Merge #310: Add exhaustive test for group functions on a low-order subgroup
b4ceedfAdd exhaustive test for verification (Andrew Poelstra)83836a9Add exhaustive tests for group arithmetic, signing, and ecmult on a small group (Andrew Poelstra)20b8877Add exhaustive test for group functions on a low-order subgroup (Andrew Poelstra)
This commit is contained in:
Pieter Wuille
commit
a8abae7e5f
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@ -6,6 +6,7 @@ bench_schnorr_verify
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bench_recover
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bench_internal
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tests
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exhaustive_tests
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gen_context
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*.exe
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*.so
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14
Makefile.am
14
Makefile.am
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@ -12,9 +12,11 @@ noinst_HEADERS =
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noinst_HEADERS += src/scalar.h
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noinst_HEADERS += src/scalar_4x64.h
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noinst_HEADERS += src/scalar_8x32.h
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noinst_HEADERS += src/scalar_low.h
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noinst_HEADERS += src/scalar_impl.h
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noinst_HEADERS += src/scalar_4x64_impl.h
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noinst_HEADERS += src/scalar_8x32_impl.h
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noinst_HEADERS += src/scalar_low_impl.h
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noinst_HEADERS += src/group.h
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noinst_HEADERS += src/group_impl.h
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noinst_HEADERS += src/num_gmp.h
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@ -87,13 +89,23 @@ bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB)
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bench_internal_CPPFLAGS = -DSECP256K1_BUILD $(SECP_INCLUDES)
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endif
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TESTS =
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if USE_TESTS
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noinst_PROGRAMS += tests
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tests_SOURCES = src/tests.c
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tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES)
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tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB)
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tests_LDFLAGS = -static
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TESTS = tests
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TESTS += tests
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endif
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if USE_EXHAUSTIVE_TESTS
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noinst_PROGRAMS += exhaustive_tests
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exhaustive_tests_SOURCES = src/tests_exhaustive.c
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exhaustive_tests_CPPFLAGS = -DSECP256K1_BUILD -DVERIFY -I$(top_srcdir)/src $(SECP_INCLUDES)
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exhaustive_tests_LDADD = $(SECP_LIBS)
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exhaustive_tests_LDFLAGS = -static
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TESTS += exhaustive_tests
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endif
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JAVAROOT=src/java
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@ -104,6 +104,11 @@ AC_ARG_ENABLE(experimental,
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[use_experimental=$enableval],
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[use_experimental=no])
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AC_ARG_ENABLE(exhaustive_tests,
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AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests (default is yes)]),
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[use_exhaustive_tests=$enableval],
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[use_exhaustive_tests=yes])
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AC_ARG_ENABLE(endomorphism,
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AS_HELP_STRING([--enable-endomorphism],[enable endomorphism (default is no)]),
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[use_endomorphism=$enableval],
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@ -456,6 +461,7 @@ AC_SUBST(SECP_LIBS)
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AC_SUBST(SECP_TEST_LIBS)
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AC_SUBST(SECP_TEST_INCLUDES)
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AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"])
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AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$use_exhaustive_tests" != x"no"])
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AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"])
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AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$set_precomp" = x"yes"])
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AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"])
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@ -203,7 +203,9 @@ static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const
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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) {
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unsigned char c[32];
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secp256k1_scalar sn, u1, u2;
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#if !defined(EXHAUSTIVE_TEST_ORDER)
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secp256k1_fe xr;
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#endif
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secp256k1_gej pubkeyj;
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secp256k1_gej pr;
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@ -219,6 +221,21 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
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if (secp256k1_gej_is_infinity(&pr)) {
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return 0;
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}
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#if defined(EXHAUSTIVE_TEST_ORDER)
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{
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secp256k1_scalar computed_r;
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int overflow = 0;
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secp256k1_ge pr_ge;
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secp256k1_ge_set_gej(&pr_ge, &pr);
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secp256k1_fe_normalize(&pr_ge.x);
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secp256k1_fe_get_b32(c, &pr_ge.x);
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secp256k1_scalar_set_b32(&computed_r, c, &overflow);
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/* we fully expect overflow */
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return secp256k1_scalar_eq(sigr, &computed_r);
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}
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#else
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secp256k1_scalar_get_b32(c, sigr);
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secp256k1_fe_set_b32(&xr, c);
