECK(secp256k1_memcmp_var(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
     ctmp2[31] = 2;
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
     ctmp2[31] = 1;
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1);
-    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     /* Tweak mul * 2 = 1+1. */
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
     ctmp2[31] = 2;
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1);
-    CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     /* Test argument errors. */
     ecount = 0;
     secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
@@ -4131,12 +4215,12 @@ void run_eckey_edge_case_test(void) {
     memset(&pubkey, 0, 32);
     CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
     CHECK(ecount == 1);
-    CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(pubkey)) == 0);
     memcpy(&pubkey, &pubkey2, sizeof(pubkey));
     memset(&pubkey2, 0, 32);
     CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0);
     CHECK(ecount == 2);
-    CHECK(memcmp(&pubkey2, zeros, sizeof(pubkey2)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey2, zeros, sizeof(pubkey2)) == 0);
     /* Plain argument errors. */
     ecount = 0;
     CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
@@ -4176,7 +4260,7 @@ void run_eckey_edge_case_test(void) {
     memset(&pubkey, 1, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
     CHECK(ecount == 2);
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     /* secp256k1_ec_pubkey_combine tests. */
     ecount = 0;
     pubkeys[0] = &pubkey_one;
@@ -4187,28 +4271,28 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     CHECK(ecount == 1);
     CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0);
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     CHECK(ecount == 2);
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     CHECK(ecount == 3);
     pubkeys[0] = &pubkey_negone;
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     CHECK(ecount == 3);
     len = 33;
     CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
     CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1);
-    CHECK(memcmp(ctmp, ctmp2, 33) == 0);
+    CHECK(secp256k1_memcmp_var(ctmp, ctmp2, 33) == 0);
     /* Result is infinity. */
     pubkeys[0] = &pubkey_one;
     pubkeys[1] = &pubkey_negone;
@@ -4216,7 +4300,7 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
     CHECK(ecount == 3);
     /* Passes through infinity but comes out one. */
     pubkeys[2] = &pubkey_one;
@@ -4224,19 +4308,19 @@ void run_eckey_edge_case_test(void) {
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     CHECK(ecount == 3);
     len = 33;
     CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
     CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1);
-    CHECK(memcmp(ctmp, ctmp2, 33) == 0);
+    CHECK(secp256k1_memcmp_var(ctmp, ctmp2, 33) == 0);
     /* Adds to two. */
     pubkeys[1] = &pubkey_one;
     memset(&pubkey, 255, sizeof(secp256k1_pubkey));
     VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
     CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1);
     VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
-    CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
+    CHECK(secp256k1_memcmp_var(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
     CHECK(ecount == 3);
     secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
 }
@@ -4250,21 +4334,21 @@ void run_eckey_negate_test(void) {
 
     /* Verify negation changes the key and changes it back */
     CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1);
-    CHECK(memcmp(seckey, seckey_tmp, 32) != 0);
+    CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) != 0);
     CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1);
-    CHECK(memcmp(seckey, seckey_tmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0);
 
     /* Check that privkey alias gives same result */
     CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1);
     CHECK(secp256k1_ec_privkey_negate(ctx, seckey_tmp) == 1);
-    CHECK(memcmp(seckey, seckey_tmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0);
 
     /* Negating all 0s fails */
     memset(seckey, 0, 32);
     memset(seckey_tmp, 0, 32);
     CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 0);
     /* Check that seckey is not modified */
-    CHECK(memcmp(seckey, seckey_tmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0);
 
     /* Negating an overflowing seckey fails and the seckey is zeroed. In this
      * test, the seckey has 16 random bytes to ensure that ec_seckey_negate
@@ -4273,7 +4357,7 @@ void run_eckey_negate_test(void) {
     memset(seckey, 0xFF, 16);
     memset(seckey_tmp, 0, 32);
     CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 0);
-    CHECK(memcmp(seckey, seckey_tmp, 32) == 0);
+    CHECK(secp256k1_memcmp_var(seckey, seckey_tmp, 32) == 0);
 }
 
 void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
@@ -4295,7 +4379,7 @@ void test_ecdsa_sign_verify(void) {
     random_scalar_order_test(&key);
     secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
     secp256k1_ge_set_gej(&pub, &pubj);
-    getrec = secp256k1_rand_bits(1);
+    getrec = secp256k1_testrand_bits(1);
     random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL);
     if (getrec) {
         CHECK(recid >= 0 && recid < 4);
@@ -4362,7 +4446,7 @@ static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char
 
 int is_empty_signature(const secp256k1_ecdsa_signature *sig) {
     static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0};
-    return memcmp(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
+    return secp256k1_memcmp_var(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
 }
 
 void test_ecdsa_end_to_end(void) {
@@ -4395,31 +4479,31 @@ void test_ecdsa_end_to_end(void) {
     CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
 
     /* Verify exporting and importing public key. */
-    CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_rand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
+    CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_testrand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
     memset(&pubkey, 0, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
 
     /* Verify negation changes the key and changes it back */
     memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey));
     CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
-    CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0);
+    CHECK(secp256k1_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0);
     CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1);
-    CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0);
+    CHECK(secp256k1_memcmp_var(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0);
 
     /* Verify private key import and export. */
-    CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1));
+    CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_testrand_bits(1) == 1));
     CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1);
-    CHECK(memcmp(privkey, privkey2, 32) == 0);
+    CHECK(secp256k1_memcmp_var(privkey, privkey2, 32) == 0);
 
     /* Optionally tweak the keys using addition. */
-    if (secp256k1_rand_int(3) == 0) {
+    if (secp256k1_testrand_int(3) == 0) {
         int ret1;
         int ret2;
         int ret3;
         unsigned char rnd[32];
         unsigned char privkey_tmp[32];
         secp256k1_pubkey pubkey2;
-        secp256k1_rand256_test(rnd);
+        secp256k1_testrand256_test(rnd);
         memcpy(privkey_tmp, privkey, 32);
         ret1 = secp256k1_ec_seckey_tweak_add(ctx, privkey, rnd);
         ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd);
@@ -4430,20 +4514,20 @@ void test_ecdsa_end_to_end(void) {
         if (ret1 == 0) {
             return;
         }
-        CHECK(memcmp(privkey, privkey_tmp, 32) == 0);
+        CHECK(secp256k1_memcmp_var(privkey, privkey_tmp, 32) == 0);
         CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
-        CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+        CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     }
 
