New "i15" implementation of big integers (faster, and constant-time, on ARM Cortex M0/M0+); imported into EC, ECDSA, RSA.

src/ec/ecdsa_i15_vrfy_raw.c

@@ -0,0 +1,166 @@
+/*
+ * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining 
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be 
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+#define I15_LEN     ((BR_MAX_EC_SIZE + 29) / 15)
+#define POINT_LEN   (1 + (((BR_MAX_EC_SIZE + 7) >> 3) << 1))
+
+/* see bearssl_ec.h */
+uint32_t
+br_ecdsa_i15_vrfy_raw(const br_ec_impl *impl,
+	const void *hash, size_t hash_len,
+	const br_ec_public_key *pk,
+	const void *sig, size_t sig_len)
+{
+	/*
+	 * IMPORTANT: this code is fit only for curves with a prime
+	 * order. This is needed so that modular reduction of the X
+	 * coordinate of a point can be done with a simple subtraction.
+	 */
+	const br_ec_curve_def *cd;
+	uint16_t n[I15_LEN], r[I15_LEN], s[I15_LEN], t1[I15_LEN], t2[I15_LEN];
+	unsigned char tx[(BR_MAX_EC_SIZE + 7) >> 3];
+	unsigned char ty[(BR_MAX_EC_SIZE + 7) >> 3];
+	unsigned char eU[POINT_LEN];
+	size_t nlen, rlen, ulen;
+	uint16_t n0i;
+	uint32_t res;
+
+	/*
+	 * If the curve is not supported, then report an error.
+	 */
+	if (((impl->supported_curves >> pk->curve) & 1) == 0) {
+		return 0;
+	}
+
+	/*
+	 * Get the curve parameters (generator and order).
+	 */
+	switch (pk->curve) {
+	case BR_EC_secp256r1:
+		cd = &br_secp256r1;
+		break;
+	case BR_EC_secp384r1:
+		cd = &br_secp384r1;
+		break;
+	case BR_EC_secp521r1:
+		cd = &br_secp521r1;
+		break;
+	default:
+		return 0;
+	}
+
+	/*
+	 * Signature length must be even.
+	 */
+	if (sig_len & 1) {
+		return 0;
+	}
+	rlen = sig_len >> 1;
+
+	/*
+	 * Public key point must have the proper size for this curve.
+	 */
+	if (pk->qlen != cd->generator_len) {
+		return 0;
+	}
+
+	/*
+	 * Get modulus; then decode the r and s values. They must be
+	 * lower than the modulus, and s must not be null.
+	 */
+	nlen = cd->order_len;
+	br_i15_decode(n, cd->order, nlen);
+	n0i = br_i15_ninv15(n[1]);
+	if (!br_i15_decode_mod(r, sig, rlen, n)) {
+		return 0;
+	}
+	if (!br_i15_decode_mod(s, (const unsigned char *)sig + rlen, rlen, n)) {
+		return 0;
+	}
+	if (br_i15_iszero(s)) {
+		return 0;
+	}
+
+	/*
+	 * Invert s. We do that with a modular exponentiation; we use
+	 * the fact that for all the curves we support, the least
+	 * significant byte is not 0 or 1, so we can subtract 2 without
+	 * any carry to process.
+	 * We also want 1/s in Montgomery representation, which can be
+	 * done by converting _from_ Montgomery representation before
+	 * the inversion (because (1/s)*R = 1/(s/R)).
+	 */
+	br_i15_from_monty(s, n, n0i);
+	memcpy(tx, cd->order, nlen);
+	tx[nlen - 1] -= 2;
+	br_i15_modpow(s, tx, nlen, n, n0i, t1, t2);
+
+	/*
+	 * Truncate the hash to the modulus length (in bits) and reduce
+	 * it modulo the curve order. The modular reduction can be done
+	 * with a subtraction since the truncation already reduced the
+	 * value to the modulus bit length.
+	 */
+	br_ecdsa_i15_bits2int(t1, hash, hash_len, n[0]);
+	br_i15_sub(t1, n, br_i15_sub(t1, n, 0) ^ 1);
+
+	/*
+	 * Multiply the (truncated, reduced) hash value with 1/s, result in
+	 * t2, encoded in ty.
+	 */
+	br_i15_montymul(t2, t1, s, n, n0i);
+	br_i15_encode(ty, nlen, t2);
+
+	/*
+	 * Multiply r with 1/s, result in t1, encoded in tx.
+	 */
+	br_i15_montymul(t1, r, s, n, n0i);
+	br_i15_encode(tx, nlen, t1);
+
+	/*
+	 * Compute the point x*Q + y*G.
+	 */
+	ulen = cd->generator_len;
+	memcpy(eU, pk->q, ulen);
+	res = impl->muladd(eU, cd->generator, ulen,
+		tx, nlen, ty, nlen, cd->curve);
+
+	/*
+	 * Get the X coordinate, reduce modulo the curve order, and
+	 * compare with the 'r' value.
+	 *
+	 * The modular reduction can be done with subtractions because
+	 * we work with curves of prime order, so the curve order is
+	 * close to the field order (Hasse's theorem).
+	 */
+	br_i15_zero(t1, n[0]);
+	br_i15_decode(t1, &eU[1], ulen >> 1);
+	t1[0] = n[0];
+	br_i15_sub(t1, n, br_i15_sub(t1, n, 0) ^ 1);
+	res &= ~br_i15_sub(t1, r, 1);
+	res &= br_i15_iszero(t1);
+	return res;
+}