Update libsecp256k1 to master

src/secp256k1/.gitignore

@@ -6,6 +6,7 @@ bench_schnorr_verify
 bench_recover
 bench_internal
 tests
+exhaustive_tests
 gen_context
 *.exe
 *.so

src/secp256k1/.travis.yml

@@ -11,7 +11,7 @@ cache:
   - src/java/guava/
 env:
   global:
-    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  schnorr=no  RECOVERY=no  EXPERIMENTAL=no
+    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  RECOVERY=no  EXPERIMENTAL=no
     - GUAVA_URL=https://search.maven.org/remotecontent?filepath=com/google/guava/guava/18.0/guava-18.0.jar GUAVA_JAR=src/java/guava/guava-18.0.jar
   matrix:
     - SCALAR=32bit    RECOVERY=yes
@@ -22,15 +22,14 @@ env:
     - FIELD=64bit     ENDOMORPHISM=yes  ECDH=yes EXPERIMENTAL=yes
     - FIELD=64bit                       ASM=x86_64
     - FIELD=64bit     ENDOMORPHISM=yes  ASM=x86_64
-    - FIELD=32bit     SCHNORR=yes EXPERIMENTAL=yes
     - FIELD=32bit     ENDOMORPHISM=yes
     - BIGNUM=no
-    - BIGNUM=no       ENDOMORPHISM=yes SCHNORR=yes  RECOVERY=yes EXPERIMENTAL=yes
+    - BIGNUM=no       ENDOMORPHISM=yes RECOVERY=yes EXPERIMENTAL=yes
     - BIGNUM=no       STATICPRECOMPUTATION=no
     - BUILD=distcheck
     - EXTRAFLAGS=CPPFLAGS=-DDETERMINISTIC
     - EXTRAFLAGS=CFLAGS=-O0
-    - BUILD=check-java ECDH=yes SCHNORR=yes EXPERIMENTAL=yes
+    - BUILD=check-java ECDH=yes EXPERIMENTAL=yes
 matrix:
   fast_finish: true
   include:
@@ -66,5 +65,5 @@ before_script: ./autogen.sh
 script:
  - if [ -n "$HOST" ]; then export USE_HOST="--host=$HOST"; fi
  - if [ "x$HOST" = "xi686-linux-gnu" ]; then export CC="$CC -m32"; fi
- - ./configure --enable-experimental=$EXPERIMENTAL --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-schnorr=$SCHNORR --enable-module-recovery=$RECOVERY $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
+ - ./configure --enable-experimental=$EXPERIMENTAL --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-recovery=$RECOVERY $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
 os: linux

src/secp256k1/Makefile.am

@@ -12,9 +12,11 @@ noinst_HEADERS =
 noinst_HEADERS += src/scalar.h
 noinst_HEADERS += src/scalar_4x64.h
 noinst_HEADERS += src/scalar_8x32.h
+noinst_HEADERS += src/scalar_low.h
 noinst_HEADERS += src/scalar_impl.h
 noinst_HEADERS += src/scalar_4x64_impl.h
 noinst_HEADERS += src/scalar_8x32_impl.h
+noinst_HEADERS += src/scalar_low_impl.h
 noinst_HEADERS += src/group.h
 noinst_HEADERS += src/group_impl.h
 noinst_HEADERS += src/num_gmp.h
@@ -87,13 +89,23 @@ bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB)
 bench_internal_CPPFLAGS = -DSECP256K1_BUILD $(SECP_INCLUDES)
 endif
 
+TESTS =
 if USE_TESTS
 noinst_PROGRAMS += tests
 tests_SOURCES = src/tests.c
 tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
 tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
 tests_LDFLAGS = -static
-TESTS = tests
+TESTS += tests
+endif
+
+if USE_EXHAUSTIVE_TESTS
+noinst_PROGRAMS += exhaustive_tests
+exhaustive_tests_SOURCES = src/tests_exhaustive.c
+exhaustive_tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src $(SECP_INCLUDES)
+exhaustive_tests_LDADD = $(SECP_LIBS)
+exhaustive_tests_LDFLAGS = -static
+TESTS += exhaustive_tests
 endif
 
 JAVAROOT=src/java
@@ -154,10 +166,6 @@ if ENABLE_MODULE_ECDH
 include src/modules/ecdh/Makefile.am.include
 endif
 
-if ENABLE_MODULE_SCHNORR
-include src/modules/schnorr/Makefile.am.include
-endif
-
 if ENABLE_MODULE_RECOVERY
 include src/modules/recovery/Makefile.am.include
 endif

src/secp256k1/build-aux/m4/bitcoin_secp.m4

@@ -46,6 +46,10 @@ if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then
     ECDSA_sign(0, NULL, 0, NULL, NULL, eckey);
     ECDSA_verify(0, NULL, 0, NULL, 0, eckey);
     EC_KEY_free(eckey);
+    ECDSA_SIG *sig_openssl;
+    sig_openssl = ECDSA_SIG_new();
+    (void)sig_openssl->r;
+    ECDSA_SIG_free(sig_openssl);
   ]])],[has_openssl_ec=yes],[has_openssl_ec=no])
   AC_MSG_RESULT([$has_openssl_ec])
 fi

src/secp256k1/configure.ac

@@ -104,6 +104,11 @@ AC_ARG_ENABLE(experimental,
     [use_experimental=$enableval],
     [use_experimental=no])
 
+AC_ARG_ENABLE(exhaustive_tests,
+    AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests (default is yes)]),
+    [use_exhaustive_tests=$enableval],
+    [use_exhaustive_tests=yes])
+
 AC_ARG_ENABLE(endomorphism,
     AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
     [use_endomorphism=$enableval],
@@ -119,11 +124,6 @@ AC_ARG_ENABLE(module_ecdh,
     [enable_module_ecdh=$enableval],
     [enable_module_ecdh=no])
 
-AC_ARG_ENABLE(module_schnorr,
-    AS_HELP_STRING([--enable-module-schnorr],[enable Schnorr signature module (experimental)]),
-    [enable_module_schnorr=$enableval],
-    [enable_module_schnorr=no])
-
 AC_ARG_ENABLE(module_recovery,
     AS_HELP_STRING([--enable-module-recovery],[enable ECDSA pubkey recovery module (default is no)]),
     [enable_module_recovery=$enableval],
@@ -381,9 +381,6 @@ fi
 if test x"$use_jni" != x"no"; then
   AX_JNI_INCLUDE_DIR
   have_jni_dependencies=yes
-  if test x"$enable_module_schnorr" = x"no"; then
-    have_jni_dependencies=no
-  fi
   if test x"$enable_module_ecdh" = x"no"; then
     have_jni_dependencies=no
   fi
@@ -392,7 +389,7 @@ if test x"$use_jni" != x"no"; then
   fi
   if test "x$have_jni_dependencies" = "xno"; then
     if test x"$use_jni" = x"yes"; then
-      AC_MSG_ERROR([jni support explicitly requested but headers/dependencies were not found. Enable ECDH and Schnorr and try again.])
+      AC_MSG_ERROR([jni support explicitly requested but headers/dependencies were not found. Enable ECDH and try again.])
     fi
     AC_MSG_WARN([jni headers/dependencies not found. jni support disabled])
     use_jni=no
@@ -413,7 +410,7 @@ if test x"$use_endomorphism" = x"yes"; then
   AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization])
 fi
 
-if test x"$use_ecmult_static_precomputation" = x"yes"; then
+if test x"$set_precomp" = x"yes"; then
   AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table])
 fi
 
@@ -421,10 +418,6 @@ if test x"$enable_module_ecdh" = x"yes"; then
   AC_DEFINE(ENABLE_MODULE_ECDH, 1, [Define this symbol to enable the ECDH module])
 fi
 
-if test x"$enable_module_schnorr" = x"yes"; then
-  AC_DEFINE(ENABLE_MODULE_SCHNORR, 1, [Define this symbol to enable the Schnorr signature module])
-fi
-
 if test x"$enable_module_recovery" = x"yes"; then
   AC_DEFINE(ENABLE_MODULE_RECOVERY, 1, [Define this symbol to enable the ECDSA pubkey recovery module])
 fi
@@ -442,7 +435,6 @@ AC_MSG_NOTICE([Using bignum implementation: $set_bignum])
 AC_MSG_NOTICE([Using scalar implementation: $set_scalar])
 AC_MSG_NOTICE([Using endomorphism optimizations: $use_endomorphism])
 AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
-AC_MSG_NOTICE([Building Schnorr signatures module: $enable_module_schnorr])
 AC_MSG_NOTICE([Building ECDSA pubkey recovery module: $enable_module_recovery])
 AC_MSG_NOTICE([Using jni: $use_jni])
 
