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Add unit tests for scalars. 

Also add a secp256k1_scalar_is_one function.
This commit is contained in:
Pieter Wuille 2014-10-29 00:35:38 -07:00
parent eca6cdb123
commit 79359302fb
3 changed files with 268 additions and 0 deletions
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3
src/scalar.h
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@ -45,6 +45,9 @@ void static secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scala
/** Check whether a scalar equals zero. */
int static secp256k1_scalar_is_zero(const secp256k1_scalar_t *a);
/** Check whether a scalar equals one. */
int static secp256k1_scalar_is_one(const secp256k1_scalar_t *a);
/** Check whether a scalar is higher than the group order divided by 2. */
int static secp256k1_scalar_is_high(const secp256k1_scalar_t *a);

5
src/scalar_impl.h
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@ -54,12 +54,17 @@ void static secp256k1_scalar_inverse(secp256k1_scalar_t *r, const secp256k1_scal
void static secp256k1_scalar_negate(secp256k1_scalar_t *r, const secp256k1_scalar_t *a) {
secp256k1_num_sub(&r->n, &secp256k1_ge_consts->order, &a->n);
secp256k1_num_mod(&r->n, &secp256k1_ge_consts->order);
}
int static secp256k1_scalar_is_zero(const secp256k1_scalar_t *a) {
return secp256k1_num_is_zero(&a->n);
}
int static secp256k1_scalar_is_one(const secp256k1_scalar_t *a) {
return secp256k1_num_bits(&a->n) == 1;
}
int static secp256k1_scalar_is_high(const secp256k1_scalar_t *a) {
return secp256k1_num_cmp(&a->n, &secp256k1_ge_consts->half_order) > 0;
}

260
src/tests.c
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@ -221,6 +221,263 @@ void run_num_smalltests() {
run_num_int();
}
/***** SCALAR TESTS *****/
int secp256k1_scalar_eq(const secp256k1_scalar_t *s1, const secp256k1_scalar_t *s2) {
secp256k1_scalar_t t;
secp256k1_scalar_init(&t);
secp256k1_scalar_negate(&t, s2);
secp256k1_scalar_add(&t, &t, s1);
int ret = secp256k1_scalar_is_zero(&t);
secp256k1_scalar_free(&t);
return ret;
}
void scalar_test(void) {
unsigned char c[32];
// Set 's' to a random scalar, with value 'snum'.
secp256k1_rand256_test(c);
secp256k1_scalar_t s;
secp256k1_scalar_init(&s);
secp256k1_scalar_set_b32(&s, c, NULL);
secp256k1_num_t snum;
secp256k1_num_init(&snum);
secp256k1_num_set_bin(&snum, c, 32);
secp256k1_num_mod(&snum, &secp256k1_ge_consts->order);
// Set 's1' to a random scalar, with value 's1num'.
secp256k1_rand256_test(c);
secp256k1_scalar_t s1;
secp256k1_scalar_init(&s1);
secp256k1_scalar_set_b32(&s1, c, NULL);
secp256k1_num_t s1num;
secp256k1_num_init(&s1num);
secp256k1_num_set_bin(&s1num, c, 32);
secp256k1_num_mod(&s1num, &secp256k1_ge_consts->order);
// Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'.
secp256k1_rand256_test(c);
secp256k1_scalar_t s2;
secp256k1_scalar_init(&s2);
int overflow = 0;
secp256k1_scalar_set_b32(&s2, c, &overflow);
secp256k1_num_t s2num;
secp256k1_num_init(&s2num);
secp256k1_num_set_bin(&s2num, c, 32);
secp256k1_num_mod(&s2num, &secp256k1_ge_consts->order);
{
// Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it.