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@ -252,6 +269,7 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const
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return 1;
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}
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return 0;
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#endif
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}
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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) {
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@ -78,7 +78,7 @@ static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
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/* Negative numbers will be negated to keep their bit representation below the maximum width */
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flip = secp256k1_scalar_is_high(&s);
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/* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
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bit = flip ^ (s.d[0] & 1);
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bit = flip ^ !secp256k1_scalar_is_even(&s);
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/* We check for negative one, since adding 2 to it will cause an overflow */
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secp256k1_scalar_negate(&neg_s, &s);
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not_neg_one = !secp256k1_scalar_is_one(&neg_s);
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@ -7,15 +7,29 @@
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#ifndef _SECP256K1_ECMULT_IMPL_H_
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#define _SECP256K1_ECMULT_IMPL_H_
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#include <string.h>
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#include "group.h"
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#include "scalar.h"
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#include "ecmult.h"
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#include <string.h>
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#if defined(EXHAUSTIVE_TEST_ORDER)
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/* We need to lower these values for exhaustive tests because
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* the tables cannot have infinities in them (this breaks the
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* affine-isomorphism stuff which tracks z-ratios) */
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# if EXHAUSTIVE_TEST_ORDER > 128
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# define WINDOW_A 5
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# define WINDOW_G 8
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# elif EXHAUSTIVE_TEST_ORDER > 8
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# define WINDOW_A 4
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# define WINDOW_G 4
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# else
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# define WINDOW_A 2
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# define WINDOW_G 2
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# endif
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#else
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/* optimal for 128-bit and 256-bit exponents. */
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#define WINDOW_A 5
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/** larger numbers may result in slightly better performance, at the cost of
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exponentially larger precomputed tables. */
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#ifdef USE_ENDOMORPHISM
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@ -25,6 +39,7 @@
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/** One table for window size 16: 1.375 MiB. */
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#define WINDOW_G 16
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#endif
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#endif
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/** The number of entries a table with precomputed multiples needs to have. */
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#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
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@ -30,6 +30,8 @@
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#error "Please select field implementation"
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#endif
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#include "util.h"
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/** Normalize a field element. */
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static void secp256k1_fe_normalize(secp256k1_fe *r);
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@ -50,6 +52,9 @@ static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
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/** Set a field element equal to a small integer. Resulting field element is normalized. */
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static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
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/** Sets a field element equal to zero, initializing all fields. */
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static void secp256k1_fe_clear(secp256k1_fe *a);
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/** Verify whether a field element is zero. Requires the input to be normalized. */
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static int secp256k1_fe_is_zero(const secp256k1_fe *a);
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@ -11,6 +11,53 @@
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#include "field.h"
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#include "group.h"
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/* These points can be generated in sage as follows:
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*
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* 0. Setup a worksheet with the following parameters.
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* b = 4 # whatever CURVE_B will be set to
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* F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
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* C = EllipticCurve ([F (0), F (b)])
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*
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* 1. Determine all the small orders available to you. (If there are
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* no satisfactory ones, go back and change b.)
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* print C.order().factor(limit=1000)
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*
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* 2. Choose an order as one of the prime factors listed in the above step.
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* (You can also multiply some to get a composite order, though the
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* tests will crash trying to invert scalars during signing.) We take a
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* random point and scale it to drop its order to the desired value.
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* There is some probability this won't work; just try again.
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* order = 199
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* P = C.random_point()
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* P = (int(P.order()) / int(order)) * P
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* assert(P.order() == order)
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*
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* 3. Print the values. You'll need to use a vim macro or something to
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* split the hex output into 4-byte chunks.