@@ -451,12 +443,8 @@ if test x"$enable_experimental" = x"yes"; then
   AC_MSG_NOTICE([WARNING: experimental build])
   AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.])
   AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh])
-  AC_MSG_NOTICE([Building Schnorr signatures module: $enable_module_schnorr])
   AC_MSG_NOTICE([******])
 else
-  if test x"$enable_module_schnorr" = x"yes"; then
-    AC_MSG_ERROR([Schnorr signature module is experimental. Use --enable-experimental to allow.])
-  fi
   if test x"$enable_module_ecdh" = x"yes"; then
     AC_MSG_ERROR([ECDH module is experimental. Use --enable-experimental to allow.])
   fi
@@ -473,10 +461,10 @@ AC_SUBST(SECP_LIBS)
 AC_SUBST(SECP_TEST_LIBS)
 AC_SUBST(SECP_TEST_INCLUDES)
 AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
+AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$use_exhaustive_tests" != x"no"])
 AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
-AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$use_ecmult_static_precomputation" = x"yes"])
+AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$set_precomp" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
-AM_CONDITIONAL([ENABLE_MODULE_SCHNORR], [test x"$enable_module_schnorr" = x"yes"])
 AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"])
 AM_CONDITIONAL([USE_JNI], [test x"$use_jni" == x"yes"])
 AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$use_external_asm" = x"yes"])

src/secp256k1/include/secp256k1.h

@@ -47,11 +47,8 @@ typedef struct secp256k1_context_struct secp256k1_context;
  *  The exact representation of data inside is implementation defined and not
  *  guaranteed to be portable between different platforms or versions. It is
  *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
- *  If you need to convert to a format suitable for storage or transmission, use
- *  secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse.
- *
- *  Furthermore, it is guaranteed that identical public keys (ignoring
- *  compression) will have identical representation, so they can be memcmp'ed.
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse.
  */
 typedef struct {
     unsigned char data[64];
@@ -62,12 +59,9 @@ typedef struct {
  *  The exact representation of data inside is implementation defined and not
  *  guaranteed to be portable between different platforms or versions. It is
  *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
- *  If you need to convert to a format suitable for storage or transmission, use
- *  the secp256k1_ecdsa_signature_serialize_* and
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use the secp256k1_ecdsa_signature_serialize_* and
  *  secp256k1_ecdsa_signature_serialize_* functions.
- *
- *  Furthermore, it is guaranteed to identical signatures will have identical
- *  representation, so they can be memcmp'ed.
  */
 typedef struct {
     unsigned char data[64];

src/secp256k1/include/secp256k1_schnorr.h

@@ -1,173 +0,0 @@
-#ifndef _SECP256K1_SCHNORR_
-# define _SECP256K1_SCHNORR_
-
-# include "secp256k1.h"
-
-# ifdef __cplusplus
-extern "C" {
-# endif
-
-/** Create a signature using a custom EC-Schnorr-SHA256 construction. It
- *  produces non-malleable 64-byte signatures which support public key recovery
- *  batch validation, and multiparty signing.
- *  Returns: 1: signature created
- *           0: the nonce generation function failed, or the private key was
- *              invalid.
- *  Args:    ctx:    pointer to a context object, initialized for signing
- *                   (cannot be NULL)
- *  Out:     sig64:  pointer to a 64-byte array where the signature will be
- *                   placed (cannot be NULL)
- *  In:      msg32:  the 32-byte message hash being signed (cannot be NULL)
- *           seckey: pointer to a 32-byte secret key (cannot be NULL)
- *           noncefp:pointer to a nonce generation function. If NULL,
- *                   secp256k1_nonce_function_default is used
- *           ndata:  pointer to arbitrary data used by the nonce generation
- *                   function (can be NULL)
- */
-SECP256K1_API int secp256k1_schnorr_sign(
-  const secp256k1_context* ctx,
-  unsigned char *sig64,
-  const unsigned char *msg32,
-  const unsigned char *seckey,
-  secp256k1_nonce_function noncefp,
-  const void *ndata
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
-
-/** Verify a signature created by secp256k1_schnorr_sign.
- *  Returns: 1: correct signature
- *           0: incorrect signature
- *  Args:    ctx:       a secp256k1 context object, initialized for verification.
- *  In:      sig64:     the 64-byte signature being verified (cannot be NULL)
- *           msg32:     the 32-byte message hash being verified (cannot be NULL)
- *           pubkey:    the public key to verify with (cannot be NULL)
- */
-SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_verify(
-  const secp256k1_context* ctx,
-  const unsigned char *sig64,
-  const unsigned char *msg32,
-  const secp256k1_pubkey *pubkey
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
-
-/** Recover an EC public key from a Schnorr signature created using
- *  secp256k1_schnorr_sign.
- *  Returns: 1: public key successfully recovered (which guarantees a correct
- *           signature).
- *           0: otherwise.
- *  Args:    ctx:        pointer to a context object, initialized for
- *                       verification (cannot be NULL)
- *  Out:     pubkey:     pointer to a pubkey to set to the recovered public key
- *                       (cannot be NULL).
- *  In:      sig64:      signature as 64 byte array (cannot be NULL)
- *           msg32:      the 32-byte message hash assumed to be signed (cannot
- *                       be NULL)
- */
-SECP256K1_API int secp256k1_schnorr_recover(
-  const secp256k1_context* ctx,
-  secp256k1_pubkey *pubkey,
-  const unsigned char *sig64,
-  const unsigned char *msg32
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
-
-/** Generate a nonce pair deterministically for use with
- *  secp256k1_schnorr_partial_sign.
- *  Returns: 1: valid nonce pair was generated.
- *           0: otherwise (nonce generation function failed)
- *  Args:    ctx:         pointer to a context object, initialized for signing
- *                        (cannot be NULL)
- *  Out:     pubnonce:    public side of the nonce (cannot be NULL)
- *           privnonce32: private side of the nonce (32 byte) (cannot be NULL)
- *  In:      msg32:       the 32-byte message hash assumed to be signed (cannot
- *                        be NULL)
- *           sec32:       the 32-byte private key (cannot be NULL)
- *           noncefp:     pointer to a nonce generation function. If NULL,
- *                        secp256k1_nonce_function_default is used
- *           noncedata:   pointer to arbitrary data used by the nonce generation
- *                        function (can be NULL)
- *
- *  Do not use the output as a private/public key pair for signing/validation.
- */
-SECP256K1_API int secp256k1_schnorr_generate_nonce_pair(
-  const secp256k1_context* ctx,
-  secp256k1_pubkey *pubnonce,
-  unsigned char *privnonce32,
-  const unsigned char *msg32,
-  const unsigned char *sec32,
-  secp256k1_nonce_function noncefp,
-  const void* noncedata
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
-
-/** Produce a partial Schnorr signature, which can be combined using
- *  secp256k1_schnorr_partial_combine, to end up with a full signature that is
- *  verifiable using secp256k1_schnorr_verify.
- *  Returns: 1: signature created successfully.
- *           0: no valid signature exists with this combination of keys, nonces
- *              and message (chance around 1 in 2^128)
- *          -1: invalid private key, nonce, or public nonces.
- *  Args: ctx:             pointer to context object, initialized for signing (cannot
- *                         be NULL)
- *  Out:  sig64:           pointer to 64-byte array to put partial signature in
- *  In:   msg32:           pointer to 32-byte message to sign
- *        sec32:           pointer to 32-byte private key
- *        pubnonce_others: pointer to pubkey containing the sum of the other's
- *                         nonces (see secp256k1_ec_pubkey_combine)
- *        secnonce32:      pointer to 32-byte array containing our nonce
- *
- * The intended procedure for creating a multiparty signature is:
- * - Each signer S[i] with private key x[i] and public key Q[i] runs
- *   secp256k1_schnorr_generate_nonce_pair to produce a pair (k[i],R[i]) of
- *   private/public nonces.
- * - All signers communicate their public nonces to each other (revealing your
- *   private nonce can lead to discovery of your private key, so it should be
- *   considered secret).
- * - All signers combine all the public nonces they received (excluding their
- *   own) using secp256k1_ec_pubkey_combine to obtain an
- *   Rall[i] = sum(R[0..i-1,i+1..n]).
- * - All signers produce a partial signature using
- *   secp256k1_schnorr_partial_sign, passing in their own private key x[i],
- *   their own private nonce k[i], and the sum of the others' public nonces
- *   Rall[i].
- * - All signers communicate their partial signatures to each other.
- * - Someone combines all partial signatures using
- *   secp256k1_schnorr_partial_combine, to obtain a full signature.
- * - The resulting signature is validatable using secp256k1_schnorr_verify, with
- *   public key equal to the result of secp256k1_ec_pubkey_combine of the
- *   signers' public keys (sum(Q[0..n])).
- *
- *  Note that secp256k1_schnorr_partial_combine and secp256k1_ec_pubkey_combine
- *  function take their arguments in any order, and it is possible to
- *  pre-combine several inputs already with one call, and add more inputs later
- *  by calling the function again (they are commutative and associative).
- */
-SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_partial_sign(
-  const secp256k1_context* ctx,
-  unsigned char *sig64,
-  const unsigned char *msg32,
-  const unsigned char *sec32,
-  const secp256k1_pubkey *pubnonce_others,
-  const unsigned char *secnonce32
-) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(6);
-
-/** Combine multiple Schnorr partial signatures.
- * Returns: 1: the passed signatures were successfully combined.
- *          0: the resulting signature is not valid (chance of 1 in 2^256)
- *         -1: some inputs were invalid, or the signatures were not created
- *             using the same set of nonces
- * Args:   ctx:      pointer to a context object
- * Out:    sig64:    pointer to a 64-byte array to place the combined signature
- *                   (cannot be NULL)
- * In:     sig64sin: pointer to an array of n pointers to 64-byte input
- *                   signatures
- *         n:        the number of signatures to combine (at least 1)
- */
-SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_partial_combine(
-  const secp256k1_context* ctx,
-  unsigned char *sig64,
-  const unsigned char * const * sig64sin,
-  size_t n
-) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
-
-# ifdef __cplusplus
-}
-# endif
-
-#endif

src/secp256k1/src/ecdsa_impl.h

@@ -203,7 +203,9 @@ static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const
 static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
     unsigned char c[32];
     secp256k1_scalar sn, u1, u2;
+#if !defined(EXHAUSTIVE_TEST_ORDER)
     secp256k1_fe xr;
+#endif
     secp256k1_gej pubkeyj;
     secp256k1_gej pr;
 
@@ -219,6 +221,21 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
     if (secp256k1_gej_is_infinity(&pr)) {
         return 0;
     }
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+{
+    secp256k1_scalar computed_r;
+    int overflow = 0;
+    secp256k1_ge pr_ge;
+    secp256k1_ge_set_gej(&pr_ge, &pr);
+    secp256k1_fe_normalize(&pr_ge.x);
+
+    secp256k1_fe_get_b32(c, &pr_ge.x);
+    secp256k1_scalar_set_b32(&computed_r, c, &overflow);
+    /* we fully expect overflow */
+    return secp256k1_scalar_eq(sigr, &computed_r);
+}
+#else
     secp256k1_scalar_get_b32(c, sigr);
     secp256k1_fe_set_b32(&xr, c);
 