secp256k1_num_t n, t, m;
secp256k1_num_init(&n);
secp256k1_num_init(&t);
secp256k1_num_init(&m);
secp256k1_num_set_int(&n, 0);
secp256k1_num_set_int(&m, 16);
for (int i = 0; i < 256; i += 4) {
secp256k1_num_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
secp256k1_num_mul(&n, &n, &m);
secp256k1_num_add(&n, &n, &t);
}
CHECK(secp256k1_num_eq(&n, &snum));
secp256k1_num_free(&m);
secp256k1_num_free(&t);
secp256k1_num_free(&n);
}
{
// Test that get_b32 returns the same as get_bin on the number.
unsigned char r1[32];
secp256k1_scalar_get_b32(r1, &s2);
unsigned char r2[32];
secp256k1_num_get_bin(r2, 32, &s2num);
CHECK(memcmp(r1, r2, 32) == 0);
// If no overflow occurred when assigning, it should also be equal to the original byte array.
CHECK((memcmp(r1, c, 32) == 0) == (overflow == 0));
}
{
// Test that adding the scalars together is equal to adding their numbers together modulo the order.
secp256k1_num_t rnum;
secp256k1_num_init(&rnum);
secp256k1_num_add(&rnum, &snum, &s2num);
secp256k1_num_mod(&rnum, &secp256k1_ge_consts->order);
secp256k1_scalar_t r;
secp256k1_scalar_init(&r);
secp256k1_scalar_add(&r, &s, &s2);
secp256k1_num_t r2num;
secp256k1_num_init(&r2num);
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
secp256k1_num_free(&r2num);
secp256k1_num_free(&rnum);
secp256k1_scalar_free(&r);
}
{
// Test that multipying the scalars is equal to multiplying their numbers modulo the order.
secp256k1_num_t rnum;
secp256k1_num_init(&rnum);
secp256k1_num_mul(&rnum, &snum, &s2num);
secp256k1_num_mod(&rnum, &secp256k1_ge_consts->order);
secp256k1_scalar_t r;
secp256k1_scalar_init(&r);
secp256k1_scalar_mul(&r, &s, &s2);
secp256k1_num_t r2num;
secp256k1_num_init(&r2num);
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
// The result can only be zero if at least one of the factors was zero.
CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2)));
// The results can only be equal to one of the factors if that factor was zero, or the other factor was one.
CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2)));
CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s)));
secp256k1_num_free(&r2num);
secp256k1_num_free(&rnum);
secp256k1_scalar_free(&r);
}
{
// Check that comparison with zero matches comparison with zero on the number.
CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
// Check that comparison with the half order is equal to testing for high scalar.
CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &secp256k1_ge_consts->half_order) > 0));
secp256k1_scalar_t neg;
secp256k1_scalar_init(&neg);
secp256k1_scalar_negate(&neg, &s);
secp256k1_num_t negnum;
secp256k1_num_init(&negnum);
secp256k1_num_sub(&negnum, &secp256k1_ge_consts->order, &snum);
secp256k1_num_mod(&negnum, &secp256k1_ge_consts->order);
// Check that comparison with the half order is equal to testing for high scalar after negation.
CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &secp256k1_ge_consts->half_order) > 0));
// Negating should change the high property, unless the value was already zero.
CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
secp256k1_num_t negnum2;
secp256k1_num_init(&negnum2);
secp256k1_scalar_get_num(&negnum2, &neg);
// Negating a scalar should be equal to (order - n) mod order on the number.
CHECK(secp256k1_num_eq(&negnum, &negnum2));
secp256k1_scalar_add(&neg, &neg, &s);
// Adding a number to its negation should result in zero.
CHECK(secp256k1_scalar_is_zero(&neg));
secp256k1_scalar_negate(&neg, &neg);
// Negating zero should still result in zero.