     /* Optionally tweak the keys using multiplication. */
-    if (secp256k1_rand_int(3) == 0) {
+    if (secp256k1_testrand_int(3) == 0) {
         int ret1;
         int ret2;
         int ret3;
         unsigned char rnd[32];
         unsigned char privkey_tmp[32];
         secp256k1_pubkey pubkey2;
-        secp256k1_rand256_test(rnd);
+        secp256k1_testrand256_test(rnd);
         memcpy(privkey_tmp, privkey, 32);
         ret1 = secp256k1_ec_seckey_tweak_mul(ctx, privkey, rnd);
         ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd);
@@ -4454,9 +4538,9 @@ void test_ecdsa_end_to_end(void) {
         if (ret1 == 0) {
             return;
         }
-        CHECK(memcmp(privkey, privkey_tmp, 32) == 0);
+        CHECK(secp256k1_memcmp_var(privkey, privkey_tmp, 32) == 0);
         CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
-        CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
+        CHECK(secp256k1_memcmp_var(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
     }
 
     /* Sign. */
@@ -4468,13 +4552,13 @@ void test_ecdsa_end_to_end(void) {
     extra[31] = 0;
     extra[0] = 1;
     CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1);
-    CHECK(memcmp(&signature[0], &signature[4], sizeof(signature[0])) == 0);
-    CHECK(memcmp(&signature[0], &signature[1], sizeof(signature[0])) != 0);
-    CHECK(memcmp(&signature[0], &signature[2], sizeof(signature[0])) != 0);
-    CHECK(memcmp(&signature[0], &signature[3], sizeof(signature[0])) != 0);
-    CHECK(memcmp(&signature[1], &signature[2], sizeof(signature[0])) != 0);
-    CHECK(memcmp(&signature[1], &signature[3], sizeof(signature[0])) != 0);
-    CHECK(memcmp(&signature[2], &signature[3], sizeof(signature[0])) != 0);
+    CHECK(secp256k1_memcmp_var(&signature[0], &signature[4], sizeof(signature[0])) == 0);
+    CHECK(secp256k1_memcmp_var(&signature[0], &signature[1], sizeof(signature[0])) != 0);
+    CHECK(secp256k1_memcmp_var(&signature[0], &signature[2], sizeof(signature[0])) != 0);
+    CHECK(secp256k1_memcmp_var(&signature[0], &signature[3], sizeof(signature[0])) != 0);
+    CHECK(secp256k1_memcmp_var(&signature[1], &signature[2], sizeof(signature[0])) != 0);
+    CHECK(secp256k1_memcmp_var(&signature[1], &signature[3], sizeof(signature[0])) != 0);
+    CHECK(secp256k1_memcmp_var(&signature[2], &signature[3], sizeof(signature[0])) != 0);
     /* Verify. */
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1);
@@ -4495,7 +4579,7 @@ void test_ecdsa_end_to_end(void) {
     secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
     CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
     CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
-    CHECK(memcmp(&signature[5], &signature[0], 64) == 0);
+    CHECK(secp256k1_memcmp_var(&signature[5], &signature[0], 64) == 0);
 
     /* Serialize/parse DER and verify again */
     CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
@@ -4505,7 +4589,7 @@ void test_ecdsa_end_to_end(void) {
     /* Serialize/destroy/parse DER and verify again. */
     siglen = 74;
     CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
-    sig[secp256k1_rand_int(siglen)] += 1 + secp256k1_rand_int(255);
+    sig[secp256k1_testrand_int(siglen)] += 1 + secp256k1_testrand_int(255);
     CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 ||
           secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0);
 }
@@ -4515,23 +4599,23 @@ void test_random_pubkeys(void) {
     secp256k1_ge elem2;
     unsigned char in[65];
     /* Generate some randomly sized pubkeys. */
-    size_t len = secp256k1_rand_bits(2) == 0 ? 65 : 33;
-    if (secp256k1_rand_bits(2) == 0) {
-        len = secp256k1_rand_bits(6);
+    size_t len = secp256k1_testrand_bits(2) == 0 ? 65 : 33;
+    if (secp256k1_testrand_bits(2) == 0) {
+        len = secp256k1_testrand_bits(6);
     }
     if (len == 65) {
-      in[0] = secp256k1_rand_bits(1) ? 4 : (secp256k1_rand_bits(1) ? 6 : 7);
+      in[0] = secp256k1_testrand_bits(1) ? 4 : (secp256k1_testrand_bits(1) ? 6 : 7);
     } else {
-      in[0] = secp256k1_rand_bits(1) ? 2 : 3;
+      in[0] = secp256k1_testrand_bits(1) ? 2 : 3;
     }
-    if (secp256k1_rand_bits(3) == 0) {
-        in[0] = secp256k1_rand_bits(8);
+    if (secp256k1_testrand_bits(3) == 0) {
+        in[0] = secp256k1_testrand_bits(8);
     }
     if (len > 1) {
-        secp256k1_rand256(&in[1]);
+        secp256k1_testrand256(&in[1]);
     }
     if (len > 33) {
-        secp256k1_rand256(&in[33]);
+        secp256k1_testrand256(&in[33]);
     }
     if (secp256k1_eckey_pubkey_parse(&elem, in, len)) {
         unsigned char out[65];
@@ -4542,7 +4626,7 @@ void test_random_pubkeys(void) {
         /* If the pubkey can be parsed, it should round-trip... */
         CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33));
         CHECK(size == len);
-        CHECK(memcmp(&in[1], &out[1], len-1) == 0);
+        CHECK(secp256k1_memcmp_var(&in[1], &out[1], len-1) == 0);
         /* ... except for the type of hybrid inputs. */
         if ((in[0] != 6) && (in[0] != 7)) {
             CHECK(in[0] == out[0]);
@@ -4553,7 +4637,7 @@ void test_random_pubkeys(void) {
         CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size));
         ge_equals_ge(&elem,&elem2);
         /* Check that the X9.62 hybrid type is checked. */
-        in[0] = secp256k1_rand_bits(1) ? 6 : 7;
+        in[0] = secp256k1_testrand_bits(1) ? 6 : 7;
         res = secp256k1_eckey_pubkey_parse(&elem2, in, size);
         if (firstb == 2 || firstb == 3) {
             if (in[0] == firstb + 4) {
@@ -4565,7 +4649,7 @@ void test_random_pubkeys(void) {
         if (res) {
             ge_equals_ge(&elem,&elem2);
             CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0));
-            CHECK(memcmp(&in[1], &out[1], 64) == 0);
+            CHECK(secp256k1_memcmp_var(&in[1], &out[1], 64) == 0);
         }
     }
 }
@@ -4621,21 +4705,21 @@ int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_
     parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen);
     if (parsed_der) {
         ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0;
-        valid_der = (memcmp(compact_der, zeroes, 32) != 0) && (memcmp(compact_der + 32, zeroes, 32) != 0);
+        valid_der = (secp256k1_memcmp_var(compact_der, zeroes, 32) != 0) && (secp256k1_memcmp_var(compact_der + 32, zeroes, 32) != 0);
     }
     if (valid_der) {
         ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1;
-        roundtrips_der = (len_der == siglen) && memcmp(roundtrip_der, sig, siglen) == 0;
+        roundtrips_der = (len_der == siglen) && secp256k1_memcmp_var(roundtrip_der, sig, siglen) == 0;
     }
 
     parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen);
     if (parsed_der_lax) {
         ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10;
-        valid_der_lax = (memcmp(compact_der_lax, zeroes, 32) != 0) && (memcmp(compact_der_lax + 32, zeroes, 32) != 0);
+        valid_der_lax = (secp256k1_memcmp_var(compact_der_lax, zeroes, 32) != 0) && (secp256k1_memcmp_var(compact_der_lax + 32, zeroes, 32) != 0);
     }
     if (valid_der_lax) {
         ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11;
-        roundtrips_der_lax = (len_der_lax == siglen) && memcmp(roundtrip_der_lax, sig, siglen) == 0;
+        roundtrips_der_lax = (len_der_lax == siglen) && secp256k1_memcmp_var(roundtrip_der_lax, sig, siglen) == 0;
     }
 
     if (certainly_der) {
@@ -4651,7 +4735,7 @@ int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_
     if (valid_der) {
         ret |= (!roundtrips_der_lax) << 12;
         ret |= (len_der != len_der_lax) << 13;
-        ret |= ((len_der != len_der_lax) || (memcmp(roundtrip_der_lax, roundtrip_der, len_der) != 0)) << 14;
+        ret |= ((len_der != len_der_lax) || (secp256k1_memcmp_var(roundtrip_der_lax, roundtrip_der, len_der) != 0)) << 14;
     }
     ret |= (roundtrips_der != roundtrips_der_lax) << 15;
     if (parsed_der) {
@@ -4668,19 +4752,19 @@ int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_
         if (valid_openssl) {
             unsigned char tmp[32] = {0};
             BN_bn2bin(r, tmp + 32 - BN_num_bytes(r));
-            valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
+            valid_openssl = secp256k1_memcmp_var(tmp, max_scalar, 32) < 0;
         }
         if (valid_openssl) {
             unsigned char tmp[32] = {0};
             BN_bn2bin(s, tmp + 32 - BN_num_bytes(s));
-            valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
+            valid_openssl = secp256k1_memcmp_var(tmp, max_scalar, 32) < 0;
         }
     }
     len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL);
     if (len_openssl <= 2048) {
         unsigned char *ptr = roundtrip_openssl;
         CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl);
-        roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (memcmp(roundtrip_openssl, sig, siglen) == 0);
+        roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (secp256k1_memcmp_var(roundtrip_openssl, sig, siglen) == 0);
     } else {
         len_openssl = 0;
     }
@@ -4692,7 +4776,7 @@ int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_
     ret |= (roundtrips_der != roundtrips_openssl) << 7;
     if (roundtrips_openssl) {
         ret |= (len_der != (size_t)len_openssl) << 8;
-        ret |= ((len_der != (size_t)len_openssl) || (memcmp(roundtrip_der, roundtrip_openssl, len_der) != 0)) << 9;
+        ret |= ((len_der != (size_t)len_openssl) || (secp256k1_memcmp_var(roundtrip_der, roundtrip_openssl, len_der) != 0)) << 9;
     }
 #endif
     return ret;
@@ -4712,27 +4796,27 @@ 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);
+    int action = secp256k1_testrand_bits(3);
     if (action < 1 && *len > 3) {
         /* Delete a byte. */
-        pos = secp256k1_rand_int(*len);
+        pos = secp256k1_testrand_int(*len);
         memmove(sig + pos, sig + pos + 1, *len - pos - 1);
         (*len)--;
         return;
     } else if (action < 2 && *len < 2048) {
         /* Insert a byte. */
-        pos = secp256k1_rand_int(1 + *len);
+        pos = secp256k1_testrand_int(1 + *len);
         memmove(sig + pos + 1, sig + pos, *len - pos);
-        sig[pos] = secp256k1_rand_bits(8);
+        sig[pos] = secp256k1_testrand_bits(8);
         (*len)++;
         return;
     } else if (action < 4) {
         /* Modify a byte. */
-        sig[secp256k1_rand_int(*len)] += 1 + secp256k1_rand_int(255);
+        sig[secp256k1_testrand_int(*len)] += 1 + secp256k1_testrand_int(255);
         return;
     } else { /* action < 8 */
         /* Modify a bit. */
-        sig[secp256k1_rand_int(*len)] ^= 1 << secp256k1_rand_bits(3);
+        sig[secp256k1_testrand_int(*len)] ^= 1 << secp256k1_testrand_bits(3);
         return;
     }
 }
@@ -4745,23 +4829,23 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
     int n;
 
     *len = 0;
-    der = secp256k1_rand_bits(2) == 0;
+    der = secp256k1_testrand_bits(2) == 0;
     *certainly_der = der;
     *certainly_not_der = 0;
-    indet = der ? 0 : secp256k1_rand_int(10) == 0;
+    indet = der ? 0 : secp256k1_testrand_int(10) == 0;
 
     for (n = 0; n < 2; n++) {
         /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
-        nlow[n] = der ? 1 : (secp256k1_rand_bits(3) != 0);
+        nlow[n] = der ? 1 : (secp256k1_testrand_bits(3) != 0);
         /* The length of the number in bytes (the first byte of which will always be nonzero) */
-        nlen[n] = nlow[n] ? secp256k1_rand_int(33) : 32 + secp256k1_rand_int(200) * secp256k1_rand_int(8) / 8;
+        nlen[n] = nlow[n] ? secp256k1_testrand_int(33) : 32 + secp256k1_testrand_int(200) * secp256k1_testrand_int(8) / 8;
         CHECK(nlen[n] <= 232);
         /* The top bit of the number. */
-        nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_rand_bits(1));
+        nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_testrand_bits(1));
         /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
-        nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_rand_bits(7) : 1 + secp256k1_rand_int(127));
+        nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_testrand_bits(7) : 1 + secp256k1_testrand_int(127));
         /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
-        nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_rand_int(3) : secp256k1_rand_int(300 - nlen[n]) * secp256k1_rand_int(8) / 8);
+        nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_testrand_int(3) : secp256k1_testrand_int(300 - nlen[n]) * secp256k1_testrand_int(8) / 8);
         if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
             *certainly_not_der = 1;
         }
@@ -4770,7 +4854,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
         nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
         if (!der) {
             /* nlenlen[n] max 127 bytes */
-            int add = secp256k1_rand_int(127 - nlenlen[n]) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
+            int add = secp256k1_testrand_int(127 - nlenlen[n]) * secp256k1_testrand_int(16) * secp256k1_testrand_int(16) / 256;
             nlenlen[n] += add;
             if (add != 0) {
                 *certainly_not_der = 1;
@@ -4784,7 +4868,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
     CHECK(tlen <= 856);
 