@@ -252,6 +269,7 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
         return 1;
     }
     return 0;
+#endif
 }
 
 static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {

src/secp256k1/src/ecmult_const_impl.h

@@ -78,7 +78,7 @@ static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
     /* Negative numbers will be negated to keep their bit representation below the maximum width */
     flip = secp256k1_scalar_is_high(&s);
     /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
-    bit = flip ^ (s.d[0] & 1);
+    bit = flip ^ !secp256k1_scalar_is_even(&s);
     /* We check for negative one, since adding 2 to it will cause an overflow */
     secp256k1_scalar_negate(&neg_s, &s);
     not_neg_one = !secp256k1_scalar_is_one(&neg_s);

src/secp256k1/src/ecmult_gen_impl.h

@@ -77,7 +77,7 @@ static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx
                 secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
             }
         }
-        secp256k1_ge_set_all_gej_var(1024, prec, precj, cb);
+        secp256k1_ge_set_all_gej_var(prec, precj, 1024, cb);
     }
     for (j = 0; j < 64; j++) {
         for (i = 0; i < 16; i++) {

src/secp256k1/src/ecmult_impl.h

@@ -7,15 +7,29 @@
 #ifndef _SECP256K1_ECMULT_IMPL_H_
 #define _SECP256K1_ECMULT_IMPL_H_
 
+#include <string.h>
+
 #include "group.h"
 #include "scalar.h"
 #include "ecmult.h"
 
-#include <string.h>
-
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/* We need to lower these values for exhaustive tests because
+ * the tables cannot have infinities in them (this breaks the
+ * affine-isomorphism stuff which tracks z-ratios) */
+#  if EXHAUSTIVE_TEST_ORDER > 128
+#    define WINDOW_A 5
+#    define WINDOW_G 8
+#  elif EXHAUSTIVE_TEST_ORDER > 8
+#    define WINDOW_A 4
+#    define WINDOW_G 4
+#  else
+#    define WINDOW_A 2
+#    define WINDOW_G 2
+#  endif
+#else
 /* optimal for 128-bit and 256-bit exponents. */
 #define WINDOW_A 5
-
 /** larger numbers may result in slightly better performance, at the cost of
     exponentially larger precomputed tables. */
 #ifdef USE_ENDOMORPHISM
@@ -25,6 +39,7 @@
 /** One table for window size 16: 1.375 MiB. */
 #define WINDOW_G 16
 #endif
+#endif
 
 /** The number of entries a table with precomputed multiples needs to have. */
 #define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
@@ -103,7 +118,7 @@ static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge
     /* Compute the odd multiples in Jacobian form. */
     secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
     /* Convert them in batch to affine coordinates. */
-    secp256k1_ge_set_table_gej_var(n, prea, prej, zr);
+    secp256k1_ge_set_table_gej_var(prea, prej, zr, n);
     /* Convert them to compact storage form. */
     for (i = 0; i < n; i++) {
         secp256k1_ge_to_storage(&pre[i], &prea[i]);

src/secp256k1/src/field.h

@@ -30,6 +30,8 @@
 #error "Please select field implementation"
 #endif
 
+#include "util.h"
+
 /** Normalize a field element. */
 static void secp256k1_fe_normalize(secp256k1_fe *r);
 
@@ -50,6 +52,9 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
 /** Set a field element equal to a small integer. Resulting field element is normalized. */
 static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
 
+/** Sets a field element equal to zero, initializing all fields. */
+static void secp256k1_fe_clear(secp256k1_fe *a);
+
 /** Verify whether a field element is zero. Requires the input to be normalized. */
 static int secp256k1_fe_is_zero(const secp256k1_fe *a);
 
@@ -110,7 +115,7 @@ static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
 /** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be
  *  at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and
  *  outputs must not overlap in memory. */
-static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a);
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len);
 
 /** Convert a field element to the storage type. */
 static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);

src/secp256k1/src/field_impl.h

@@ -260,7 +260,7 @@ static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
 #endif
 }
 
-static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe *r, const secp256k1_fe *a) {
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) {
     secp256k1_fe u;
     size_t i;
     if (len < 1) {

src/secp256k1/src/group.h

@@ -65,12 +65,12 @@ static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
 static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
 
 /** Set a batch of group elements equal to the inputs given in jacobian coordinates */
-static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb);
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, const secp256k1_callback *cb);
 
 /** Set a batch of group elements equal to the inputs given in jacobian
  *  coordinates (with known z-ratios). zr must contain the known z-ratios such
  *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. */
-static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr);
+static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len);
 
 /** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
  *  the same global z "denominator". zr must contain the known z-ratios such

src/secp256k1/src/group_impl.h

@@ -11,6 +11,53 @@
 #include "field.h"
 #include "group.h"
 
+/* These points can be generated in sage as follows:
+ *
+ * 0. Setup a worksheet with the following parameters.
+ *   b = 4  # whatever CURVE_B will be set to
+ *   F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
+ *   C = EllipticCurve ([F (0), F (b)])
+ *
+ * 1. Determine all the small orders available to you. (If there are
+ *    no satisfactory ones, go back and change b.)
+ *   print C.order().factor(limit=1000)
+ *
+ * 2. Choose an order as one of the prime factors listed in the above step.
+ *    (You can also multiply some to get a composite order, though the
+ *    tests will crash trying to invert scalars during signing.) We take a
+ *    random point and scale it to drop its order to the desired value.
+ *    There is some probability this won't work; just try again.
+ *   order = 199
+ *   P = C.random_point()
+ *   P = (int(P.order()) / int(order)) * P
+ *   assert(P.order() == order)
+ *
+ * 3. Print the values. You'll need to use a vim macro or something to
+ *    split the hex output into 4-byte chunks.
+ *   print "%x %x" % P.xy()
+ */
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#  if EXHAUSTIVE_TEST_ORDER == 199
+const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0xFA7CC9A7, 0x0737F2DB, 0xA749DD39, 0x2B4FB069,
+    0x3B017A7D, 0xA808C2F1, 0xFB12940C, 0x9EA66C18,
+    0x78AC123A, 0x5ED8AEF3, 0x8732BC91, 0x1F3A2868,
+    0x48DF246C, 0x808DAE72, 0xCFE52572, 0x7F0501ED
+);
+
+const int CURVE_B = 4;
+#  elif EXHAUSTIVE_TEST_ORDER == 13
+const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
+    0xedc60018, 0xa51a786b, 0x2ea91f4d, 0x4c9416c0,
+    0x9de54c3b, 0xa1316554, 0x6cf4345c, 0x7277ef15,
+    0x54cb1b6b, 0xdc8c1273, 0x087844ea, 0x43f4603e,
+    0x0eaf9a43, 0xf6effe55, 0x939f806d, 0x37adf8ac
+);
+const int CURVE_B = 2;
+#  else
+#    error No known generator for the specified exhaustive test group order.
+#  endif
+#else
 /** Generator for secp256k1, value 'g' defined in
  *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
  */
@@ -21,8 +68,11 @@ static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
     0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
 );
 
+const int CURVE_B = 7;
+#endif
+
 static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
-    secp256k1_fe zi2; 
+    secp256k1_fe zi2;
     secp256k1_fe zi3;
     secp256k1_fe_sqr(&zi2, zi);
     secp256k1_fe_mul(&zi3, &zi2, zi);
@@ -76,7 +126,7 @@ static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
     r->y = a->y;
 }
 
-static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_callback *cb) {
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, const secp256k1_callback *cb) {
     secp256k1_fe *az;
     secp256k1_fe *azi;
     size_t i;
@@ -89,7 +139,7 @@ static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp
     }
 
     azi = (secp256k1_fe *)checked_malloc(cb, sizeof(secp256k1_fe) * count);
-    secp256k1_fe_inv_all_var(count, azi, az);
+    secp256k1_fe_inv_all_var(azi, az, count);
     free(az);
 
     count = 0;
@@ -102,7 +152,7 @@ static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge *r, const secp
     free(azi);
 }
 
-static void secp256k1_ge_set_table_gej_var(size_t len, secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr) {
+static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len) {
     size_t i = len - 1;
     secp256k1_fe zi;
 