CHECK(secp256k1_scalar_is_zero(&neg));
secp256k1_num_free(&negnum);
secp256k1_num_free(&negnum2);
secp256k1_scalar_free(&neg);
}
{
// Test that scalar inverses are equal to the inverse of their number modulo the order.
if (!secp256k1_scalar_is_zero(&s)) {
secp256k1_scalar_t inv;
secp256k1_scalar_init(&inv);
secp256k1_scalar_inverse(&inv, &s);
secp256k1_num_t invnum;
secp256k1_num_init(&invnum);
secp256k1_num_mod_inverse(&invnum, &snum, &secp256k1_ge_consts->order);
secp256k1_num_t invnum2;
secp256k1_num_init(&invnum2);
secp256k1_scalar_get_num(&invnum2, &inv);
CHECK(secp256k1_num_eq(&invnum, &invnum2));
secp256k1_scalar_mul(&inv, &inv, &s);
// Multiplying a scalar with its inverse must result in one.
CHECK(secp256k1_scalar_is_one(&inv));
secp256k1_scalar_inverse(&inv, &inv);
// Inverting one must result in one.
CHECK(secp256k1_scalar_is_one(&inv));
secp256k1_num_free(&invnum);
secp256k1_num_free(&invnum2);
secp256k1_scalar_free(&inv);
}
}
{
// Test commutativity of add.
secp256k1_scalar_t r1, r2;
secp256k1_scalar_init(&r1);
secp256k1_scalar_init(&r2);
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
secp256k1_scalar_free(&r1);
secp256k1_scalar_free(&r2);
}
{
// Test commutativity of mul.
secp256k1_scalar_t r1, r2;
secp256k1_scalar_init(&r1);
secp256k1_scalar_init(&r2);
secp256k1_scalar_mul(&r1, &s1, &s2);
secp256k1_scalar_mul(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
secp256k1_scalar_free(&r1);
secp256k1_scalar_free(&r2);
}
{
// Test associativity of add.
secp256k1_scalar_t r1, r2;
secp256k1_scalar_init(&r1);
secp256k1_scalar_init(&r2);
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r1, &r1, &s);
secp256k1_scalar_add(&r2, &s2, &s);
secp256k1_scalar_add(&r2, &s1, &r2);
CHECK(secp256k1_scalar_eq(&r1, &r2));
secp256k1_scalar_free(&r1);
secp256k1_scalar_free(&r2);
}
{
// Test associativity of mul.
secp256k1_scalar_t r1, r2;
secp256k1_scalar_init(&r1);
secp256k1_scalar_init(&r2);
secp256k1_scalar_mul(&r1, &s1, &s2);
secp256k1_scalar_mul(&r1, &r1, &s);
secp256k1_scalar_mul(&r2, &s2, &s);
secp256k1_scalar_mul(&r2, &s1, &r2);
CHECK(secp256k1_scalar_eq(&r1, &r2));
secp256k1_scalar_free(&r1);
secp256k1_scalar_free(&r2);
}
{
// Test distributitivity of mul over add.
secp256k1_scalar_t r1, r2, t;
secp256k1_scalar_init(&r1);
secp256k1_scalar_init(&r2);
secp256k1_scalar_init(&t);
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_mul(&r1, &r1, &s);
secp256k1_scalar_mul(&r2, &s1, &s);
secp256k1_scalar_mul(&t, &s2, &s);
secp256k1_scalar_add(&r2, &r2, &t);
CHECK(secp256k1_scalar_eq(&r1, &r2));
secp256k1_scalar_free(&r1);
secp256k1_scalar_free(&r2);
secp256k1_scalar_free(&t);
}
secp256k1_num_free(&snum);
secp256k1_scalar_free(&s);
secp256k1_num_free(&s1num);
secp256k1_scalar_free(&s1);
secp256k1_num_free(&s2num);
secp256k1_scalar_free(&s2);
}
void run_scalar_tests(void) {
for (int i = 0; i < 128 * count; i++) {
scalar_test();
}
}
/***** FIELD TESTS *****/
void random_fe(secp256k1_fe_t *x) {
@ -746,6 +1003,9 @@ int main(int argc, char **argv) {
// num tests
run_num_smalltests();
// scalar tests
run_scalar_tests();
// field tests
run_field_inv();
run_field_inv_var();