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/* $OpenBSD: bn_mod_sqrt.c,v 1.3 2023/04/04 15:32:02 tb Exp $ */
/*
* Copyright (c) 2022 Theo Buehler <tb@openbsd.org>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
#include <err.h>
#include <stdio.h>
#include <openssl/bn.h>
/* Test that sqrt * sqrt = A (mod p) where p is a prime */
struct mod_sqrt_test {
const char *sqrt;
const char *a;
const char *p;
int bn_mod_sqrt_fails;
} mod_sqrt_test_data[] = {
{
.sqrt = "1",
.a = "1",
.p = "2",
.bn_mod_sqrt_fails = 0,
},
{
.sqrt = "-1",
.a = "20a7ee",
.p = "460201", /* 460201 == 4D5 * E7D */
.bn_mod_sqrt_fails = 1,
},
{
.sqrt = "-1",
.a = "65bebdb00a96fc814ec44b81f98b59fba3c30203928fa521"
"4c51e0a97091645280c947b005847f239758482b9bfc45b0"
"66fde340d1fe32fc9c1bf02e1b2d0ed",
.p = "9df9d6cc20b8540411af4e5357ef2b0353cb1f2ab5ffc3e2"
"46b41c32f71e951f",
.bn_mod_sqrt_fails = 1,
},
};
const size_t N_TESTS = sizeof(mod_sqrt_test_data) / sizeof(*mod_sqrt_test_data);
static int
mod_sqrt_test(struct mod_sqrt_test *test, BN_CTX *ctx)
{
BIGNUM *a, *p, *want, *got, *diff, *sum;
int failed = 1;
BN_CTX_start(ctx);
if ((a = BN_CTX_get(ctx)) == NULL)
errx(1, "a = BN_CTX_get()");
if ((p = BN_CTX_get(ctx)) == NULL)
errx(1, "p = BN_CTX_get()");
if ((want = BN_CTX_get(ctx)) == NULL)
errx(1, "want = BN_CTX_get()");
if ((got = BN_CTX_get(ctx)) == NULL)
errx(1, "got = BN_CTX_get()");
if ((diff = BN_CTX_get(ctx)) == NULL)
errx(1, "diff = BN_CTX_get()");
if ((sum = BN_CTX_get(ctx)) == NULL)
errx(1, "sum = BN_CTX_get()");
if (!BN_hex2bn(&a, test->a)) {
fprintf(stderr, "BN_hex2bn(a) failed\n");
goto out;
}
if (!BN_hex2bn(&p, test->p)) {
fprintf(stderr, "BN_hex2bn(p) failed\n");
goto out;
}
if (!BN_hex2bn(&want, test->sqrt)) {
fprintf(stderr, "BN_hex2bn(want) failed\n");
goto out;
}
if ((BN_mod_sqrt(got, a, p, ctx) == NULL) != test->bn_mod_sqrt_fails) {
fprintf(stderr, "BN_mod_sqrt %s unexpectedly\n",
test->bn_mod_sqrt_fails ? "succeeded" : "failed");
goto out;
}
if (test->bn_mod_sqrt_fails) {
failed = 0;
goto out;
}
if (!BN_mod_sub(diff, want, got, p, ctx)) {
fprintf(stderr, "BN_mod_sub() failed\n");
goto out;
}
if (!BN_mod_add(sum, want, got, p, ctx)) {
fprintf(stderr, "BN_mod_add() failed\n");
goto out;
}
/* XXX - Remove sum once we return the canonical square root. */
if (!BN_is_zero(diff) && !BN_is_zero(sum)) {
fprintf(stderr, "want != got\n");
fprintf(stderr, "a: %s\n", test->a);
fprintf(stderr, "p: %s\n", test->p);
fprintf(stderr, "want: %s:", test->sqrt);
fprintf(stderr, "got: ");
BN_print_fp(stderr, got);
fprintf(stderr, "\n\n");
goto out;
}
failed = 0;
out:
BN_CTX_end(ctx);
return failed;
}
static int
bn_mod_sqrt_test(void)
{
BN_CTX *ctx;
size_t i;
int failed = 0;
if ((ctx = BN_CTX_new()) == NULL)
errx(1, "BN_CTX_new()");
for (i = 0; i < N_TESTS; i++)
failed |= mod_sqrt_test(&mod_sqrt_test_data[i], ctx);
BN_CTX_free(ctx);
return failed;
}
int
main(void)
{
int failed = 0;
failed |= bn_mod_sqrt_test();
return failed;
}
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