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* print "%x %x" % P.xy()
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*/
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#if defined(EXHAUSTIVE_TEST_ORDER)
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# if EXHAUSTIVE_TEST_ORDER == 199
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const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
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0xFA7CC9A7, 0x0737F2DB, 0xA749DD39, 0x2B4FB069,
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0x3B017A7D, 0xA808C2F1, 0xFB12940C, 0x9EA66C18,
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0x78AC123A, 0x5ED8AEF3, 0x8732BC91, 0x1F3A2868,
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0x48DF246C, 0x808DAE72, 0xCFE52572, 0x7F0501ED
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);
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const int CURVE_B = 4;
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# elif EXHAUSTIVE_TEST_ORDER == 13
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const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
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0xedc60018, 0xa51a786b, 0x2ea91f4d, 0x4c9416c0,
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0x9de54c3b, 0xa1316554, 0x6cf4345c, 0x7277ef15,
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0x54cb1b6b, 0xdc8c1273, 0x087844ea, 0x43f4603e,
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0x0eaf9a43, 0xf6effe55, 0x939f806d, 0x37adf8ac
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);
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const int CURVE_B = 2;
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# else
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# error No known generator for the specified exhaustive test group order.
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# endif
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#else
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/** Generator for secp256k1, value 'g' defined in
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* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
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*/
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@ -21,6 +68,9 @@ static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST(
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0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
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);
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const int CURVE_B = 7;
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#endif
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static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
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secp256k1_fe zi2;
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secp256k1_fe zi3;
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@ -145,9 +195,15 @@ static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp
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static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
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r->infinity = 1;
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secp256k1_fe_set_int(&r->x, 0);
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secp256k1_fe_set_int(&r->y, 0);
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secp256k1_fe_set_int(&r->z, 0);
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secp256k1_fe_clear(&r->x);
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secp256k1_fe_clear(&r->y);
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secp256k1_fe_clear(&r->z);
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}
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static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
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r->infinity = 1;
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secp256k1_fe_clear(&r->x);
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secp256k1_fe_clear(&r->y);
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}
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static void secp256k1_gej_clear(secp256k1_gej *r) {
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@ -169,7 +225,7 @@ static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) {
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secp256k1_fe_sqr(&x2, x);
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secp256k1_fe_mul(&x3, x, &x2);
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r->infinity = 0;
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secp256k1_fe_set_int(&c, 7);
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secp256k1_fe_set_int(&c, CURVE_B);
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secp256k1_fe_add(&c, &x3);
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return secp256k1_fe_sqrt(&r->y, &c);
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}
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@ -228,7 +284,7 @@ static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) {
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secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
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secp256k1_fe_sqr(&z2, &a->z);
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secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
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secp256k1_fe_mul_int(&z6, 7);
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secp256k1_fe_mul_int(&z6, CURVE_B);
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secp256k1_fe_add(&x3, &z6);
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secp256k1_fe_normalize_weak(&x3);
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return secp256k1_fe_equal_var(&y2, &x3);
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@ -242,7 +298,7 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
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/* y^2 = x^3 + 7 */
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secp256k1_fe_sqr(&y2, &a->y);
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secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
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secp256k1_fe_set_int(&c, 7);
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secp256k1_fe_set_int(&c, CURVE_B);
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secp256k1_fe_add(&x3, &c);
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secp256k1_fe_normalize_weak(&x3);
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return secp256k1_fe_equal_var(&y2, &x3);
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@ -13,7 +13,9 @@
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#include "libsecp256k1-config.h"
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#endif