@@ -145,9 +195,15 @@ static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp
 
 static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
     r->infinity = 1;
-    secp256k1_fe_set_int(&r->x, 0);
-    secp256k1_fe_set_int(&r->y, 0);
-    secp256k1_fe_set_int(&r->z, 0);
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
+    secp256k1_fe_clear(&r->z);
+}
+
+static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
+    r->infinity = 1;
+    secp256k1_fe_clear(&r->x);
+    secp256k1_fe_clear(&r->y);
 }
 
 static void secp256k1_gej_clear(secp256k1_gej *r) {
@@ -169,7 +225,7 @@ static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) {
     secp256k1_fe_sqr(&x2, x);
     secp256k1_fe_mul(&x3, x, &x2);
     r->infinity = 0;
-    secp256k1_fe_set_int(&c, 7);
+    secp256k1_fe_set_int(&c, CURVE_B);
     secp256k1_fe_add(&c, &x3);
     return secp256k1_fe_sqrt(&r->y, &c);
 }
@@ -228,7 +284,7 @@ static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
     secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
     secp256k1_fe_sqr(&z2, &a->z);
     secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
-    secp256k1_fe_mul_int(&z6, 7);
+    secp256k1_fe_mul_int(&z6, CURVE_B);
     secp256k1_fe_add(&x3, &z6);
     secp256k1_fe_normalize_weak(&x3);
     return secp256k1_fe_equal_var(&y2, &x3);
@@ -242,7 +298,7 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
     /* y^2 = x^3 + 7 */
     secp256k1_fe_sqr(&y2, &a->y);
     secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
-    secp256k1_fe_set_int(&c, 7);
+    secp256k1_fe_set_int(&c, CURVE_B);
     secp256k1_fe_add(&x3, &c);
     secp256k1_fe_normalize_weak(&x3);
     return secp256k1_fe_equal_var(&y2, &x3);
@@ -260,7 +316,7 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
     /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
      *  Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
      *  y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
-     *  
+     *
      *  Having said this, if this function receives a point on a sextic twist, e.g. by
      *  a fault attack, it is possible for y to be 0. This happens for y^2 = x^3 + 6,
      *  since -6 does have a cube root mod p. For this point, this function will not set

src/secp256k1/src/java/org/bitcoin/NativeSecp256k1.java

@@ -32,7 +32,7 @@ import static org.bitcoin.NativeSecp256k1Util.*;
  * <p>You can find an example library that can be used for this at https://github.com/bitcoin/secp256k1</p>
  *
  * <p>To build secp256k1 for use with bitcoinj, run
- * `./configure --enable-jni --enable-experimental --enable-module-schnorr --enable-module-ecdh`
+ * `./configure --enable-jni --enable-experimental --enable-module-ecdh`
  * and `make` then copy `.libs/libsecp256k1.so` to your system library path
  * or point the JVM to the folder containing it with -Djava.library.path
  * </p>
@@ -417,36 +417,6 @@ public class NativeSecp256k1 {
         }
     }
 
-    public static byte[] schnorrSign(byte[] data, byte[] sec) throws AssertFailException {
-        Preconditions.checkArgument(data.length == 32 && sec.length <= 32);
-
-        ByteBuffer byteBuff = nativeECDSABuffer.get();
-        if (byteBuff == null) {
-            byteBuff = ByteBuffer.allocateDirect(32 + 32);
-            byteBuff.order(ByteOrder.nativeOrder());
-            nativeECDSABuffer.set(byteBuff);
-        }
-        byteBuff.rewind();
-        byteBuff.put(data);
-        byteBuff.put(sec);
-
-        byte[][] retByteArray;
-
-        r.lock();
-        try {
-          retByteArray = secp256k1_schnorr_sign(byteBuff, Secp256k1Context.getContext());
-        } finally {
-          r.unlock();
-        }
-
-        byte[] sigArr = retByteArray[0];
-        int retVal = new BigInteger(new byte[] { retByteArray[1][0] }).intValue();
-
-        assertEquals(sigArr.length, 64, "Got bad signature length.");
-
-        return retVal == 0 ? new byte[0] : sigArr;
-    }
-
     private static native long secp256k1_ctx_clone(long context);
 
     private static native int secp256k1_context_randomize(ByteBuffer byteBuff, long context);
@@ -471,8 +441,6 @@ public class NativeSecp256k1 {
 
     private static native byte[][] secp256k1_ec_pubkey_parse(ByteBuffer byteBuff, long context, int inputLen);
 
-    private static native byte[][] secp256k1_schnorr_sign(ByteBuffer byteBuff, long context);
-
     private static native byte[][] secp256k1_ecdh(ByteBuffer byteBuff, long context, int inputLen);
 
 }

src/secp256k1/src/java/org/bitcoin/NativeSecp256k1Test.java

@@ -167,22 +167,6 @@ public class NativeSecp256k1Test {
         assertEquals( result, true, "testRandomize");
     }
 
-    /**
-      * This tests signSchnorr() for a valid secretkey
-      */
-    public static void testSchnorrSign() throws AssertFailException{
-
-        byte[] data = BaseEncoding.base16().lowerCase().decode("CF80CD8AED482D5D1527D7DC72FCEFF84E6326592848447D2DC0B0E87DFC9A90".toLowerCase()); //sha256hash of "testing"
-        byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
-
-        byte[] resultArr = NativeSecp256k1.schnorrSign(data, sec);
-        String sigString = javax.xml.bind.DatatypeConverter.printHexBinary(resultArr);
-        assertEquals( sigString, "C5E929AA058B982048760422D3B563749B7D0E50C5EBD8CD2FFC23214BD6A2F1B072C13880997EBA847CF20F2F90FCE07C1CA33A890A4127095A351127F8D95F" , "testSchnorrSign");
-    }
-
-    /**
-      * This tests signSchnorr() for a valid secretkey
-      */
     public static void testCreateECDHSecret() throws AssertFailException{
 
         byte[] sec = BaseEncoding.base16().lowerCase().decode("67E56582298859DDAE725F972992A07C6C4FB9F62A8FFF58CE3CA926A1063530".toLowerCase());
@@ -216,11 +200,6 @@ public class NativeSecp256k1Test {
         testSignPos();
         testSignNeg();
 
-        //Test Schnorr (partial support) //TODO
-        testSchnorrSign();
-        //testSchnorrVerify
-        //testSchnorrRecovery
-
         //Test privKeyTweakAdd() 1
         testPrivKeyTweakAdd_1();
 

src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.c

@@ -5,7 +5,6 @@
 #include "include/secp256k1.h"
 #include "include/secp256k1_ecdh.h"
 #include "include/secp256k1_recovery.h"
-#include "include/secp256k1_schnorr.h"
 
 
 SECP256K1_API jlong JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ctx_1clone
@@ -333,39 +332,6 @@ SECP256K1_API jlong JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdsa_1p
   return 0;
 }
 
-SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1schnorr_1sign
-  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l)
-{
-  secp256k1_context *ctx = (secp256k1_context*)(uintptr_t)ctx_l;
-  unsigned char* data = (unsigned char*) (*env)->GetDirectBufferAddress(env, byteBufferObject);
-  unsigned char* secKey = (unsigned char*) (data + 32);
-
-  jobjectArray retArray;
-  jbyteArray sigArray, intsByteArray;
-  unsigned char intsarray[1];
-  unsigned char sig[64];
-
-  int ret = secp256k1_schnorr_sign(ctx, sig, data, secKey, NULL, NULL);
-
-  intsarray[0] = ret;
-
-  retArray = (*env)->NewObjectArray(env, 2,
-    (*env)->FindClass(env, "[B"),
-    (*env)->NewByteArray(env, 1));
-
-  sigArray = (*env)->NewByteArray(env, 64);
-  (*env)->SetByteArrayRegion(env, sigArray, 0, 64, (jbyte*)sig);
-  (*env)->SetObjectArrayElement(env, retArray, 0, sigArray);
-
-  intsByteArray = (*env)->NewByteArray(env, 1);
-  (*env)->SetByteArrayRegion(env, intsByteArray, 0, 1, (jbyte*)intsarray);
-  (*env)->SetObjectArrayElement(env, retArray, 1, intsByteArray);
-
-  (void)classObject;
-
-  return retArray;
-}
-
 SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ecdh
   (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l, jint publen)
 {

src/secp256k1/src/java/org_bitcoin_NativeSecp256k1.h

@@ -104,14 +104,6 @@ SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1e
 SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1ec_1pubkey_1parse
   (JNIEnv *, jclass, jobject, jlong, jint);
 
-/*
- * Class:     org_bitcoin_NativeSecp256k1
- * Method:    secp256k1_schnorr_sign
- * Signature: (Ljava/nio/ByteBuffer;JI)[[B
- */
-SECP256K1_API jobjectArray JNICALL Java_org_bitcoin_NativeSecp256k1_secp256k1_1schnorr_1sign
-  (JNIEnv* env, jclass classObject, jobject byteBufferObject, jlong ctx_l);
-
 /*
  * Class:     org_bitcoin_NativeSecp256k1
  * Method:    secp256k1_ecdh

src/secp256k1/src/modules/recovery/main_impl.h

@@ -138,16 +138,15 @@ int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecd
     secp256k1_scalar_set_b32(&sec, seckey, &overflow);
     /* Fail if the secret key is invalid. */
     if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned char nonce32[32];
         unsigned int count = 0;
         secp256k1_scalar_set_b32(&msg, msg32, NULL);
         while (1) {
-            unsigned char nonce32[32];
             ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
             if (!ret) {
                 break;
             }
             secp256k1_scalar_set_b32(&non, nonce32, &overflow);
-            memset(nonce32, 0, 32);
             if (!secp256k1_scalar_is_zero(&non) && !overflow) {
                 if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, &recid)) {
                     break;
@@ -155,6 +154,7 @@ int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecd
             }
             count++;
         }
+        memset(nonce32, 0, 32);
         secp256k1_scalar_clear(&msg);
         secp256k1_scalar_clear(&non);
         secp256k1_scalar_clear(&sec);

src/secp256k1/src/modules/schnorr/Makefile.am.include

@@ -1,10 +0,0 @@
-include_HEADERS += include/secp256k1_schnorr.h
-noinst_HEADERS += src/modules/schnorr/main_impl.h
-noinst_HEADERS += src/modules/schnorr/schnorr.h
-noinst_HEADERS += src/modules/schnorr/schnorr_impl.h
-noinst_HEADERS += src/modules/schnorr/tests_impl.h
-if USE_BENCHMARK
-noinst_PROGRAMS += bench_schnorr_verify
-bench_schnorr_verify_SOURCES = src/bench_schnorr_verify.c
-bench_schnorr_verify_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
-endif

