/** 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; }