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#if defined(USE_SCALAR_4X64)
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#if defined(EXHAUSTIVE_TEST_ORDER)
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#include "scalar_low.h"
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#elif defined(USE_SCALAR_4X64)
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#include "scalar_4x64.h"
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#elif defined(USE_SCALAR_8X32)
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#include "scalar_8x32.h"
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@ -14,7 +14,9 @@
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#include "libsecp256k1-config.h"
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#endif
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#if defined(USE_SCALAR_4X64)
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#if defined(EXHAUSTIVE_TEST_ORDER)
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#include "scalar_low_impl.h"
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#elif defined(USE_SCALAR_4X64)
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#include "scalar_4x64_impl.h"
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#elif defined(USE_SCALAR_8X32)
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#include "scalar_8x32_impl.h"
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@ -31,17 +33,37 @@ static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a
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/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
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static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
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#if defined(EXHAUSTIVE_TEST_ORDER)
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static const unsigned char order[32] = {
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0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER
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};
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#else
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static const unsigned char order[32] = {
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
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0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
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0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
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};
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#endif
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secp256k1_num_set_bin(r, order, 32);
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}
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#endif
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static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
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#if defined(EXHAUSTIVE_TEST_ORDER)
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int i;
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*r = 0;
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for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++)
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if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1)
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*r = i;
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/* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus
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* have a composite group order; fix it in exhaustive_tests.c). */
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VERIFY_CHECK(*r != 0);
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}
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#else
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secp256k1_scalar *t;
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int i;
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/* First compute x ^ (2^N - 1) for some values of N. */
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@ -233,9 +255,9 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
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}
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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
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
@ -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
|
||||
|
|
@ -0,0 +1,329 @@
|
|||
/***********************************************************************
|
||||
* Copyright (c) 2016 Andrew Poelstra *
|
||||
* Distributed under the MIT software license, see the accompanying *
|
||||
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
|
||||
**********************************************************************/
|
||||
|
||||
#if defined HAVE_CONFIG_H
|
||||
#include "libsecp256k1-config.h"
|
||||
#endif
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
|
||||
#include <time.h>
|
||||
|
||||
#undef USE_ECMULT_STATIC_PRECOMPUTATION
|
||||
|
||||
#ifndef EXHAUSTIVE_TEST_ORDER
|
||||
/* see group_impl.h for allowable values */
|
||||
#define EXHAUSTIVE_TEST_ORDER 13
|
||||
#define EXHAUSTIVE_TEST_LAMBDA 9 /* cube root of 1 mod 13 */
|
||||
#endif
|
||||
|
||||
#include "include/secp256k1.h"
|
||||
#include "group.h"
|
||||
#include "secp256k1.c"
|
||||
#include "testrand_impl.h"
|
||||
|
||||
/** stolen from tests.c */
|
||||
void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
|
||||
CHECK(a->infinity == b->infinity);
|
||||
if (a->infinity) {
|
||||
return;
|
||||
}
|
||||
CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
|
||||
CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
|
||||
}
|
||||
|
||||
void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
|
||||
secp256k1_fe z2s;
|
||||
secp256k1_fe u1, u2, s1, s2;
|
||||
CHECK(a->infinity == b->infinity);
|
||||
if (a->infinity) {
|
||||
return;
|
||||
}
|
||||
/* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
|
||||
secp256k1_fe_sqr(&z2s, &b->z);
|
||||
secp256k1_fe_mul(&u1, &a->x, &z2s);
|
||||
u2 = b->x; secp256k1_fe_normalize_weak(&u2);
|
||||
secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
|
||||
s2 = b->y; secp256k1_fe_normalize_weak(&s2);
|
||||
CHECK(secp256k1_fe_equal_var(&u1, &u2));
|
||||
CHECK(secp256k1_fe_equal_var(&s1, &s2));
|
||||
}
|
||||
|
||||
void random_fe(secp256k1_fe *x) {
|
||||
unsigned char bin[32];
|
||||
do {
|
||||
secp256k1_rand256(bin);
|
||||
if (secp256k1_fe_set_b32(x, bin)) {
|
||||
return;
|
||||
}
|
||||
} while(1);
|
||||
}
|
||||
/** END stolen from tests.c */
|
||||
|
||||
int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32,
|
||||
const unsigned char *key32, const unsigned char *algo16,
|
||||
void *data, unsigned int attempt) {
|
||||
secp256k1_scalar s;
|
||||
int *idata = data;
|
||||
(void)msg32;
|
||||
(void)key32;
|
||||
(void)algo16;
|
||||
/* Some nonces cannot be used because they'd cause s and/or r to be zero.