     /* The length of the garbage inside the tuple. */
-    elen = (der || indet) ? 0 : secp256k1_rand_int(980 - tlen) * secp256k1_rand_int(8) / 8;
+    elen = (der || indet) ? 0 : secp256k1_testrand_int(980 - tlen) * secp256k1_testrand_int(8) / 8;
     if (elen != 0) {
         *certainly_not_der = 1;
     }
@@ -4792,7 +4876,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
     CHECK(tlen <= 980);
 
     /* The length of the garbage after the end of the tuple. */
-    glen = der ? 0 : secp256k1_rand_int(990 - tlen) * secp256k1_rand_int(8) / 8;
+    glen = der ? 0 : secp256k1_testrand_int(990 - tlen) * secp256k1_testrand_int(8) / 8;
     if (glen != 0) {
         *certainly_not_der = 1;
     }
@@ -4807,7 +4891,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
     } else {
         int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
         if (!der) {
-            int add = secp256k1_rand_int(127 - tlenlen) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
+            int add = secp256k1_testrand_int(127 - tlenlen) * secp256k1_testrand_int(16) * secp256k1_testrand_int(16) / 256;
             tlenlen += add;
             if (add != 0) {
                 *certainly_not_der = 1;
@@ -4858,13 +4942,13 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
             nlen[n]--;
         }
         /* Generate remaining random bytes of number */
-        secp256k1_rand_bytes_test(sig + *len, nlen[n]);
+        secp256k1_testrand_bytes_test(sig + *len, nlen[n]);
         *len += nlen[n];
         nlen[n] = 0;
     }
 
     /* Generate random garbage inside tuple. */
-    secp256k1_rand_bytes_test(sig + *len, elen);
+    secp256k1_testrand_bytes_test(sig + *len, elen);
     *len += elen;
 
     /* Generate end-of-contents bytes. */
@@ -4876,7 +4960,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly
     CHECK(tlen + glen <= 1121);
 
     /* Generate random garbage outside tuple. */
-    secp256k1_rand_bytes_test(sig + *len, glen);
+    secp256k1_testrand_bytes_test(sig + *len, glen);
     *len += glen;
     tlen += glen;
     CHECK(tlen <= 1121);
@@ -5208,11 +5292,11 @@ void test_ecdsa_edge_cases(void) {
         CHECK(!is_empty_signature(&sig));
         CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1);
         CHECK(!is_empty_signature(&sig2));
-        CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
+        CHECK(secp256k1_memcmp_var(&sig, &sig2, sizeof(sig)) == 0);
         /* The default nonce function is deterministic. */
         CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
         CHECK(!is_empty_signature(&sig2));
-        CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
+        CHECK(secp256k1_memcmp_var(&sig, &sig2, sizeof(sig)) == 0);
         /* The default nonce function changes output with different messages. */
         for(i = 0; i < 256; i++) {
             int j;
@@ -5259,12 +5343,12 @@ void test_ecdsa_edge_cases(void) {
         VG_CHECK(nonce3,32);
         CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1);
         VG_CHECK(nonce4,32);
-        CHECK(memcmp(nonce, nonce2, 32) != 0);
-        CHECK(memcmp(nonce, nonce3, 32) != 0);
-        CHECK(memcmp(nonce, nonce4, 32) != 0);
-        CHECK(memcmp(nonce2, nonce3, 32) != 0);
-        CHECK(memcmp(nonce2, nonce4, 32) != 0);
-        CHECK(memcmp(nonce3, nonce4, 32) != 0);
+        CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0);
+        CHECK(secp256k1_memcmp_var(nonce, nonce3, 32) != 0);
+        CHECK(secp256k1_memcmp_var(nonce, nonce4, 32) != 0);
+        CHECK(secp256k1_memcmp_var(nonce2, nonce3, 32) != 0);
+        CHECK(secp256k1_memcmp_var(nonce2, nonce4, 32) != 0);
+        CHECK(secp256k1_memcmp_var(nonce3, nonce4, 32) != 0);
     }
 
 
@@ -5293,7 +5377,7 @@ EC_KEY *get_openssl_key(const unsigned char *key32) {
     unsigned char privkey[300];
     size_t privkeylen;
     const unsigned char* pbegin = privkey;
-    int compr = secp256k1_rand_bits(1);
+    int compr = secp256k1_testrand_bits(1);
     EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1);
     CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr));
     CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen));
@@ -5314,7 +5398,7 @@ void test_ecdsa_openssl(void) {
     unsigned char message[32];
     unsigned char signature[80];
     unsigned char key32[32];
-    secp256k1_rand256_test(message);
+    secp256k1_testrand256_test(message);
     secp256k1_scalar_set_b32(&msg, message, NULL);
     random_scalar_order_test(&key);
     secp256k1_scalar_get_b32(key32, &key);
@@ -5367,12 +5451,12 @@ void run_memczero_test(void) {
     /* memczero(..., ..., 0) is a noop. */
     memcpy(buf2, buf1, sizeof(buf1));
     memczero(buf1, sizeof(buf1), 0);
-    CHECK(memcmp(buf1, buf2, sizeof(buf1)) == 0);
+    CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0);
 
     /* memczero(..., ..., 1) zeros the buffer. */
     memset(buf2, 0, sizeof(buf2));
     memczero(buf1, sizeof(buf1) , 1);
-    CHECK(memcmp(buf1, buf2, sizeof(buf1)) == 0);
+    CHECK(secp256k1_memcmp_var(buf1, buf2, sizeof(buf1)) == 0);
 }
 
 void int_cmov_test(void) {
@@ -5411,23 +5495,23 @@ void fe_cmov_test(void) {
     secp256k1_fe a = zero;
 
     secp256k1_fe_cmov(&r, &a, 0);
-    CHECK(memcmp(&r, &max, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
 
     r = zero; a = max;
     secp256k1_fe_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &max, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
 
     a = zero;
     secp256k1_fe_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &zero, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0);
 
     a = one;
     secp256k1_fe_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &one, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
 
     r = one; a = zero;
     secp256k1_fe_cmov(&r, &a, 0);
-    CHECK(memcmp(&r, &one, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
 }
 
