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Share common SAE and EAP-pwd functionality: is_quadratic_residue

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Use a shared helper function for the blinded mechanism of determining
the Legendre symbol.

Signed-off-by: Jouni Malinen <jouni@codeaurora.org>
This commit is contained in:
Jouni Malinen 2019-04-25 22:35:14 +03:00 • committed by Jouni Malinen
parent a9615b1b88
commit 17749e948a
4 changed files with 93 additions and 115 deletions
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76
src/common/dragonfly.c
View file

@ -10,6 +10,7 @@
#include "utils/includes.h"
#include "utils/common.h"
#include "utils/const_time.h"
#include "crypto/crypto.h"
#include "dragonfly.h"
@ -60,7 +61,7 @@ int dragonfly_get_random_qr_qnr(const struct crypto_bignum *prime,
}
struct crypto_bignum *
static struct crypto_bignum *
dragonfly_get_rand_1_to_p_1(const struct crypto_bignum *prime)
{
struct crypto_bignum *tmp, *pm1, *one;
@ -80,3 +81,76 @@ dragonfly_get_rand_1_to_p_1(const struct crypto_bignum *prime)
crypto_bignum_deinit(one, 0);
return tmp;
}
int dragonfly_is_quadratic_residue_blind(struct crypto_ec *ec,
const u8 *qr, const u8 *qnr,
const struct crypto_bignum *val)
{
struct crypto_bignum *r, *num, *qr_or_qnr = NULL;
int check, res = -1;
u8 qr_or_qnr_bin[DRAGONFLY_MAX_ECC_PRIME_LEN];
const struct crypto_bignum *prime;
size_t prime_len;
unsigned int mask;
prime = crypto_ec_get_prime(ec);
prime_len = crypto_ec_prime_len(ec);
/*
* Use a blinding technique to mask val while determining whether it is
* a quadratic residue modulo p to avoid leaking timing information
* while determining the Legendre symbol.
*
* v = val
* r = a random number between 1 and p-1, inclusive
* num = (v * r * r) modulo p
*/
r = dragonfly_get_rand_1_to_p_1(prime);
if (!r)
return -1;
num = crypto_bignum_init();
if (!num ||
crypto_bignum_mulmod(val, r, prime, num) < 0 ||
crypto_bignum_mulmod(num, r, prime, num) < 0)
goto fail;
/*
* Need to minimize differences in handling different cases, so try to
* avoid branches and timing differences.
*
* If r is odd:
* num = (num * qr) module p
* LGR(num, p) = 1 ==> quadratic residue
* else:
* num = (num * qnr) module p
* LGR(num, p) = -1 ==> quadratic residue
*
* mask is set to !odd(r)
*/
mask = const_time_is_zero(crypto_bignum_is_odd(r));
const_time_select_bin(mask, qnr, qr, prime_len, qr_or_qnr_bin);
qr_or_qnr = crypto_bignum_init_set(qr_or_qnr_bin, prime_len);
if (!qr_or_qnr ||
crypto_bignum_mulmod(num, qr_or_qnr, prime, num) < 0)
goto fail;
/* branchless version of check = odd(r) ? 1 : -1, */
check = const_time_select_int(mask, -1, 1);
/* Determine the Legendre symbol on the masked value */
res = crypto_bignum_legendre(num, prime);
if (res == -2) {
res = -1;
goto fail;
}
/* branchless version of res = res == check
* (res is -1, 0, or 1; check is -1 or 1) */
mask = const_time_eq(res, check);
res = const_time_select_int(mask, 1, 0);
fail:
crypto_bignum_deinit(num, 1);
crypto_bignum_deinit(r, 1);
crypto_bignum_deinit(qr_or_qnr, 1);
return res;
}