|
||||
* The signing function has retry logic here that just re-calls the nonce
|
||||
* function with an increased `attempt`. So if attempt > 0 this means we
|
||||
* need to change the nonce to avoid an infinite loop. */
|
||||
if (attempt > 0) {
|
||||
(*idata)++;
|
||||
}
|
||||
secp256k1_scalar_set_int(&s, *idata);
|
||||
secp256k1_scalar_get_b32(nonce32, &s);
|
||||
return 1;
|
||||
}
|
||||
|
||||
#ifdef USE_ENDOMORPHISM
|
||||
void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) {
|
||||
int i;
|
||||
for (i = 0; i < order; i++) {
|
||||
secp256k1_ge res;
|
||||
secp256k1_ge_mul_lambda(&res, &group[i]);
|
||||
ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res);
|
||||
}
|
||||
}
|
||||
#endif
|
||||
|
||||
void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
|
||||
int i, j;
|
||||
|
||||
/* Sanity-check (and check infinity functions) */
|
||||
CHECK(secp256k1_ge_is_infinity(&group[0]));
|
||||
CHECK(secp256k1_gej_is_infinity(&groupj[0]));
|
||||
for (i = 1; i < order; i++) {
|
||||
CHECK(!secp256k1_ge_is_infinity(&group[i]));
|
||||
CHECK(!secp256k1_gej_is_infinity(&groupj[i]));
|
||||
}
|
||||
|
||||
/* Check all addition formulae */
|
||||
for (j = 0; j < order; j++) {
|
||||
secp256k1_fe fe_inv;
|
||||
secp256k1_fe_inv(&fe_inv, &groupj[j].z);
|
||||
for (i = 0; i < order; i++) {
|
||||
secp256k1_ge zless_gej;
|
||||
secp256k1_gej tmp;
|
||||
/* add_var */
|
||||
secp256k1_gej_add_var(&tmp, &groupj[i], &groupj[j], NULL);
|
||||
ge_equals_gej(&group[(i + j) % order], &tmp);
|
||||
/* add_ge */
|
||||
if (j > 0) {
|
||||
secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]);
|
||||
ge_equals_gej(&group[(i + j) % order], &tmp);
|
||||
}
|
||||
/* add_ge_var */
|
||||
secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL);
|
||||
ge_equals_gej(&group[(i + j) % order], &tmp);
|
||||
/* add_zinv_var */
|
||||
zless_gej.infinity = groupj[j].infinity;
|
||||
zless_gej.x = groupj[j].x;
|
||||
zless_gej.y = groupj[j].y;
|
||||
secp256k1_gej_add_zinv_var(&tmp, &groupj[i], &zless_gej, &fe_inv);
|
||||
ge_equals_gej(&group[(i + j) % order], &tmp);
|
||||
}
|
||||
}
|
||||
|
||||
/* Check doubling */
|
||||
for (i = 0; i < order; i++) {
|
||||
secp256k1_gej tmp;
|
||||
if (i > 0) {
|
||||
secp256k1_gej_double_nonzero(&tmp, &groupj[i], NULL);