src/secp256k1/src/modules/schnorr/main_impl.h

@@ -1,164 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2014-2015 Pieter Wuille                              *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef SECP256K1_MODULE_SCHNORR_MAIN
-#define SECP256K1_MODULE_SCHNORR_MAIN
-
-#include "include/secp256k1_schnorr.h"
-#include "modules/schnorr/schnorr_impl.h"
-
-static void secp256k1_schnorr_msghash_sha256(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32) {
-    secp256k1_sha256_t sha;
-    secp256k1_sha256_initialize(&sha);
-    secp256k1_sha256_write(&sha, r32, 32);
-    secp256k1_sha256_write(&sha, msg32, 32);
-    secp256k1_sha256_finalize(&sha, h32);
-}
-
-static const unsigned char secp256k1_schnorr_algo16[17] = "Schnorr+SHA256  ";
-
-int secp256k1_schnorr_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
-    secp256k1_scalar sec, non;
-    int ret = 0;
-    int overflow = 0;
-    unsigned int count = 0;
-    VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
-    ARG_CHECK(msg32 != NULL);
-    ARG_CHECK(sig64 != NULL);
-    ARG_CHECK(seckey != NULL);
-    if (noncefp == NULL) {
-        noncefp = secp256k1_nonce_function_default;
-    }
-
-    secp256k1_scalar_set_b32(&sec, seckey, NULL);
-    while (1) {
-        unsigned char nonce32[32];
-        ret = noncefp(nonce32, msg32, seckey, secp256k1_schnorr_algo16, (void*)noncedata, count);
-        if (!ret) {
-            break;
-        }
-        secp256k1_scalar_set_b32(&non, nonce32, &overflow);
-        memset(nonce32, 0, 32);
-        if (!secp256k1_scalar_is_zero(&non) && !overflow) {
-            if (secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64, &sec, &non, NULL, secp256k1_schnorr_msghash_sha256, msg32)) {
-                break;
-            }
-        }
-        count++;
-    }
-    if (!ret) {
-        memset(sig64, 0, 64);
-    }
-    secp256k1_scalar_clear(&non);
-    secp256k1_scalar_clear(&sec);
-    return ret;
-}
-
-int secp256k1_schnorr_verify(const secp256k1_context* ctx, const unsigned char *sig64, const unsigned char *msg32, const secp256k1_pubkey *pubkey) {
-    secp256k1_ge q;
-    VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
-    ARG_CHECK(msg32 != NULL);
-    ARG_CHECK(sig64 != NULL);
-    ARG_CHECK(pubkey != NULL);
-
-    secp256k1_pubkey_load(ctx, &q, pubkey);
-    return secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64, &q, secp256k1_schnorr_msghash_sha256, msg32);
-}
-
-int secp256k1_schnorr_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *sig64, const unsigned char *msg32) {
-    secp256k1_ge q;
-
-    VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
-    ARG_CHECK(msg32 != NULL);
-    ARG_CHECK(sig64 != NULL);
-    ARG_CHECK(pubkey != NULL);
-
-    if (secp256k1_schnorr_sig_recover(&ctx->ecmult_ctx, sig64, &q, secp256k1_schnorr_msghash_sha256, msg32)) {
-        secp256k1_pubkey_save(pubkey, &q);
-        return 1;
-    } else {
-        memset(pubkey, 0, sizeof(*pubkey));
-        return 0;
-    }
-}
-
-int secp256k1_schnorr_generate_nonce_pair(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, unsigned char *privnonce32, const unsigned char *sec32, const unsigned char *msg32, secp256k1_nonce_function noncefp, const void* noncedata) {
-    int count = 0;
-    int ret = 1;
-    secp256k1_gej Qj;
-    secp256k1_ge Q;
-    secp256k1_scalar sec;
-
-    VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
-    ARG_CHECK(msg32 != NULL);
-    ARG_CHECK(sec32 != NULL);
-    ARG_CHECK(pubnonce != NULL);
-    ARG_CHECK(privnonce32 != NULL);
-
-    if (noncefp == NULL) {
-        noncefp = secp256k1_nonce_function_default;
-    }
-
-    do {
-        int overflow;
-        ret = noncefp(privnonce32, sec32, msg32, secp256k1_schnorr_algo16, (void*)noncedata, count++);
-        if (!ret) {
-            break;
-        }
-        secp256k1_scalar_set_b32(&sec, privnonce32, &overflow);
-        if (overflow || secp256k1_scalar_is_zero(&sec)) {
-            continue;
-        }
-        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sec);
-        secp256k1_ge_set_gej(&Q, &Qj);
-
-        secp256k1_pubkey_save(pubnonce, &Q);
-        break;
-    } while(1);
-
-    secp256k1_scalar_clear(&sec);
-    if (!ret) {
-        memset(pubnonce, 0, sizeof(*pubnonce));
-    }
-    return ret;
-}
-
-int secp256k1_schnorr_partial_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const unsigned char *sec32, const secp256k1_pubkey *pubnonce_others, const unsigned char *secnonce32) {
-    int overflow = 0;
-    secp256k1_scalar sec, non;
-    secp256k1_ge pubnon;
-    VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
-    ARG_CHECK(msg32 != NULL);
-    ARG_CHECK(sig64 != NULL);
-    ARG_CHECK(sec32 != NULL);
-    ARG_CHECK(secnonce32 != NULL);
-    ARG_CHECK(pubnonce_others != NULL);
-
-    secp256k1_scalar_set_b32(&sec, sec32, &overflow);
-    if (overflow || secp256k1_scalar_is_zero(&sec)) {
-        return -1;
-    }
-    secp256k1_scalar_set_b32(&non, secnonce32, &overflow);
-    if (overflow || secp256k1_scalar_is_zero(&non)) {
-        return -1;
-    }
-    secp256k1_pubkey_load(ctx, &pubnon, pubnonce_others);
-    return secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64, &sec, &non, &pubnon, secp256k1_schnorr_msghash_sha256, msg32);
-}
-
-int secp256k1_schnorr_partial_combine(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char * const *sig64sin, size_t n) {
-    ARG_CHECK(sig64 != NULL);
-    ARG_CHECK(n >= 1);
-    ARG_CHECK(sig64sin != NULL);
-    return secp256k1_schnorr_sig_combine(sig64, n, sig64sin);
-}
-
-#endif

src/secp256k1/src/modules/schnorr/schnorr.h

@@ -1,20 +0,0 @@
-/***********************************************************************
- * Copyright (c) 2014-2015 Pieter Wuille                               *
- * Distributed under the MIT software license, see the accompanying    *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php. *
- ***********************************************************************/
-
-#ifndef _SECP256K1_MODULE_SCHNORR_H_
-#define _SECP256K1_MODULE_SCHNORR_H_
-
-#include "scalar.h"
-#include "group.h"
-
-typedef void (*secp256k1_schnorr_msghash)(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32);
-
-static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
-static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
-static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32);
-static int secp256k1_schnorr_sig_combine(unsigned char *sig64, size_t n, const unsigned char * const *sig64ins);
-
-#endif

src/secp256k1/src/modules/schnorr/schnorr_impl.h

@@ -1,207 +0,0 @@
-/***********************************************************************
- * Copyright (c) 2014-2015 Pieter Wuille                               *
- * Distributed under the MIT software license, see the accompanying    *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php. *
- ***********************************************************************/
-
-#ifndef _SECP256K1_SCHNORR_IMPL_H_
-#define _SECP256K1_SCHNORR_IMPL_H_
-
-#include <string.h>
-
-#include "schnorr.h"
-#include "num.h"
-#include "field.h"
-#include "group.h"
-#include "ecmult.h"
-#include "ecmult_gen.h"
-
-/**
- * Custom Schnorr-based signature scheme. They support multiparty signing, public key
- * recovery and batch validation.
- *
- * Rationale for verifying R's y coordinate:
- * In order to support batch validation and public key recovery, the full R point must
- * be known to verifiers, rather than just its x coordinate. In order to not risk
- * being more strict in batch validation than normal validation, validators must be
- * required to reject signatures with incorrect y coordinate. This is only possible
- * by including a (relatively slow) field inverse, or a field square root. However,
- * batch validation offers potentially much higher benefits than this cost.
- *
- * Rationale for having an implicit y coordinate oddness:
- * If we commit to having the full R point known to verifiers, there are two mechanism.
- * Either include its oddness in the signature, or give it an implicit fixed value.
- * As the R y coordinate can be flipped by a simple negation of the nonce, we choose the
- * latter, as it comes with nearly zero impact on signing or validation performance, and
- * saves a byte in the signature.
- *
- * Signing:
- *   Inputs: 32-byte message m, 32-byte scalar key x (!=0), 32-byte scalar nonce k (!=0)
- *
- *   Compute point R = k * G. Reject nonce if R's y coordinate is odd (or negate nonce).
- *   Compute 32-byte r, the serialization of R's x coordinate.
- *   Compute scalar h = Hash(r || m). Reject nonce if h == 0 or h >= order.
- *   Compute scalar s = k - h * x.
- *   The signature is (r, s).
- *
- *
- * Verification:
- *   Inputs: 32-byte message m, public key point Q, signature: (32-byte r, scalar s)
- *
- *   Signature is invalid if s >= order.
- *   Signature is invalid if r >= p.
- *   Compute scalar h = Hash(r || m). Signature is invalid if h == 0 or h >= order.
- *   Option 1 (faster for single verification):
- *     Compute point R = h * Q + s * G. Signature is invalid if R is infinity or R's y coordinate is odd.
- *     Signature is valid if the serialization of R's x coordinate equals r.
- *   Option 2 (allows batch validation and pubkey recovery):
- *     Decompress x coordinate r into point R, with odd y coordinate. Fail if R is not on the curve.
- *     Signature is valid if R + h * Q + s * G == 0.
- */
-
-static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context* ctx, unsigned char *sig64, const secp256k1_scalar *key, const secp256k1_scalar *nonce, const secp256k1_ge *pubnonce, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
-    secp256k1_gej Rj;
-    secp256k1_ge Ra;
-    unsigned char h32[32];
-    secp256k1_scalar h, s;
-    int overflow;
-    secp256k1_scalar n;
-
-    if (secp256k1_scalar_is_zero(key) || secp256k1_scalar_is_zero(nonce)) {
-        return 0;
-    }
-    n = *nonce;
-
-    secp256k1_ecmult_gen(ctx, &Rj, &n);
-    if (pubnonce != NULL) {
-        secp256k1_gej_add_ge(&Rj, &Rj, pubnonce);
-    }
-    secp256k1_ge_set_gej(&Ra, &Rj);
-    secp256k1_fe_normalize(&Ra.y);
-    if (secp256k1_fe_is_odd(&Ra.y)) {
-        /* R's y coordinate is odd, which is not allowed (see rationale above).
-           Force it to be even by negating the nonce. Note that this even works
-           for multiparty signing, as the R point is known to all participants,
-           which can all decide to flip the sign in unison, resulting in the
-           overall R point to be negated too. */
-        secp256k1_scalar_negate(&n, &n);
-    }
-    secp256k1_fe_normalize(&Ra.x);
-    secp256k1_fe_get_b32(sig64, &Ra.x);
-    hash(h32, sig64, msg32);
-    overflow = 0;
-    secp256k1_scalar_set_b32(&h, h32, &overflow);
-    if (overflow || secp256k1_scalar_is_zero(&h)) {
-        secp256k1_scalar_clear(&n);
-        return 0;
-    }
-    secp256k1_scalar_mul(&s, &h, key);
-    secp256k1_scalar_negate(&s, &s);
-    secp256k1_scalar_add(&s, &s, &n);
-    secp256k1_scalar_clear(&n);
-    secp256k1_scalar_get_b32(sig64 + 32, &s);
-    return 1;
-}
-
-static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, const secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
-    secp256k1_gej Qj, Rj;
-    secp256k1_ge Ra;
-    secp256k1_fe Rx;
-    secp256k1_scalar h, s;
-    unsigned char hh[32];
-    int overflow;
-
-    if (secp256k1_ge_is_infinity(pubkey)) {
-        return 0;
-    }
-    hash(hh, sig64, msg32);
-    overflow = 0;
-    secp256k1_scalar_set_b32(&h, hh, &overflow);
-    if (overflow || secp256k1_scalar_is_zero(&h)) {
-        return 0;
-    }
-    overflow = 0;
-    secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
-    if (overflow) {
-        return 0;
-    }
-    if (!secp256k1_fe_set_b32(&Rx, sig64)) {
-        return 0;
-    }
-    secp256k1_gej_set_ge(&Qj, pubkey);
-    secp256k1_ecmult(ctx, &Rj, &Qj, &h, &s);
-    if (secp256k1_gej_is_infinity(&Rj)) {
-        return 0;
-    }
-    secp256k1_ge_set_gej_var(&Ra, &Rj);
-    secp256k1_fe_normalize_var(&Ra.y);
-    if (secp256k1_fe_is_odd(&Ra.y)) {
-        return 0;
-    }
-    return secp256k1_fe_equal_var(&Rx, &Ra.x);
-}
-
-static int secp256k1_schnorr_sig_recover(const secp256k1_ecmult_context* ctx, const unsigned char *sig64, secp256k1_ge *pubkey, secp256k1_schnorr_msghash hash, const unsigned char *msg32) {
-    secp256k1_gej Qj, Rj;
-    secp256k1_ge Ra;
-    secp256k1_fe Rx;
-    secp256k1_scalar h, s;
-    unsigned char hh[32];
-    int overflow;
-
-    hash(hh, sig64, msg32);
-    overflow = 0;
-    secp256k1_scalar_set_b32(&h, hh, &overflow);
-    if (overflow || secp256k1_scalar_is_zero(&h)) {
-        return 0;
-    }
-    overflow = 0;
-    secp256k1_scalar_set_b32(&s, sig64 + 32, &overflow);
-    if (overflow) {
-        return 0;
-    }
-    if (!secp256k1_fe_set_b32(&Rx, sig64)) {
-        return 0;
-    }
-    if (!secp256k1_ge_set_xo_var(&Ra, &Rx, 0)) {
-        return 0;
-    }
-    secp256k1_gej_set_ge(&Rj, &Ra);
-    secp256k1_scalar_inverse_var(&h, &h);
-    secp256k1_scalar_negate(&s, &s);
-    secp256k1_scalar_mul(&s, &s, &h);
-    secp256k1_ecmult(ctx, &Qj, &Rj, &h, &s);
-    if (secp256k1_gej_is_infinity(&Qj)) {
-        return 0;
-    }
-    secp256k1_ge_set_gej(pubkey, &Qj);
-    return 1;
-}
-
-static int secp256k1_schnorr_sig_combine(unsigned char *sig64, size_t n, const unsigned char * const *sig64ins) {
-    secp256k1_scalar s = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
-    size_t i;
-    for (i = 0; i < n; i++) {
-        secp256k1_scalar si;
-        int overflow;
-        secp256k1_scalar_set_b32(&si, sig64ins[i] + 32, &overflow);
-        if (overflow) {
-            return -1;
-        }
-        if (i) {
-            if (memcmp(sig64ins[i - 1], sig64ins[i], 32) != 0) {
-                return -1;
-            }
-        }
-        secp256k1_scalar_add(&s, &s, &si);
-    }
-    if (secp256k1_scalar_is_zero(&s)) {
-        return 0;
-    }
-    memcpy(sig64, sig64ins[0], 32);
-    secp256k1_scalar_get_b32(sig64 + 32, &s);
-    secp256k1_scalar_clear(&s);
-    return 1;
-}
-
-#endif

src/secp256k1/src/modules/schnorr/tests_impl.h

@@ -1,175 +0,0 @@
-/**********************************************************************
- * Copyright (c) 2014-2015 Pieter Wuille                              *
- * Distributed under the MIT software license, see the accompanying   *
- * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
- **********************************************************************/
-
-#ifndef SECP256K1_MODULE_SCHNORR_TESTS
-#define SECP256K1_MODULE_SCHNORR_TESTS
-
-#include "include/secp256k1_schnorr.h"
-
-void test_schnorr_end_to_end(void) {
-    unsigned char privkey[32];
-    unsigned char message[32];
-    unsigned char schnorr_signature[64];
-    secp256k1_pubkey pubkey, recpubkey;
-
-    /* Generate a random key and message. */
-    {
-        secp256k1_scalar key;
-        random_scalar_order_test(&key);
-        secp256k1_scalar_get_b32(privkey, &key);
-        secp256k1_rand256_test(message);
-    }
-
-    /* Construct and verify corresponding public key. */
-    CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
-    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
-
-    /* Schnorr sign. */
-    CHECK(secp256k1_schnorr_sign(ctx, schnorr_signature, message, privkey, NULL, NULL) == 1);
-    CHECK(secp256k1_schnorr_verify(ctx, schnorr_signature, message, &pubkey) == 1);
-    CHECK(secp256k1_schnorr_recover(ctx, &recpubkey, schnorr_signature, message) == 1);
-    CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0);
-    /* Destroy signature and verify again. */
-    schnorr_signature[secp256k1_rand_bits(6)] += 1 + secp256k1_rand_int(255);
-    CHECK(secp256k1_schnorr_verify(ctx, schnorr_signature, message, &pubkey) == 0);
-    CHECK(secp256k1_schnorr_recover(ctx, &recpubkey, schnorr_signature, message) != 1 ||
-          memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0);
-}
-
-/** Horribly broken hash function. Do not use for anything but tests. */
-void test_schnorr_hash(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32) {
-    int i;
-    for (i = 0; i < 32; i++) {
-        h32[i] = r32[i] ^ msg32[i];
-    }
-}
-
-void test_schnorr_sign_verify(void) {
-    unsigned char msg32[32];
-    unsigned char sig64[3][64];
-    secp256k1_gej pubkeyj[3];
-    secp256k1_ge pubkey[3];
-    secp256k1_scalar nonce[3], key[3];
-    int i = 0;
-    int k;
-
-    secp256k1_rand256_test(msg32);
-
-    for (k = 0; k < 3; k++) {
-        random_scalar_order_test(&key[k]);
-
-        do {
-            random_scalar_order_test(&nonce[k]);
-            if (secp256k1_schnorr_sig_sign(&ctx->ecmult_gen_ctx, sig64[k], &key[k], &nonce[k], NULL, &test_schnorr_hash, msg32)) {
-                break;
-            }
-        } while(1);
-
-        secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubkeyj[k], &key[k]);
-        secp256k1_ge_set_gej_var(&pubkey[k], &pubkeyj[k]);
-        CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64[k], &pubkey[k], &test_schnorr_hash, msg32));
-
-        for (i = 0; i < 4; i++) {
-            int pos = secp256k1_rand_bits(6);
-            int mod = 1 + secp256k1_rand_int(255);
-            sig64[k][pos] ^= mod;
-            CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64[k], &pubkey[k], &test_schnorr_hash, msg32) == 0);
-            sig64[k][pos] ^= mod;
-        }
-    }
-}
-
-void test_schnorr_threshold(void) {
-    unsigned char msg[32];
-    unsigned char sec[5][32];
-    secp256k1_pubkey pub[5];
-    unsigned char nonce[5][32];
-    secp256k1_pubkey pubnonce[5];
-    unsigned char sig[5][64];
-    const unsigned char* sigs[5];
-    unsigned char allsig[64];
-    const secp256k1_pubkey* pubs[5];
-    secp256k1_pubkey allpub;
-    int n, i;
-    int damage;
-    int ret = 0;
-
-    damage = secp256k1_rand_bits(1) ? (1 + secp256k1_rand_int(4)) : 0;
-    secp256k1_rand256_test(msg);
-    n = 2 + secp256k1_rand_int(4);
-    for (i = 0; i < n; i++) {
-        do {
-            secp256k1_rand256_test(sec[i]);
-        } while (!secp256k1_ec_seckey_verify(ctx, sec[i]));
-        CHECK(secp256k1_ec_pubkey_create(ctx, &pub[i], sec[i]));
-        CHECK(secp256k1_schnorr_generate_nonce_pair(ctx, &pubnonce[i], nonce[i], msg, sec[i], NULL, NULL));
-        pubs[i] = &pub[i];
-    }
-    if (damage == 1) {
-        nonce[secp256k1_rand_int(n)][secp256k1_rand_int(32)] ^= 1 + secp256k1_rand_int(255);
-    } else if (damage == 2) {
-        sec[secp256k1_rand_int(n)][secp256k1_rand_int(32)] ^= 1 + secp256k1_rand_int(255);
-    }
-    for (i = 0; i < n; i++) {
-        secp256k1_pubkey allpubnonce;
-        const secp256k1_pubkey *pubnonces[4];
-        int j;
-        for (j = 0; j < i; j++) {
-            pubnonces[j] = &pubnonce[j];
-        }
-        for (j = i + 1; j < n; j++) {
-            pubnonces[j - 1] = &pubnonce[j];
-        }
-        CHECK(secp256k1_ec_pubkey_combine(ctx, &allpubnonce, pubnonces, n - 1));
-        ret |= (secp256k1_schnorr_partial_sign(ctx, sig[i], msg, sec[i], &allpubnonce, nonce[i]) != 1) * 1;
-        sigs[i] = sig[i];
-    }
-    if (damage == 3) {
-        sig[secp256k1_rand_int(n)][secp256k1_rand_bits(6)] ^= 1 + secp256k1_rand_int(255);
-    }
-    ret |= (secp256k1_ec_pubkey_combine(ctx, &allpub, pubs, n) != 1) * 2;
-    if ((ret & 1) == 0) {
-        ret |= (secp256k1_schnorr_partial_combine(ctx, allsig, sigs, n) != 1) * 4;
-    }
-    if (damage == 4) {
-        allsig[secp256k1_rand_int(32)] ^= 1 + secp256k1_rand_int(255);
-    }
-    if ((ret & 7) == 0) {
-        ret |= (secp256k1_schnorr_verify(ctx, allsig, msg, &allpub) != 1) * 8;
-    }
-    CHECK((ret == 0) == (damage == 0));
-}
-
-void test_schnorr_recovery(void) {
-    unsigned char msg32[32];
-    unsigned char sig64[64];
-    secp256k1_ge Q;
-
-    secp256k1_rand256_test(msg32);
-    secp256k1_rand256_test(sig64);
-    secp256k1_rand256_test(sig64 + 32);
-    if (secp256k1_schnorr_sig_recover(&ctx->ecmult_ctx, sig64, &Q, &test_schnorr_hash, msg32) == 1) {
-        CHECK(secp256k1_schnorr_sig_verify(&ctx->ecmult_ctx, sig64, &Q, &test_schnorr_hash, msg32) == 1);
-    }
-}
-
-void run_schnorr_tests(void) {
-    int i;
-    for (i = 0; i < 32*count; i++) {
-        test_schnorr_end_to_end();
-    }
-    for (i = 0; i < 32 * count; i++) {
-         test_schnorr_sign_verify();
-    }
-    for (i = 0; i < 16 * count; i++) {
-         test_schnorr_recovery();
-    }
-    for (i = 0; i < 10 * count; i++) {
-         test_schnorr_threshold();
-    }
-}
-
-#endif

src/secp256k1/src/scalar.h

@@ -13,7 +13,9 @@
 #include "libsecp256k1-config.h"
 #endif
 
-#if defined(USE_SCALAR_4X64)
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low.h"
+#elif defined(USE_SCALAR_4X64)
 #include "scalar_4x64.h"
 #elif defined(USE_SCALAR_8X32)
 #include "scalar_8x32.h"

src/secp256k1/src/scalar_4x64_impl.h

@@ -282,8 +282,8 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "movq 56(%%rsi), %%r14\n"
     /* Initialize r8,r9,r10 */
     "movq 0(%%rsi), %%r8\n"
-    "movq $0, %%r9\n"
-    "movq $0, %%r10\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
     /* (r8,r9) += n0 * c0 */
     "movq %8, %%rax\n"
     "mulq %%r11\n"
@@ -291,7 +291,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq %%rdx, %%r9\n"
     /* extract m0 */
     "movq %%r8, %q0\n"
-    "movq $0, %%r8\n"
+    "xorq %%r8, %%r8\n"
     /* (r9,r10) += l1 */
     "addq 8(%%rsi), %%r9\n"
     "adcq $0, %%r10\n"
@@ -309,7 +309,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r8\n"
     /* extract m1 */
     "movq %%r9, %q1\n"
-    "movq $0, %%r9\n"
+    "xorq %%r9, %%r9\n"
     /* (r10,r8,r9) += l2 */
     "addq 16(%%rsi), %%r10\n"
     "adcq $0, %%r8\n"
@@ -332,7 +332,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r9\n"
     /* extract m2 */
     "movq %%r10, %q2\n"
-    "movq $0, %%r10\n"
+    "xorq %%r10, %%r10\n"
     /* (r8,r9,r10) += l3 */
     "addq 24(%%rsi), %%r8\n"
     "adcq $0, %%r9\n"
@@ -355,7 +355,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r10\n"
     /* extract m3 */
     "movq %%r8, %q3\n"
-    "movq $0, %%r8\n"
+    "xorq %%r8, %%r8\n"
     /* (r9,r10,r8) += n3 * c1 */
     "movq %9, %%rax\n"
     "mulq %%r14\n"
@@ -387,8 +387,8 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "movq %q11, %%r13\n"
     /* Initialize (r8,r9,r10) */
     "movq %q5, %%r8\n"
-    "movq $0, %%r9\n"
-    "movq $0, %%r10\n"
+    "xorq %%r9, %%r9\n"
+    "xorq %%r10, %%r10\n"
     /* (r8,r9) += m4 * c0 */
     "movq %12, %%rax\n"
     "mulq %%r11\n"
@@ -396,7 +396,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq %%rdx, %%r9\n"
     /* extract p0 */
     "movq %%r8, %q0\n"
-    "movq $0, %%r8\n"
+    "xorq %%r8, %%r8\n"
     /* (r9,r10) += m1 */
     "addq %q6, %%r9\n"
     "adcq $0, %%r10\n"
@@ -414,7 +414,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r8\n"
     /* extract p1 */
     "movq %%r9, %q1\n"
-    "movq $0, %%r9\n"
+    "xorq %%r9, %%r9\n"
     /* (r10,r8,r9) += m2 */
     "addq %q7, %%r10\n"
     "adcq $0, %%r8\n"
@@ -472,7 +472,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "movq %%rax, 0(%q6)\n"
     /* Move to (r8,r9) */
     "movq %%rdx, %%r8\n"
-    "movq $0, %%r9\n"
+    "xorq %%r9, %%r9\n"
     /* (r8,r9) += p1 */
     "addq %q2, %%r8\n"
     "adcq $0, %%r9\n"
@@ -483,7 +483,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq %%rdx, %%r9\n"
     /* Extract r1 */
     "movq %%r8, 8(%q6)\n"
-    "movq $0, %%r8\n"
+    "xorq %%r8, %%r8\n"
     /* (r9,r8) += p4 */
     "addq %%r10, %%r9\n"
     "adcq $0, %%r8\n"
@@ -492,7 +492,7 @@ static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l)
     "adcq $0, %%r8\n"
     /* Extract r2 */
     "movq %%r9, 16(%q6)\n"
-    "movq $0, %%r9\n"
+    "xorq %%r9, %%r9\n"
     /* (r8,r9) += p3 */
     "addq %q4, %%r8\n"
     "adcq $0, %%r9\n"

src/secp256k1/src/scalar_impl.h

@@ -14,7 +14,9 @@
 #include "libsecp256k1-config.h"
 #endif
 
-#if defined(USE_SCALAR_4X64)
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low_impl.h"
+#elif defined(USE_SCALAR_4X64)
 #include "scalar_4x64_impl.h"
 #elif defined(USE_SCALAR_8X32)
 #include "scalar_8x32_impl.h"
@@ -31,17 +33,37 @@ static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a
 
 /** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
 static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    static const unsigned char order[32] = {
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER
+    };
+#else
     static const unsigned char order[32] = {
         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
         0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
         0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
         0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
     };
+#endif
     secp256k1_num_set_bin(r, order, 32);
 }
 #endif
 
 static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    int i;
+    *r = 0;
+    for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++)
+        if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1)
+            *r = i;
+    /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus
+     * have a composite group order; fix it in exhaustive_tests.c). */
+    VERIFY_CHECK(*r != 0);
+}
+#else
     secp256k1_scalar *t;
     int i;
     /* First compute x ^ (2^N - 1) for some values of N. */
@@ -233,9 +255,9 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
 }
 
 SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
-    /* d[0] is present and is the lowest word for all representations */
     return !(a->d[0] & 1);
 }
+#endif
 
 static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
 #if defined(USE_SCALAR_INV_BUILTIN)
@@ -259,6 +281,18 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_sc
 }
 
 #ifdef USE_ENDOMORPHISM
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/**
+ * Find k1 and k2 given k, such that k1 + k2 * lambda == k mod n; unlike in the
+ * full case we don't bother making k1 and k2 be small, we just want them to be
+ * nontrivial to get full test coverage for the exhaustive tests. We therefore
+ * (arbitrarily) set k2 = k + 5 and k1 = k - k2 * lambda.
+ */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r2 = (*a + 5) % EXHAUSTIVE_TEST_ORDER;
+    *r1 = (*a + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER;
+}
+#else
 /**
  * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
  * lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
@@ -331,5 +365,6 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar
     secp256k1_scalar_add(r1, r1, a);
 }
 #endif
+#endif
 
 #endif

src/secp256k1/src/scalar_low.h

@@ -0,0 +1,15 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_REPR_
+#define _SECP256K1_SCALAR_REPR_
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef uint32_t secp256k1_scalar;
+
+#endif

src/secp256k1/src/scalar_low_impl.h

@@ -0,0 +1,114 @@
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCALAR_REPR_IMPL_H_
+#define _SECP256K1_SCALAR_REPR_IMPL_H_
+
+#include "scalar.h"
+
+#include <string.h>
+
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    return !(*a & 1);
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { *r = 0; }
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { *r = v; }
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    if (offset < 32)
+        return ((*a >> offset) & ((((uint32_t)1) << count) - 1));
+    else
+        return 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    return secp256k1_scalar_get_bits(a, offset, count);
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { return *a >= EXHAUSTIVE_TEST_ORDER; }
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a + *b) % EXHAUSTIVE_TEST_ORDER;
+    return *r < *b;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    if (flag && bit < 32)
+        *r += (1 << bit);
+#ifdef VERIFY
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    const int base = 0x100 % EXHAUSTIVE_TEST_ORDER;
+    int i;
+    *r = 0;
+    for (i = 0; i < 32; i++) {
+       *r = ((*r * base) + b32[i]) % EXHAUSTIVE_TEST_ORDER;
+    }
+    /* just deny overflow, it basically always happens */
+    if (overflow) *overflow = 0;
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    memset(bin, 0, 32);
+    bin[28] = *a >> 24; bin[29] = *a >> 16; bin[30] = *a >> 8; bin[31] = *a;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return *a == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    if (*a == 0) {
+        *r = 0;
+    } else {
+        *r = EXHAUSTIVE_TEST_ORDER - *a;
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return *a == 1;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    return *a > EXHAUSTIVE_TEST_ORDER / 2;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    if (flag) secp256k1_scalar_negate(r, r);
+    return flag ? -1 : 1;
+}
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a * *b) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = *r & ((1 << n) - 1);
+    *r >>= n;
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    *r = (*a * *a) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r1 = *a;
+    *r2 = 0;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return *a == *b;
+}
+
+#endif

src/secp256k1/src/secp256k1.c

@@ -359,16 +359,15 @@ int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature
     secp256k1_scalar_set_b32(&sec, seckey, &overflow);
     /* Fail if the secret key is invalid. */
     if (!overflow && !secp256k1_scalar_is_zero(&sec)) {
+        unsigned char nonce32[32];
         unsigned int count = 0;
         secp256k1_scalar_set_b32(&msg, msg32, NULL);
         while (1) {
-            unsigned char nonce32[32];
             ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count);
             if (!ret) {
                 break;
             }
             secp256k1_scalar_set_b32(&non, nonce32, &overflow);
-            memset(nonce32, 0, 32);
             if (!overflow && !secp256k1_scalar_is_zero(&non)) {
                 if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL)) {
                     break;
@@ -376,6 +375,7 @@ int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature
             }
             count++;
         }
+        memset(nonce32, 0, 32);
         secp256k1_scalar_clear(&msg);
         secp256k1_scalar_clear(&non);
         secp256k1_scalar_clear(&sec);

src/secp256k1/src/tests.c

@@ -520,7 +520,7 @@ void test_num_mod(void) {
     secp256k1_num order, n;
 
     /* check that 0 mod anything is 0 */
-    random_scalar_order_test(&s); 
+    random_scalar_order_test(&s);
     secp256k1_scalar_get_num(&order, &s);
     secp256k1_scalar_set_int(&s, 0);
     secp256k1_scalar_get_num(&n, &s);
@@ -535,7 +535,7 @@ void test_num_mod(void) {
     CHECK(secp256k1_num_is_zero(&n));
 
     /* check that increasing the number past 2^256 does not break this */
-    random_scalar_order_test(&s); 
+    random_scalar_order_test(&s);
     secp256k1_scalar_get_num(&n, &s);
     /* multiply by 2^8, which'll test this case with high probability */
     for (i = 0; i < 8; ++i) {
@@ -568,7 +568,7 @@ void test_num_jacobi(void) {
     /* we first need a scalar which is not a multiple of 5 */
     do {
         secp256k1_num fiven;
-        random_scalar_order_test(&sqr); 
+        random_scalar_order_test(&sqr);
         secp256k1_scalar_get_num(&fiven, &five);
         secp256k1_scalar_get_num(&n, &sqr);
         secp256k1_num_mod(&n, &fiven);
@@ -587,7 +587,7 @@ void test_num_jacobi(void) {
 
     /** test with secp group order as order */
     secp256k1_scalar_order_get_num(&order);
-    random_scalar_order_test(&sqr); 
+    random_scalar_order_test(&sqr);
     secp256k1_scalar_sqr(&sqr, &sqr);
     /* test residue */
     secp256k1_scalar_get_num(&n, &sqr);
@@ -1733,18 +1733,18 @@ void run_field_inv_all_var(void) {
     secp256k1_fe x[16], xi[16], xii[16];
     int i;
     /* Check it's safe to call for 0 elements */
-    secp256k1_fe_inv_all_var(0, xi, x);
+    secp256k1_fe_inv_all_var(xi, x, 0);
     for (i = 0; i < count; i++) {
         size_t j;
         size_t len = secp256k1_rand_int(15) + 1;
         for (j = 0; j < len; j++) {
             random_fe_non_zero(&x[j]);
         }
-        secp256k1_fe_inv_all_var(len, xi, x);
+        secp256k1_fe_inv_all_var(xi, x, len);
         for (j = 0; j < len; j++) {
             CHECK(check_fe_inverse(&x[j], &xi[j]));
         }
-        secp256k1_fe_inv_all_var(len, xii, xi);
+        secp256k1_fe_inv_all_var(xii, xi, len);
         for (j = 0; j < len; j++) {
             CHECK(check_fe_equal(&x[j], &xii[j]));
         }
@@ -1930,7 +1930,7 @@ void test_ge(void) {
                 zs[i] = gej[i].z;
             }
         }
-        secp256k1_fe_inv_all_var(4 * runs + 1, zinv, zs);
+        secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1);
         free(zs);
     }
 
@@ -2050,8 +2050,8 @@ void test_ge(void) {
                 secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z);
             }
         }
-        secp256k1_ge_set_table_gej_var(4 * runs + 1, ge_set_table, gej, zr);
-        secp256k1_ge_set_all_gej_var(4 * runs + 1, ge_set_all, gej, &ctx->error_callback);
+        secp256k1_ge_set_table_gej_var(ge_set_table, gej, zr, 4 * runs + 1);
+        secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1, &ctx->error_callback);
         for (i = 0; i < 4 * runs + 1; i++) {
             secp256k1_fe s;
             random_fe_non_zero(&s);

src/secp256k1/src/tests_exhaustive.c

@@ -0,0 +1,329 @@
+/***********************************************************************
+ * Copyright (c) 2016 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <time.h>
+
+#undef USE_ECMULT_STATIC_PRECOMPUTATION
+
+#ifndef EXHAUSTIVE_TEST_ORDER
+/* see group_impl.h for allowable values */
+#define EXHAUSTIVE_TEST_ORDER 13
+#define EXHAUSTIVE_TEST_LAMBDA 9   /* cube root of 1 mod 13 */
+#endif
+
+#include "include/secp256k1.h"
+#include "group.h"
+#include "secp256k1.c"
+#include "testrand_impl.h"
+
+/** stolen from tests.c */
+void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
+    CHECK(a->infinity == b->infinity);
+    if (a->infinity) {
+        return;
+    }
+    CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
+    CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
+}
+
+void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
+    secp256k1_fe z2s;
+    secp256k1_fe u1, u2, s1, s2;
+    CHECK(a->infinity == b->infinity);
+    if (a->infinity) {
+        return;
+    }
+    /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
+    secp256k1_fe_sqr(&z2s, &b->z);
+    secp256k1_fe_mul(&u1, &a->x, &z2s);
+    u2 = b->x; secp256k1_fe_normalize_weak(&u2);
+    secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
+    s2 = b->y; secp256k1_fe_normalize_weak(&s2);
+    CHECK(secp256k1_fe_equal_var(&u1, &u2));
+    CHECK(secp256k1_fe_equal_var(&s1, &s2));
+}
+
+void random_fe(secp256k1_fe *x) {
+    unsigned char bin[32];
+    do {
+        secp256k1_rand256(bin);
+        if (secp256k1_fe_set_b32(x, bin)) {
+            return;
+        }
+    } while(1);
+}
+/** END stolen from tests.c */
+
+int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32,
+                                      const unsigned char *key32, const unsigned char *algo16,
+                                      void *data, unsigned int attempt) {
+    secp256k1_scalar s;
+    int *idata = data;
+    (void)msg32;
+    (void)key32;
+    (void)algo16;
+    /* Some nonces cannot be used because they'd cause s and/or r to be zero.
+     * The signing function has retry logic here that just re-calls the nonce
+     * function with an increased `attempt`. So if attempt > 0 this means we
+     * need to change the nonce to avoid an infinite loop. */
+    if (attempt > 0) {
+        (*idata)++;
+    }
+    secp256k1_scalar_set_int(&s, *idata);
+    secp256k1_scalar_get_b32(nonce32, &s);
+    return 1;
+}
+
+#ifdef USE_ENDOMORPHISM
+void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) {
+    int i;
+    for (i = 0; i < order; i++) {
+        secp256k1_ge res;
+        secp256k1_ge_mul_lambda(&res, &group[i]);
+        ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res);
+    }
+}
+#endif
+
+void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
+    int i, j;
+
+    /* Sanity-check (and check infinity functions) */
+    CHECK(secp256k1_ge_is_infinity(&group[0]));
+    CHECK(secp256k1_gej_is_infinity(&groupj[0]));
+    for (i = 1; i < order; i++) {
+        CHECK(!secp256k1_ge_is_infinity(&group[i]));
+        CHECK(!secp256k1_gej_is_infinity(&groupj[i]));
+    }
+
+    /* Check all addition formulae */
+    for (j = 0; j < order; j++) {