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Add Jacobi symbol test via GMP

Also add native Jacobi symbol test (Andrew)

Rebased-by: Andrew Poelstra
Rebased-by: Pieter Wuille
master
Peter Dettman 7 years ago committed by Pieter Wuille
parent
commit
efd953a7a7
  1. 18
      src/bench_internal.c
  2. 6
      src/num.h
  3. 26
      src/num_gmp_impl.h
  4. 112
      src/tests.c

18
src/bench_internal.c

@ -299,6 +299,21 @@ void bench_context_sign(void* arg) { @@ -299,6 +299,21 @@ void bench_context_sign(void* arg) {
}
}
#ifndef USE_NUM_NONE
void bench_num_jacobi(void* arg) {
int i;
bench_inv_t *data = (bench_inv_t*)arg;
secp256k1_num nx, norder;
secp256k1_scalar_get_num(&nx, &data->scalar_x);
secp256k1_scalar_order_get_num(&norder);
secp256k1_scalar_get_num(&norder, &data->scalar_y);
for (i = 0; i < 200000; i++) {
secp256k1_num_jacobi(&nx, &norder);
}
}
#endif
int have_flag(int argc, char** argv, char *flag) {
char** argm = argv + argc;
@ -350,5 +365,8 @@ int main(int argc, char **argv) { @@ -350,5 +365,8 @@ int main(int argc, char **argv) {
if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 20);
if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 200);
#ifndef USE_NUM_NONE
if (have_flag(argc, argv, "num") || have_flag(argc, argv, "jacobi")) run_benchmark("num_jacobi", bench_num_jacobi, bench_setup, NULL, &data, 10, 200000);
#endif
return 0;
}

6
src/num.h

@ -32,6 +32,9 @@ static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsi @@ -32,6 +32,9 @@ static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsi
/** Compute a modular inverse. The input must be less than the modulus. */
static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m);
/** Compute the jacobi symbol (a|b). b must be positive and odd. */
static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b);
/** Compare the absolute value of two numbers. */
static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b);
@ -57,6 +60,9 @@ static void secp256k1_num_shift(secp256k1_num *r, int bits); @@ -57,6 +60,9 @@ static void secp256k1_num_shift(secp256k1_num *r, int bits);
/** Check whether a number is zero. */
static int secp256k1_num_is_zero(const secp256k1_num *a);
/** Check whether a number is one. */
static int secp256k1_num_is_one(const secp256k1_num *a);
/** Check whether a number is strictly negative. */
static int secp256k1_num_is_neg(const secp256k1_num *a);

26
src/num_gmp_impl.h

@ -144,6 +144,32 @@ static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, @@ -144,6 +144,32 @@ static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a,
memset(v, 0, sizeof(v));
}
static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b) {
int ret;
mpz_t ga, gb;
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
VERIFY_CHECK(!b->neg && (b->limbs > 0) && (b->data[0] & 1));
mpz_inits(ga, gb, NULL);
mpz_import(gb, b->limbs, -1, sizeof(mp_limb_t), 0, 0, b->data);
mpz_import(ga, a->limbs, -1, sizeof(mp_limb_t), 0, 0, a->data);
if (a->neg) {
mpz_neg(ga, ga);
}
ret = mpz_jacobi(ga, gb);
mpz_clears(ga, gb, NULL);
return ret;
}
static int secp256k1_num_is_one(const secp256k1_num *a) {
return (a->limbs == 1 && a->data[0] == 1);
}
static int secp256k1_num_is_zero(const secp256k1_num *a) {
return (a->limbs == 1 && a->data[0] == 0);
}

112
src/tests.c

@ -473,6 +473,8 @@ void test_num_negate(void) { @@ -473,6 +473,8 @@ void test_num_negate(void) {
}
void test_num_add_sub(void) {
int i;
secp256k1_scalar s;
secp256k1_num n1;
secp256k1_num n2;
secp256k1_num n1p2, n2p1, n1m2, n2m1;
@ -498,6 +500,110 @@ void test_num_add_sub(void) { @@ -498,6 +500,110 @@ void test_num_add_sub(void) {
CHECK(!secp256k1_num_eq(&n2p1, &n1));
secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */
CHECK(secp256k1_num_eq(&n2p1, &n1));
/* check is_one */
secp256k1_scalar_set_int(&s, 1);
secp256k1_scalar_get_num(&n1, &s);
CHECK(secp256k1_num_is_one(&n1));
/* check that 2^n + 1 is never 1 */
secp256k1_scalar_get_num(&n2, &s);
for (i = 0; i < 250; ++i) {
secp256k1_num_add(&n1, &n1, &n1); /* n1 *= 2 */
secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = n1 + 1 */
CHECK(!secp256k1_num_is_one(&n1p2));
}
}
void test_num_mod(void) {
int i;
secp256k1_scalar s;
secp256k1_num order, n;
/* check that 0 mod anything is 0 */
random_scalar_order_test(&s);
secp256k1_scalar_get_num(&order, &s);
secp256k1_scalar_set_int(&s, 0);
secp256k1_scalar_get_num(&n, &s);
secp256k1_num_mod(&n, &order);
CHECK(secp256k1_num_is_zero(&n));
/* check that anything mod 1 is 0 */
secp256k1_scalar_set_int(&s, 1);
secp256k1_scalar_get_num(&order, &s);
secp256k1_scalar_get_num(&n, &s);
secp256k1_num_mod(&n, &order);
CHECK(secp256k1_num_is_zero(&n));
/* check that increasing the number past 2^256 does not break this */
random_scalar_order_test(&s);
secp256k1_scalar_get_num(&n, &s);
/* multiply by 2^8, which'll test this case with high probability */
for (i = 0; i < 8; ++i) {
secp256k1_num_add(&n, &n, &n);
}
secp256k1_num_mod(&n, &order);
CHECK(secp256k1_num_is_zero(&n));
}
void test_num_jacobi(void) {
secp256k1_scalar sqr;
secp256k1_scalar small;
secp256k1_scalar five; /* five is not a quadratic residue */
secp256k1_num order, n;
int i;
/* squares mod 5 are 1, 4 */
const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 };
/* check some small values with 5 as the order */
secp256k1_scalar_set_int(&five, 5);
secp256k1_scalar_get_num(&order, &five);
for (i = 0; i < 10; ++i) {
secp256k1_scalar_set_int(&small, i);
secp256k1_scalar_get_num(&n, &small);
CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]);
}
/** test large values with 5 as group order */
secp256k1_scalar_get_num(&order, &five);
/* we first need a scalar which is not a multiple of 5 */
do {
secp256k1_num fiven;
random_scalar_order_test(&sqr);
secp256k1_scalar_get_num(&fiven, &five);
secp256k1_scalar_get_num(&n, &sqr);
secp256k1_num_mod(&n, &fiven);
} while (secp256k1_num_is_zero(&n));
/* next force it to be a residue. 2 is a nonresidue mod 5 so we can
* just multiply by two, i.e. add the number to itself */
if (secp256k1_num_jacobi(&n, &order) == -1) {
secp256k1_num_add(&n, &n, &n);
}
/* test residue */
CHECK(secp256k1_num_jacobi(&n, &order) == 1);
/* test nonresidue */
secp256k1_num_add(&n, &n, &n);
CHECK(secp256k1_num_jacobi(&n, &order) == -1);
/** test with secp group order as order */
secp256k1_scalar_order_get_num(&order);
random_scalar_order_test(&sqr);
secp256k1_scalar_sqr(&sqr, &sqr);
/* test residue */
secp256k1_scalar_get_num(&n, &sqr);
CHECK(secp256k1_num_jacobi(&n, &order) == 1);
/* test nonresidue */
secp256k1_scalar_mul(&sqr, &sqr, &five);
secp256k1_scalar_get_num(&n, &sqr);
CHECK(secp256k1_num_jacobi(&n, &order) == -1);
/* test multiple of the order*/
CHECK(secp256k1_num_jacobi(&order, &order) == 0);
/* check one less than the order */
secp256k1_scalar_set_int(&small, 1);
secp256k1_scalar_get_num(&n, &small);
secp256k1_num_sub(&n, &order, &n);
CHECK(secp256k1_num_jacobi(&n, &order) == 1); /* sage confirms this is 1 */
}
void run_num_smalltests(void) {
@ -505,6 +611,8 @@ void run_num_smalltests(void) { @@ -505,6 +611,8 @@ void run_num_smalltests(void) {
for (i = 0; i < 100*count; i++) {
test_num_negate();
test_num_add_sub();
test_num_mod();
test_num_jacobi();
}
}
#endif
@ -689,6 +797,10 @@ void scalar_test(void) { @@ -689,6 +797,10 @@ void scalar_test(void) {
secp256k1_scalar_inverse(&inv, &inv);
/* Inverting one must result in one. */
CHECK(secp256k1_scalar_is_one(&inv));
#ifndef USE_NUM_NONE
secp256k1_scalar_get_num(&invnum, &inv);
CHECK(secp256k1_num_is_one(&invnum));
#endif
}
}

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