|
||||
ge_equals_gej(&group[(2 * i) % order], &tmp);
|
||||
}
|
||||
secp256k1_gej_double_var(&tmp, &groupj[i], NULL);
|
||||
ge_equals_gej(&group[(2 * i) % order], &tmp);
|
||||
}
|
||||
|
||||
/* Check negation */
|
||||
for (i = 1; i < order; i++) {
|
||||
secp256k1_ge tmp;
|
||||
secp256k1_gej tmpj;
|
||||
secp256k1_ge_neg(&tmp, &group[i]);
|
||||
ge_equals_ge(&group[order - i], &tmp);
|
||||
secp256k1_gej_neg(&tmpj, &groupj[i]);
|
||||
ge_equals_gej(&group[order - i], &tmpj);
|
||||
}
|
||||
}
|
||||
|
||||
void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj, int order) {
|
||||
int i, j, r_log;
|
||||
for (r_log = 1; r_log < order; r_log++) {
|
||||
for (j = 0; j < order; j++) {
|
||||
for (i = 0; i < order; i++) {
|
||||
secp256k1_gej tmp;
|
||||
secp256k1_scalar na, ng;
|
||||
secp256k1_scalar_set_int(&na, i);
|
||||
secp256k1_scalar_set_int(&ng, j);
|
||||
|
||||
secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng);
|
||||
ge_equals_gej(&group[(i * r_log + j) % order], &tmp);
|
||||
|
||||
if (i > 0) {
|
||||
secp256k1_ecmult_const(&tmp, &group[i], &ng);
|
||||
ge_equals_gej(&group[(i * j) % order], &tmp);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k) {
|
||||
secp256k1_fe x;
|
||||
unsigned char x_bin[32];
|
||||
k %= EXHAUSTIVE_TEST_ORDER;
|
||||
x = group[k].x;
|
||||
secp256k1_fe_normalize(&x);
|
||||
secp256k1_fe_get_b32(x_bin, &x);
|
||||
secp256k1_scalar_set_b32(r, x_bin, NULL);
|
||||
}
|
||||
|
||||
void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
|
||||
int s, r, msg, key;
|
||||
for (s = 1; s < order; s++) {
|
||||
for (r = 1; r < order; r++) {
|
||||
for (msg = 1; msg < order; msg++) {
|
||||
for (key = 1; key < order; key++) {
|
||||
secp256k1_ge nonconst_ge;
|
||||
secp256k1_ecdsa_signature sig;
|
||||
secp256k1_pubkey pk;
|
||||
secp256k1_scalar sk_s, msg_s, r_s, s_s;
|
||||
secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s;
|
||||
int k, should_verify;
|
||||
unsigned char msg32[32];
|
||||
|
||||
secp256k1_scalar_set_int(&s_s, s);
|
||||
secp256k1_scalar_set_int(&r_s, r);
|
||||
secp256k1_scalar_set_int(&msg_s, msg);
|
||||
secp256k1_scalar_set_int(&sk_s, key);
|
||||
|
||||
/* Verify by hand */
|
||||
/* Run through every k value that gives us this r and check that *one* works.
