/* ecc-ecdsa-verify.c
Copyright (C) 2013 Niels MÃ¶ller
This file is part of GNU Nettle.
GNU Nettle is free software: you can redistribute it and/or
modify it under the terms of either:
* the GNU Lesser General Public License as published by the Free
Software Foundation; either version 3 of the License, or (at your
option) any later version.
or
* the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your
option) any later version.
or both in parallel, as here.
GNU Nettle 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
General Public License for more details.
You should have received copies of the GNU General Public License and
the GNU Lesser General Public License along with this program. If
not, see http://www.gnu.org/licenses/.
*/
/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include
#include
#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 call. */
return 5*ecc->size + ecc->mul_itch;
}
/* 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 */
size_t 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_itch */
ecc_mul_a (ecc, 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);
}
/* x coordinate only, modulo q */
ecc_j_to_a (ecc, 2, P2, P1, u1);
return (mpn_cmp (rp, P2, ecc->size) == 0);
#undef P2
#undef P1
#undef sinv
#undef u2
#undef hp
#undef u1
}