/**
Verify an ECC signature
@param sig The signature to verify
@param siglen The length of the signature (octets)
@param hash The hash (message digest) that was signed
@param hashlen The length of the hash (octets)
@param stat Result of signature, 1==valid, 0==invalid
@param key The corresponding public ECC key
@return CRYPT_OK if successful (even if the signature is not valid)
*/
int ecc_verify_hash(const unsigned char *sig, unsigned long siglen,
const unsigned char *hash, unsigned long hashlen,
int *stat, ecc_key *key)
{
ecc_point *mG, *mQ;
void *r, *s, *v, *w, *u1, *u2, *e, *p, *m;
void *mp;
int err;
LTC_ARGCHK(sig != NULL);
LTC_ARGCHK(hash != NULL);
LTC_ARGCHK(stat != NULL);
LTC_ARGCHK(key != NULL);
/* default to invalid signature */
*stat = 0;
mp = NULL;
/* is the IDX valid ? */
if (ltc_ecc_is_valid_idx(key->idx) != 1) {
return CRYPT_PK_INVALID_TYPE;
}
/* allocate ints */
if ((err = mp_init_multi(&r, &s, &v, &w, &u1, &u2, &p, &e, &m, NULL)) != CRYPT_OK) {
return CRYPT_MEM;
}
/* allocate points */
mG = ltc_ecc_new_point();
mQ = ltc_ecc_new_point();
if (mQ == NULL || mG == NULL) {
err = CRYPT_MEM;
goto error;
}
/* parse header */
if ((err = der_decode_sequence_multi(sig, siglen,
LTC_ASN1_INTEGER, 1UL, r,
LTC_ASN1_INTEGER, 1UL, s,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto error;
}
/* get the order */
if ((err = mp_read_radix(p, (char *)key->dp->order, 16)) != CRYPT_OK) { goto error; }
/* get the modulus */
if ((err = mp_read_radix(m, (char *)key->dp->prime, 16)) != CRYPT_OK) { goto error; }
/* check for zero */
if (mp_iszero(r) || mp_iszero(s) || mp_cmp(r, p) != LTC_MP_LT || mp_cmp(s, p) != LTC_MP_LT) {
err = CRYPT_INVALID_PACKET;
goto error;
}
/* read hash */
if ((err = mp_read_unsigned_bin(e, (unsigned char *)hash, (int)hashlen)) != CRYPT_OK) { goto error; }
/* w = s^-1 mod n */
if ((err = mp_invmod(s, p, w)) != CRYPT_OK) { goto error; }
/* u1 = ew */
if ((err = mp_mulmod(e, w, p, u1)) != CRYPT_OK) { goto error; }
/* u2 = rw */
if ((err = mp_mulmod(r, w, p, u2)) != CRYPT_OK) { goto error; }
/* find mG and mQ */
if ((err = mp_read_radix(mG->x, (char *)key->dp->Gx, 16)) != CRYPT_OK) { goto error; }
if ((err = mp_read_radix(mG->y, (char *)key->dp->Gy, 16)) != CRYPT_OK) { goto error; }
if ((err = mp_set(mG->z, 1)) != CRYPT_OK) { goto error; }
if ((err = mp_copy(key->pubkey.x, mQ->x)) != CRYPT_OK) { goto error; }
if ((err = mp_copy(key->pubkey.y, mQ->y)) != CRYPT_OK) { goto error; }
if ((err = mp_copy(key->pubkey.z, mQ->z)) != CRYPT_OK) { goto error; }
/* compute u1*mG + u2*mQ = mG */
if (ltc_mp.ecc_mul2add == NULL) {
if ((err = ltc_mp.ecc_ptmul(u1, mG, mG, m, 0)) != CRYPT_OK) { goto error; }
if ((err = ltc_mp.ecc_ptmul(u2, mQ, mQ, m, 0)) != CRYPT_OK) { goto error; }
/* find the montgomery mp */
if ((err = mp_montgomery_setup(m, &mp)) != CRYPT_OK) { goto error; }
/* add them */
if ((err = ltc_mp.ecc_ptadd(mQ, mG, mG, m, mp)) != CRYPT_OK) { goto error; }
/* reduce */
if ((err = ltc_mp.ecc_map(mG, m, mp)) != CRYPT_OK) { goto error; }
} else {
/* use Shamir's trick to compute u1*mG + u2*mQ using half of the doubles */
if ((err = ltc_mp.ecc_mul2add(mG, u1, mQ, u2, mG, m)) != CRYPT_OK) { goto error; }
}
/* v = X_x1 mod n */
if ((err = mp_mod(mG->x, p, v)) != CRYPT_OK) { goto error; }
/* does v == r */
if (mp_cmp(v, r) == LTC_MP_EQ) {
*stat = 1;
}
/* clear up and return */
err = CRYPT_OK;
error:
ltc_ecc_del_point(mG);
ltc_ecc_del_point(mQ);
mp_clear_multi(r, s, v, w, u1, u2, p, e, m, NULL);
if (mp != NULL) {
mp_montgomery_free(mp);
}
return err;
}
int ecc_test_shamir(void)
{
void *modulus, *mp, *kA, *kB, *rA, *rB;
ecc_point *G, *A, *B, *C1, *C2;
int x, y, z;
unsigned char buf[ECC_BUF_SIZE];
DO(mp_init_multi(&kA, &kB, &rA, &rB, &modulus, NULL));
LTC_ARGCHK((G = ltc_ecc_new_point()) != NULL);
LTC_ARGCHK((A = ltc_ecc_new_point()) != NULL);
LTC_ARGCHK((B = ltc_ecc_new_point()) != NULL);
LTC_ARGCHK((C1 = ltc_ecc_new_point()) != NULL);
LTC_ARGCHK((C2 = ltc_ecc_new_point()) != NULL);
for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) {
/* get the base point */
for (z = 0; ltc_ecc_sets[z].name; z++) {
if (sizes[z] < ltc_ecc_sets[z].size) break;
}
LTC_ARGCHK(ltc_ecc_sets[z].name != NULL);
/* load it */
DO(mp_read_radix(G->x, ltc_ecc_sets[z].Gx, 16));
DO(mp_read_radix(G->y, ltc_ecc_sets[z].Gy, 16));
DO(mp_set(G->z, 1));
DO(mp_read_radix(modulus, ltc_ecc_sets[z].prime, 16));
DO(mp_montgomery_setup(modulus, &mp));
/* do 100 random tests */
for (y = 0; y < 100; y++) {
/* pick a random r1, r2 */
LTC_ARGCHK(yarrow_read(buf, sizes[x], &yarrow_prng) == sizes[x]);
DO(mp_read_unsigned_bin(rA, buf, sizes[x]));
LTC_ARGCHK(yarrow_read(buf, sizes[x], &yarrow_prng) == sizes[x]);
DO(mp_read_unsigned_bin(rB, buf, sizes[x]));
/* compute rA * G = A */
DO(ltc_mp.ecc_ptmul(rA, G, A, modulus, 1));
/* compute rB * G = B */
DO(ltc_mp.ecc_ptmul(rB, G, B, modulus, 1));
/* pick a random kA, kB */
LTC_ARGCHK(yarrow_read(buf, sizes[x], &yarrow_prng) == sizes[x]);
DO(mp_read_unsigned_bin(kA, buf, sizes[x]));
LTC_ARGCHK(yarrow_read(buf, sizes[x], &yarrow_prng) == sizes[x]);
DO(mp_read_unsigned_bin(kB, buf, sizes[x]));
/* now, compute kA*A + kB*B = C1 using the older method */
DO(ltc_mp.ecc_ptmul(kA, A, C1, modulus, 0));
DO(ltc_mp.ecc_ptmul(kB, B, C2, modulus, 0));
DO(ltc_mp.ecc_ptadd(C1, C2, C1, modulus, mp));
DO(ltc_mp.ecc_map(C1, modulus, mp));
/* now compute using mul2add */
DO(ltc_mp.ecc_mul2add(A, kA, B, kB, C2, modulus));
/* is they the sames? */
if ((mp_cmp(C1->x, C2->x) != LTC_MP_EQ) || (mp_cmp(C1->y, C2->y) != LTC_MP_EQ) || (mp_cmp(C1->z, C2->z) != LTC_MP_EQ)) {
fprintf(stderr, "ECC failed shamir test: size=%d, testno=%d\n", sizes[x], y);
return 1;
}
}
mp_montgomery_free(mp);
}
ltc_ecc_del_point(C2);
ltc_ecc_del_point(C1);
ltc_ecc_del_point(B);
ltc_ecc_del_point(A);
ltc_ecc_del_point(G);
mp_clear_multi(kA, kB, rA, rB, modulus, NULL);
return 0;
}