|
||||
* Note there could be none, there could be multiple, ECDSA is weird. */
|
||||
should_verify = 0;
|
||||
for (k = 0; k < order; k++) {
|
||||
secp256k1_scalar check_x_s;
|
||||
r_from_k(&check_x_s, group, k);
|
||||
if (r_s == check_x_s) {
|
||||
secp256k1_scalar_set_int(&s_times_k_s, k);
|
||||
secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s);
|
||||
secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s);
|
||||
secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s);
|
||||
should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s);
|
||||
}
|
||||
}
|
||||
/* nb we have a "high s" rule */
|
||||
should_verify &= !secp256k1_scalar_is_high(&s_s);
|
||||
|
||||
/* Verify by calling verify */
|
||||
secp256k1_ecdsa_signature_save(&sig, &r_s, &s_s);
|
||||
memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge));
|
||||
secp256k1_pubkey_save(&pk, &nonconst_ge);
|
||||
secp256k1_scalar_get_b32(msg32, &msg_s);
|
||||
CHECK(should_verify ==
|
||||
secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
|
||||
int i, j, k;
|
||||
|
||||
/* Loop */
|
||||
for (i = 1; i < order; i++) { /* message */
|
||||
for (j = 1; j < order; j++) { /* key */
|
||||
for (k = 1; k < order; k++) { /* nonce */
|
||||
secp256k1_ecdsa_signature sig;
|
||||
secp256k1_scalar sk, msg, r, s, expected_r;
|
||||
unsigned char sk32[32], msg32[32];
|
||||
secp256k1_scalar_set_int(&msg, i);
|
||||
secp256k1_scalar_set_int(&sk, j);
|
||||
secp256k1_scalar_get_b32(sk32, &sk);
|
||||
secp256k1_scalar_get_b32(msg32, &msg);
|
||||
|
||||
secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k);
|
||||
|
||||
secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig);
|
||||
/* Note that we compute expected_r *after* signing -- this is important
|
||||
* because our nonce-computing function function might change k during
|
||||
* signing. */
|
||||
r_from_k(&expected_r, group, k);
|
||||
CHECK(r == expected_r);
|
||||
CHECK((k * s) % order == (i + r * j) % order ||
|
||||
(k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* We would like to verify zero-knowledge here by counting how often every
|
||||
* possible (s, r) tuple appears, but because the group order is larger
|
||||
* than the field order, when coercing the x-values to scalar values, some
|
||||
* appear more often than others, so we are actually not zero-knowledge.
|
||||
* (This effect also appears in the real code, but the difference is on the
|
||||
* order of 1/2^128th the field order, so the deviation is not useful to a
|
||||
* computationally bounded attacker.)
|
||||
*/
|
||||
}
|
||||
|
||||
int main(void) {
|
||||
int i;
|
||||
secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER];
|
||||
secp256k1_ge group[EXHAUSTIVE_TEST_ORDER];
|
||||
|
||||
/* Build context */
|
||||
secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
|
||||
|
||||
/* TODO set z = 1, then do num_tests runs with random z values */
|
||||
|
||||
/* Generate the entire group */
|
||||
secp256k1_gej_set_infinity(&groupj[0]);
|
||||
secp256k1_ge_set_gej(&group[0], &groupj[0]);
|
||||
for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
|
||||
/* Set a different random z-value for each Jacobian point */
|
||||
secp256k1_fe z;
|
||||
random_fe(&z);
|
||||
|
||||
secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g);
|
||||
secp256k1_ge_set_gej(&group[i], &groupj[i]);
|
||||
secp256k1_gej_rescale(&groupj[i], &z);
|
||||
|
||||
/* Verify against ecmult_gen */
|
||||
{
|
||||
secp256k1_scalar scalar_i;
|
||||
secp256k1_gej generatedj;
|
||||
secp256k1_ge generated;
|
||||
|
||||
secp256k1_scalar_set_int(&scalar_i, i);
|
||||
secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &generatedj, &scalar_i);
|
||||
secp256k1_ge_set_gej(&generated, &generatedj);
|
||||
|
||||
CHECK(group[i].infinity == 0);
|
||||
CHECK(generated.infinity == 0);
|
||||
CHECK(secp256k1_fe_equal_var(&generated.x, &group[i].x));
|
||||
CHECK(secp256k1_fe_equal_var(&generated.y, &group[i].y));
|
||||
}
|
||||
}
|
||||
|
||||
/* Run the tests */
|
||||
#ifdef USE_ENDOMORPHISM
|
||||
test_exhaustive_endomorphism(group, EXHAUSTIVE_TEST_ORDER);
|
||||
#endif
|
||||
test_exhaustive_addition(group, groupj, EXHAUSTIVE_TEST_ORDER);
|
||||
test_exhaustive_ecmult(ctx, group, groupj, EXHAUSTIVE_TEST_ORDER);
|
||||
test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER);
|
||||
test_exhaustive_verify(ctx, group, EXHAUSTIVE_TEST_ORDER);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue