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/* ecc-ecdsa-verify.c */
/* nettle, low-level cryptographics library
*
* Copyright (C) 2013 Niels Möller
*
* The nettle library is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or (at your
* option) any later version.
*
* The nettle library is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
* License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with the nettle library; see the file COPYING.LIB. If not, write to
* the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 02111-1301, USA.
*/
/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <assert.h>
#include <stdlib.h>
#include "ecdsa.h"
#include "ecc-internal.h"
/* Low-level ECDSA verify */
static int
zero_p (const mp_limb_t *xp, mp_size_t n)
{
while (n > 0)
if (xp[--n] > 0)
return 0;
return 1;
}
static int
ecdsa_in_range (const struct ecc_curve *ecc, const mp_limb_t *xp)
{
return !zero_p (xp, ecc->size)
&& mpn_cmp (xp, ecc->q, ecc->size) < 0;
}
mp_size_t
ecc_ecdsa_verify_itch (const struct ecc_curve *ecc)
{
/* Largest storage need is for the ecc_mul_a call, 6 * ecc->size +
ECC_MUL_A_ITCH (size) */
return ECC_ECDSA_VERIFY_ITCH (ecc->size);
}
/* FIXME: Use faster primitives, not requiring side-channel silence. */
int
ecc_ecdsa_verify (const struct ecc_curve *ecc,
const mp_limb_t *pp, /* Public key */
unsigned length, const uint8_t *digest,
const mp_limb_t *rp, const mp_limb_t *sp,
mp_limb_t *scratch)
{
/* Procedure, according to RFC 6090, "KT-I". q denotes the group
order.
1. Check 0 < r, s < q.
2. s' <-- s^{-1} (mod q)
3. u1 <-- h * s' (mod q)
4. u2 <-- r * s' (mod q)
5. R = u1 G + u2 Y
6. Signature is valid if R_x = r (mod q).
*/
#define P2 scratch
#define P1 (scratch + 3*ecc->size)
#define sinv (scratch + 3*ecc->size)
#define u2 (scratch + 4*ecc->size)
#define hp (scratch + 4*ecc->size)
#define u1 (scratch + 6*ecc->size)
if (! (ecdsa_in_range (ecc, rp)
&& ecdsa_in_range (ecc, sp)))
return 0;
/* FIXME: Micro optimizations: Either simultaneous multiplication.
Or convert to projective coordinates (can be done without
division, I think), and write an ecc_add_ppp. */
/* Compute sinv, use P2 as scratch */
mpn_copyi (sinv + ecc->size, sp, ecc->size);
ecc_modq_inv (ecc, sinv, sinv + ecc->size, P2);
/* u2 = r / s, P2 = u2 * Y */
ecc_modq_mul (ecc, u2, rp, sinv);
/* Total storage: 5*ecc->size + ECC_MUL_A_ITCH (ecc->size) */
ecc_mul_a (ecc, 1, P2, u2, pp, u2 + ecc->size);
/* u1 = h / s, P1 = u1 * G */
ecc_hash (ecc, hp, length, digest);
ecc_modq_mul (ecc, u1, hp, sinv);
/* u = 0 can happen only if h = 0 or h = q, which is extremely
unlikely. */
if (!zero_p (u1, ecc->size))
{
/* Total storage: 6*ecc->size + ECC_MUL_G_ITCH (ecc->size) */
ecc_mul_g (ecc, P1, u1, u1 + ecc->size);
/* NOTE: ecc_add_jjj and/or ecc_j_to_a will produce garbage in
case u1 G = +/- u2 V. However, anyone who gets his or her
hands on a signature where this happens during verification,
can also get the private key as z = +/- u1 / u_2 (mod q). And
then it doesn't matter very much if verification of
signatures with that key succeeds or fails.
u1 G = - u2 V can never happen for a correctly generated
signature, since it implies k = 0.
u1 G = u2 V is possible, if we are unlucky enough to get h /
s_1 = z. Hitting that is about as unlikely as finding the
private key by guessing.
*/
/* Total storage: 6*ecc->size + ECC_ADD_JJJ_ITCH (ecc->size) */
ecc_add_jjj (ecc, P1, P1, P2, u1);
}
ecc_j_to_a (ecc, 3, P2, P1, u1);
if (mpn_cmp (P2, ecc->q, ecc->size) >= 0)
mpn_sub_n (P2, P2, ecc->q, ecc->size);
return (mpn_cmp (rp, P2, ecc->size) == 0);
#undef P2
#undef P1
#undef sinv
#undef u2
#undef hp
#undef u1
}
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