 void fe_storage_cmov_test(void) {
@@ -5441,23 +5525,23 @@ void fe_storage_cmov_test(void) {
     secp256k1_fe_storage a = zero;
 
     secp256k1_fe_storage_cmov(&r, &a, 0);
-    CHECK(memcmp(&r, &max, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
 
     r = zero; a = max;
     secp256k1_fe_storage_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &max, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
 
     a = zero;
     secp256k1_fe_storage_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &zero, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0);
 
     a = one;
     secp256k1_fe_storage_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &one, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
 
     r = one; a = zero;
     secp256k1_fe_storage_cmov(&r, &a, 0);
-    CHECK(memcmp(&r, &one, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
 }
 
 void scalar_cmov_test(void) {
@@ -5471,23 +5555,23 @@ void scalar_cmov_test(void) {
     secp256k1_scalar a = zero;
 
     secp256k1_scalar_cmov(&r, &a, 0);
-    CHECK(memcmp(&r, &max, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
 
     r = zero; a = max;
     secp256k1_scalar_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &max, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
 
     a = zero;
     secp256k1_scalar_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &zero, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0);
 
     a = one;
     secp256k1_scalar_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &one, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
 
     r = one; a = zero;
     secp256k1_scalar_cmov(&r, &a, 0);
-    CHECK(memcmp(&r, &one, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
 }
 
 void ge_storage_cmov_test(void) {
@@ -5503,23 +5587,23 @@ void ge_storage_cmov_test(void) {
     secp256k1_ge_storage a = zero;
 
     secp256k1_ge_storage_cmov(&r, &a, 0);
-    CHECK(memcmp(&r, &max, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
 
     r = zero; a = max;
     secp256k1_ge_storage_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &max, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &max, sizeof(r)) == 0);
 
     a = zero;
     secp256k1_ge_storage_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &zero, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &zero, sizeof(r)) == 0);
 
     a = one;
     secp256k1_ge_storage_cmov(&r, &a, 1);
-    CHECK(memcmp(&r, &one, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
 
     r = one; a = zero;
     secp256k1_ge_storage_cmov(&r, &a, 0);
-    CHECK(memcmp(&r, &one, sizeof(r)) == 0);
+    CHECK(secp256k1_memcmp_var(&r, &one, sizeof(r)) == 0);
 }
 
 void run_cmov_tests(void) {
@@ -5531,9 +5615,6 @@ void run_cmov_tests(void) {
 }
 
 int main(int argc, char **argv) {
-    unsigned char seed16[16] = {0};
-    unsigned char run32[32] = {0};
-
     /* Disable buffering for stdout to improve reliability of getting
      * diagnostic information. Happens right at the start of main because
      * setbuf must be used before any other operation on the stream. */
@@ -5546,52 +5627,20 @@ int main(int argc, char **argv) {
     if (argc > 1) {
         count = strtol(argv[1], NULL, 0);
     }
+    printf("test count = %i\n", count);
 
     /* find random seed */
-    if (argc > 2) {
-        int pos = 0;
-        const char* ch = argv[2];
-        while (pos < 16 && ch[0] != 0 && ch[1] != 0) {
-            unsigned short sh;
-            if ((sscanf(ch, "%2hx", &sh)) == 1) {
-                seed16[pos] = sh;
-            } else {
-                break;
-            }
-            ch += 2;
-            pos++;
-        }
-    } else {
-        FILE *frand = fopen("/dev/urandom", "r");
-        if ((frand == NULL) || fread(&seed16, 1, sizeof(seed16), frand) != sizeof(seed16)) {
-            uint64_t t = time(NULL) * (uint64_t)1337;
-            fprintf(stderr, "WARNING: could not read 16 bytes from /dev/urandom; falling back to insecure PRNG\n");
-            seed16[0] ^= t;
-            seed16[1] ^= t >> 8;
-            seed16[2] ^= t >> 16;
-            seed16[3] ^= t >> 24;
-            seed16[4] ^= t >> 32;
-            seed16[5] ^= t >> 40;
-            seed16[6] ^= t >> 48;
-            seed16[7] ^= t >> 56;
-        }
-        if (frand) {
-            fclose(frand);
-        }
-    }
-    secp256k1_rand_seed(seed16);
-
-    printf("test count = %i\n", count);
-    printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]);
+    secp256k1_testrand_init(argc > 2 ? argv[2] : NULL);
 
     /* initialize */
     run_context_tests(0);
     run_context_tests(1);
     run_scratch_tests();
     ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
-    if (secp256k1_rand_bits(1)) {
-        secp256k1_rand256(run32);
-        CHECK(secp256k1_context_randomize(ctx, secp256k1_rand_bits(1) ? run32 : NULL));
+    if (secp256k1_testrand_bits(1)) {
+        unsigned char rand32[32];
+        secp256k1_testrand256(rand32);
+        CHECK(secp256k1_context_randomize(ctx, secp256k1_testrand_bits(1) ? rand32 : NULL));
     }
 
     run_rand_bits();
@@ -5625,6 +5674,7 @@ int main(int argc, char **argv) {
     /* ecmult tests */
     run_wnaf();
     run_point_times_order();
+    run_ecmult_near_split_bound();
     run_ecmult_chain();
     run_ecmult_constants();
     run_ecmult_gen_blind();
@@ -5633,9 +5683,7 @@ int main(int argc, char **argv) {
     run_ec_combine();
 
     /* endomorphism tests */
-#ifdef USE_ENDOMORPHISM
     run_endomorphism_tests();
-#endif
 
     /* EC point parser test */
     run_ec_pubkey_parse_test();
@@ -5679,8 +5727,7 @@ int main(int argc, char **argv) {
 
     run_cmov_tests();
 
-    secp256k1_rand256(run32);
-    printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]);
+    secp256k1_testrand_finish();
 
     /* shutdown */
     secp256k1_context_destroy(ctx);
diff --git a/src/secp256k1/src/tests_exhaustive.c b/src/secp256k1/src/tests_exhaustive.c
index 681ed80bd0..f4d5b8e176 100644
--- a/src/secp256k1/src/tests_exhaustive.c
+++ b/src/secp256k1/src/tests_exhaustive.c
@@ -18,7 +18,6 @@
 #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"
@@ -27,10 +26,7 @@
 #include "secp256k1.c"
 #include "testrand_impl.h"
 
-#ifdef ENABLE_MODULE_RECOVERY
-#include "src/modules/recovery/main_impl.h"
-#include "include/secp256k1_recovery.h"
-#endif
+static int count = 2;
 
 /** stolen from tests.c */
 void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
@@ -62,7 +58,7 @@ void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
 void random_fe(secp256k1_fe *x) {
     unsigned char bin[32];
     do {
-        secp256k1_rand256(bin);
+        secp256k1_testrand256(bin);
         if (secp256k1_fe_set_b32(x, bin)) {
             return;
         }
@@ -70,6 +66,15 @@ void random_fe(secp256k1_fe *x) {
 }
 /** END stolen from tests.c */
 
+static uint32_t num_cores = 1;
+static uint32_t this_core = 0;
+
+SECP256K1_INLINE static int skip_section(uint64_t* iter) {
+    if (num_cores == 1) return 0;
+    *iter += 0xe7037ed1a0b428dbULL;
+    return ((((uint32_t)*iter ^ (*iter >> 32)) * num_cores) >> 32) != this_core;
+}
+
 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) {
@@ -90,91 +95,93 @@ int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned cha
     return 1;
 }
 
-#ifdef USE_ENDOMORPHISM
-void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) {
+void test_exhaustive_endomorphism(const secp256k1_ge *group) {
     int i;
-    for (i = 0; i < order; i++) {
+    for (i = 0; i < EXHAUSTIVE_TEST_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) {
+void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj) {
     int i, j;
+    uint64_t iter = 0;
 
     /* 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++) {
+    for (i = 1; i < EXHAUSTIVE_TEST_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++) {
+    for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) {
         secp256k1_fe fe_inv;
+        if (skip_section(&iter)) continue;
         secp256k1_fe_inv(&fe_inv, &groupj[j].z);
-        for (i = 0; i < order; i++) {
+        for (i = 0; i < EXHAUSTIVE_TEST_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);
+            ge_equals_gej(&group[(i + j) % EXHAUSTIVE_TEST_ORDER], &tmp);
             /* add_ge */
             if (j > 0) {
                 secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]);
-                ge_equals_gej(&group[(i + j) % order], &tmp);
+                ge_equals_gej(&group[(i + j) % EXHAUSTIVE_TEST_ORDER], &tmp);
             }
             /* add_ge_var */
             secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL);
-            ge_equals_gej(&group[(i + j) % order], &tmp);
+            ge_equals_gej(&group[(i + j) % EXHAUSTIVE_TEST_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);
+            ge_equals_gej(&group[(i + j) % EXHAUSTIVE_TEST_ORDER], &tmp);
         }
     }
 
     /* Check doubling */
-    for (i = 0; i < order; i++) {
+    for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
         secp256k1_gej tmp;
         secp256k1_gej_double(&tmp, &groupj[i]);
-        ge_equals_gej(&group[(2 * i) % order], &tmp);
+        ge_equals_gej(&group[(2 * i) % EXHAUSTIVE_TEST_ORDER], &tmp);
         secp256k1_gej_double_var(&tmp, &groupj[i], NULL);
-        ge_equals_gej(&group[(2 * i) % order], &tmp);
+        ge_equals_gej(&group[(2 * i) % EXHAUSTIVE_TEST_ORDER], &tmp);
     }
 
     /* Check negation */
-    for (i = 1; i < order; i++) {
+    for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
         secp256k1_ge tmp;
         secp256k1_gej tmpj;
         secp256k1_ge_neg(&tmp, &group[i]);
-        ge_equals_ge(&group[order - i], &tmp);
+        ge_equals_ge(&group[EXHAUSTIVE_TEST_ORDER - i], &tmp);
         secp256k1_gej_neg(&tmpj, &groupj[i]);
-        ge_equals_gej(&group[order - i], &tmpj);
+        ge_equals_gej(&group[EXHAUSTIVE_TEST_ORDER - i], &tmpj);
     }
 }
 
-void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
+void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj) {
     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++) {
+    uint64_t iter = 0;
+    for (r_log = 1; r_log < EXHAUSTIVE_TEST_ORDER; r_log++) {
+        for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) {
+            if (skip_section(&iter)) continue;
+            for (i = 0; i < EXHAUSTIVE_TEST_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);
+                ge_equals_gej(&group[(i * r_log + j) % EXHAUSTIVE_TEST_ORDER], &tmp);
 
                 if (i > 0) {
                     secp256k1_ecmult_const(&tmp, &group[i], &ng, 256);
-                    ge_equals_gej(&group[(i * j) % order], &tmp);
+                    ge_equals_gej(&group[(i * j) % EXHAUSTIVE_TEST_ORDER], &tmp);
                 }
             }
         }
@@ -193,14 +200,16 @@ static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t
     return 1;
 }
 
-void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_ge *group) {
     int i, j, k, x, y;
+    uint64_t iter = 0;
     secp256k1_scratch *scratch = secp256k1_scratch_create(&ctx->error_callback, 4096);
-    for (i = 0; i < order; i++) {
-        for (j = 0; j < order; j++) {
-            for (k = 0; k < order; k++) {
-                for (x = 0; x < order; x++) {
-                    for (y = 0; y < order; y++) {
+    for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) {
+        for (j = 0; j < EXHAUSTIVE_TEST_ORDER; j++) {
+            for (k = 0; k < EXHAUSTIVE_TEST_ORDER; k++) {
+                for (x = 0; x < EXHAUSTIVE_TEST_ORDER; x++) {
+                    if (skip_section(&iter)) continue;
+                    for (y = 0; y < EXHAUSTIVE_TEST_ORDER; y++) {
                         secp256k1_gej tmp;
                         secp256k1_scalar g_sc;
                         ecmult_multi_data data;
@@ -212,7 +221,7 @@ void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_
                         data.pt[1] = group[y];
 
                         secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &tmp, &g_sc, ecmult_multi_callback, &data, 2);
-                        ge_equals_gej(&group[(i * x + j * y + k) % order], &tmp);
+                        ge_equals_gej(&group[(i * x + j * y + k) % EXHAUSTIVE_TEST_ORDER], &tmp);
                     }
                 }
             }
@@ -221,22 +230,23 @@ void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_
     secp256k1_scratch_destroy(&ctx->error_callback, scratch);
 }
 
-void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k) {
+void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k, int* overflow) {
     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);
+    secp256k1_scalar_set_b32(r, x_bin, overflow);
 }
 
-void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group) {
     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++) {
+    uint64_t iter = 0;
+    for (s = 1; s < EXHAUSTIVE_TEST_ORDER; s++) {
+        for (r = 1; r < EXHAUSTIVE_TEST_ORDER; r++) {
+            for (msg = 1; msg < EXHAUSTIVE_TEST_ORDER; msg++) {
+                for (key = 1; key < EXHAUSTIVE_TEST_ORDER; key++) {
                     secp256k1_ge nonconst_ge;
                     secp256k1_ecdsa_signature sig;
                     secp256k1_pubkey pk;
@@ -245,6 +255,8 @@ void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *gr
                     int k, should_verify;
                     unsigned char msg32[32];
 
+                    if (skip_section(&iter)) continue;
+
                     secp256k1_scalar_set_int(&s_s, s);
                     secp256k1_scalar_set_int(&r_s, r);
                     secp256k1_scalar_set_int(&msg_s, msg);
@@ -254,9 +266,9 @@ void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *gr
                     /* 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++) {
+                    for (k = 0; k < EXHAUSTIVE_TEST_ORDER; k++) {
                         secp256k1_scalar check_x_s;
-                        r_from_k(&check_x_s, group, k);
+                        r_from_k(&check_x_s, group, k, NULL);
                         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);
@@ -281,13 +293,15 @@ void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *gr
     }
 }
 
-void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
+void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group) {
     int i, j, k;
+    uint64_t iter = 0;
 
     /* Loop */
-    for (i = 1; i < order; i++) {  /* message */
-        for (j = 1; j < order; j++) {  /* key */
-            for (k = 1; k < order; k++) {  /* nonce */
+    for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {  /* message */
+        for (j = 1; j < EXHAUSTIVE_TEST_ORDER; j++) {  /* key */
+            if (skip_section(&iter)) continue;
+            for (k = 1; k < EXHAUSTIVE_TEST_ORDER; k++) {  /* nonce */
                 const int starting_k = k;
                 secp256k1_ecdsa_signature sig;
                 secp256k1_scalar sk, msg, r, s, expected_r;
@@ -303,10 +317,10 @@ void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *grou
                 /* 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);
+                r_from_k(&expected_r, group, k, NULL);
                 CHECK(r == expected_r);
-                CHECK((k * s) % order == (i + r * j) % order ||
-                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
+                CHECK((k * s) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER ||
+                      (k * (EXHAUSTIVE_TEST_ORDER - s)) % EXHAUSTIVE_TEST_ORDER == (i + r * j) % EXHAUSTIVE_TEST_ORDER);
 
                 /* Overflow means we've tried every possible nonce */
                 if (k < starting_k) {
@@ -327,184 +341,114 @@ void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *grou
 }
 
 #ifdef ENABLE_MODULE_RECOVERY
-void test_exhaustive_recovery_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 */
-                const int starting_k = k;
-                secp256k1_fe r_dot_y_normalized;
-                secp256k1_ecdsa_recoverable_signature rsig;
-                secp256k1_ecdsa_signature sig;
-                secp256k1_scalar sk, msg, r, s, expected_r;
-                unsigned char sk32[32], msg32[32];
-                int expected_recid;
-                int recid;
-                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_recoverable(ctx, &rsig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
+#include "src/modules/recovery/tests_exhaustive_impl.h"
+#endif
 
-                /* Check directly */
-                secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, &rsig);
-                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);
-                /* In computing the recid, there is an overflow condition that is disabled in
-                 * scalar_low_impl.h `secp256k1_scalar_set_b32` because almost every r.y value
-                 * will exceed the group order, and our signing code always holds out for r
-                 * values that don't overflow, so with a proper overflow check the tests would
-                 * loop indefinitely. */
-                r_dot_y_normalized = group[k].y;
-                secp256k1_fe_normalize(&r_dot_y_normalized);
-                /* Also the recovery id is flipped depending if we hit the low-s branch */
-                if ((k * s) % order == (i + r * j) % order) {
-                    expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 1 : 0;
-                } else {
-                    expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 0 : 1;
-                }
-                CHECK(recid == expected_recid);
+#ifdef ENABLE_MODULE_EXTRAKEYS
+#include "src/modules/extrakeys/tests_exhaustive_impl.h"
+#endif
 
-                /* Convert to a standard sig then check */
-                secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
-                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);
+#ifdef ENABLE_MODULE_SCHNORRSIG
+#include "src/modules/schnorrsig/tests_exhaustive_impl.h"
+#endif
 
-                /* Overflow means we've tried every possible nonce */
-                if (k < starting_k) {
-                    break;
-                }
-            }
+int main(int argc, char** argv) {
+    int i;
+    secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER];
+    secp256k1_ge group[EXHAUSTIVE_TEST_ORDER];
+    unsigned char rand32[32];
+    secp256k1_context *ctx;
+
+    /* Disable buffering for stdout to improve reliability of getting
+     * diagnostic information. Happens right at the start of main because
+     * setbuf must be used before any other operation on the stream. */
+    setbuf(stdout, NULL);
+    /* Also disable buffering for stderr because it's not guaranteed that it's
+     * unbuffered on all systems. */
+    setbuf(stderr, NULL);
+
+    printf("Exhaustive tests for order %lu\n", (unsigned long)EXHAUSTIVE_TEST_ORDER);
+
+    /* find iteration count */
+    if (argc > 1) {
+        count = strtol(argv[1], NULL, 0);
+    }
+    printf("test count = %i\n", count);
+
+    /* find random seed */
+    secp256k1_testrand_init(argc > 2 ? argv[2] : NULL);
+
+    /* set up split processing */
+    if (argc > 4) {
+        num_cores = strtol(argv[3], NULL, 0);
+        this_core = strtol(argv[4], NULL, 0);
+        if (num_cores < 1 || this_core >= num_cores) {
+            fprintf(stderr, "Usage: %s [count] [seed] [numcores] [thiscore]\n", argv[0]);
+            return 1;
         }
+        printf("running tests for core %lu (out of [0..%lu])\n", (unsigned long)this_core, (unsigned long)num_cores - 1);
     }
-}
-
-void test_exhaustive_recovery_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
-    /* This is essentially a copy of test_exhaustive_verify, with recovery added */
-    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_recoverable_signature rsig;
-                    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 recid = 0;
-                    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);
-                    secp256k1_scalar_get_b32(msg32, &msg_s);
+    while (count--) {
+        /* Build context */
+        ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+        secp256k1_testrand256(rand32);
+        CHECK(secp256k1_context_randomize(ctx, rand32));
+
+        /* 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++) {
+            secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g);
+            secp256k1_ge_set_gej(&group[i], &groupj[i]);
+            if (count != 0) {
+                /* Set a different random z-value for each Jacobian point, except z=1
+                   is used in the last iteration. */
+                secp256k1_fe z;
+                random_fe(&z);
+                secp256k1_gej_rescale(&groupj[i], &z);
+            }
 
-                    /* 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 against ecmult_gen */
+            {
+                secp256k1_scalar scalar_i;
+                secp256k1_gej generatedj;
+                secp256k1_ge generated;
 
-                    /* We would like to try recovering the pubkey and checking that it matches,
-                     * but pubkey recovery is impossible in the exhaustive tests (the reason
-                     * being that there are 12 nonzero r values, 12 nonzero points, and no
-                     * overlap between the sets, so there are no valid signatures). */
+                secp256k1_scalar_set_int(&scalar_i, i);
+                secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &generatedj, &scalar_i);
+                secp256k1_ge_set_gej(&generated, &generatedj);
 
-                    /* Verify by converting to a standard signature and calling verify */
-                    secp256k1_ecdsa_recoverable_signature_save(&rsig, &r_s, &s_s, recid);
-                    secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig);
-                    memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
-                    secp256k1_pubkey_save(&pk, &nonconst_ge);
-                    CHECK(should_verify ==
-                          secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
-                }
+                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));
             }
         }
-    }
-}
-#endif
-
-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);
+        /* Run the tests */
+        test_exhaustive_endomorphism(group);
+        test_exhaustive_addition(group, groupj);
+        test_exhaustive_ecmult(ctx, group, groupj);
+        test_exhaustive_ecmult_multi(ctx, group);
+        test_exhaustive_sign(ctx, group);
+        test_exhaustive_verify(ctx, group);
 
-    /* TODO set z = 1, then do num_tests runs with random z values */
+#ifdef ENABLE_MODULE_RECOVERY
+        test_exhaustive_recovery(ctx, group);
+#endif
+#ifdef ENABLE_MODULE_EXTRAKEYS
+        test_exhaustive_extrakeys(ctx, group);
+#endif
+#ifdef ENABLE_MODULE_SCHNORRSIG
+        test_exhaustive_schnorrsig(ctx);
+#endif
 
-    /* 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));
-        }
+        secp256k1_context_destroy(ctx);
     }
 
-    /* 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_ecmult_multi(ctx, group, EXHAUSTIVE_TEST_ORDER);
-    test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
-    test_exhaustive_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
+    secp256k1_testrand_finish();
 
-#ifdef ENABLE_MODULE_RECOVERY
-    test_exhaustive_recovery_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
-    test_exhaustive_recovery_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
-#endif
-
-    secp256k1_context_destroy(ctx);
+    printf("no problems found\n");
     return 0;
 }
-
diff --git a/src/secp256k1/src/util.h b/src/secp256k1/src/util.h
index a5cbe03ef5..3a88a41bc6 100644
--- a/src/secp256k1/src/util.h
+++ b/src/secp256k1/src/util.h
@@ -216,6 +216,24 @@ static SECP256K1_INLINE void memczero(void *s, size_t len, int flag) {
     }
 }
 
+/** Semantics like memcmp. Variable-time.
+ *
+ * We use this to avoid possible compiler bugs with memcmp, e.g.
+ * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=95189
+ */
+static SECP256K1_INLINE int secp256k1_memcmp_var(const void *s1, const void *s2, size_t n) {
+    const unsigned char *p1 = s1, *p2 = s2;
+    size_t i;
+
+    for (i = 0; i < n; i++) {
+        int diff = p1[i] - p2[i];
+        if (diff != 0) {
+            return diff;
+        }
+    }
+    return 0;
+}
+
 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized and non-negative.*/
 static SECP256K1_INLINE void secp256k1_int_cmov(int *r, const int *a, int flag) {
     unsigned int mask0, mask1, r_masked, a_masked;
diff --git a/src/secp256k1/src/valgrind_ctime_test.c b/src/secp256k1/src/valgrind_ctime_test.c
index e676a8326c..3169e3651c 100644
--- a/src/secp256k1/src/valgrind_ctime_test.c
+++ b/src/secp256k1/src/valgrind_ctime_test.c
@@ -9,19 +9,19 @@
 #include "assumptions.h"
 #include "util.h"
 
-#if ENABLE_MODULE_ECDH
+#ifdef ENABLE_MODULE_ECDH
 # include "include/secp256k1_ecdh.h"
 #endif
 
-#if ENABLE_MODULE_RECOVERY
+#ifdef ENABLE_MODULE_RECOVERY
 # include "include/secp256k1_recovery.h"
 #endif
 
-#if ENABLE_MODULE_EXTRAKEYS
+#ifdef ENABLE_MODULE_EXTRAKEYS
 # include "include/secp256k1_extrakeys.h"
 #endif
 
-#if ENABLE_MODULE_SCHNORRSIG
+#ifdef ENABLE_MODULE_SCHNORRSIG
 #include "include/secp256k1_schnorrsig.h"
 #endif
 
@@ -37,11 +37,11 @@ int main(void) {
     unsigned char key[32];
     unsigned char sig[74];
     unsigned char spubkey[33];
-#if ENABLE_MODULE_RECOVERY
+#ifdef ENABLE_MODULE_RECOVERY
     secp256k1_ecdsa_recoverable_signature recoverable_signature;
     int recid;
 #endif
-#if ENABLE_MODULE_EXTRAKEYS
+#ifdef ENABLE_MODULE_EXTRAKEYS
     secp256k1_keypair keypair;
 #endif
 
@@ -81,7 +81,7 @@ int main(void) {
     CHECK(ret);
     CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature));
 
-#if ENABLE_MODULE_ECDH
+#ifdef ENABLE_MODULE_ECDH
     /* Test ECDH. */
     VALGRIND_MAKE_MEM_UNDEFINED(key, 32);
     ret = secp256k1_ecdh(ctx, msg, &pubkey, key, NULL, NULL);
@@ -89,7 +89,7 @@ int main(void) {
     CHECK(ret == 1);
 #endif
 
-#if ENABLE_MODULE_RECOVERY
+#ifdef ENABLE_MODULE_RECOVERY
     /* Test signing a recoverable signature. */
     VALGRIND_MAKE_MEM_UNDEFINED(key, 32);
     ret = secp256k1_ecdsa_sign_recoverable(ctx, &recoverable_signature, msg, key, NULL, NULL);
@@ -129,7 +129,7 @@ int main(void) {
     CHECK(ret);
 
     /* Test keypair_create and keypair_xonly_tweak_add. */
-#if ENABLE_MODULE_EXTRAKEYS
+#ifdef ENABLE_MODULE_EXTRAKEYS
     VALGRIND_MAKE_MEM_UNDEFINED(key, 32);
     ret = secp256k1_keypair_create(ctx, &keypair, key);
     VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret));
@@ -142,7 +142,7 @@ int main(void) {
     CHECK(ret == 1);
 #endif
 
-#if ENABLE_MODULE_SCHNORRSIG
+#ifdef ENABLE_MODULE_SCHNORRSIG
     VALGRIND_MAKE_MEM_UNDEFINED(key, 32);
     ret = secp256k1_keypair_create(ctx, &keypair, key);
     VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret));