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

src/ec/ecdsa_i15_sign_raw.c

@@ -0,0 +1,184 @@
+/*
+ * 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))
+#define ORDER_LEN   ((BR_MAX_EC_SIZE + 7) >> 3)
+
+/* see bearssl_ec.h */
+size_t
+br_ecdsa_i15_sign_raw(const br_ec_impl *impl,
+	const br_hash_class *hf, const void *hash_value,
+	const br_ec_private_key *sk, void *sig)
+{
+	/*
+	 * 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.
+	 * We also rely on the last byte of the curve order to be distinct
+	 * from 0 and 1.
+	 */
+	const br_ec_curve_def *cd;
+	uint16_t n[I15_LEN], r[I15_LEN], s[I15_LEN], x[I15_LEN];
+	uint16_t m[I15_LEN], k[I15_LEN], t1[I15_LEN], t2[I15_LEN];
+	unsigned char tt[ORDER_LEN << 1];
+	unsigned char eU[POINT_LEN];
+	size_t hash_len, nlen, ulen;
+	uint16_t n0i;
+	uint32_t ctl;
+	br_hmac_drbg_context drbg;
+
+	/*
+	 * If the curve is not supported, then exit with an error.
+	 */
+	if (((impl->supported_curves >> sk->curve) & 1) == 0) {
+		return 0;
+	}
+
+	/*
+	 * Get the curve parameters (generator and order).
+	 */
+	switch (sk->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;
+	}
+
+	/*
+	 * Get modulus.
+	 */
+	nlen = cd->order_len;
+	br_i15_decode(n, cd->order, nlen);
+	n0i = br_i15_ninv15(n[1]);
+
+	/*
+	 * Get private key as an i15 integer. This also checks that the
+	 * private key is well-defined (not zero, and less than the
+	 * curve order).
+	 */
+	if (!br_i15_decode_mod(x, sk->x, sk->xlen, n)) {
+		return 0;
+	}
+	if (br_i15_iszero(x)) {
+		return 0;
+	}
+
+	/*
+	 * Get hash length.
+	 */
+	hash_len = (hf->desc >> BR_HASHDESC_OUT_OFF) & BR_HASHDESC_OUT_MASK;
+
+	/*
+	 * Truncate and reduce the hash value modulo the curve order.
+	 */
+	br_ecdsa_i15_bits2int(m, hash_value, hash_len, n[0]);
+	br_i15_sub(m, n, br_i15_sub(m, n, 0) ^ 1);
+
+	/*
+	 * RFC 6979 generation of the "k" value.
+	 *
+	 * The process uses HMAC_DRBG (with the hash function used to
+	 * process the message that is to be signed). The seed is the
+	 * concatenation of the encodings of the private key and
+	 * the hash value (after truncation and modular reduction).
+	 */
+	br_i15_encode(tt, nlen, x);
+	br_i15_encode(tt + nlen, nlen, m);
+	br_hmac_drbg_init(&drbg, hf, tt, nlen << 1);
+	for (;;) {
+		br_hmac_drbg_generate(&drbg, tt, nlen);
+		br_ecdsa_i15_bits2int(k, tt, nlen, n[0]);
+		if (br_i15_iszero(k)) {
+			continue;
+		}
+		if (br_i15_sub(k, n, 0)) {
+			break;
+		}
+	}
+
+	/*
+	 * Compute k*G and extract the X coordinate, then reduce it
+	 * modulo the curve order. Since we support only curves with
+	 * prime order, that reduction is only a matter of computing
+	 * a subtraction.
+	 */
+	ulen = cd->generator_len;
+	memcpy(eU, cd->generator, ulen);
+	br_i15_encode(tt, nlen, k);
+	if (!impl->mul(eU, ulen, tt, nlen, sk->curve)) {
+		/*
+		 * Point multiplication may fail here only if the
+		 * EC implementation does not support the curve, or the
+		 * private key is incorrect (x is a multiple of the curve
+		 * order).
+		 */
+		return 0;
+	}
+	br_i15_zero(r, n[0]);
+	br_i15_decode(r, &eU[1], ulen >> 1);
+	r[0] = n[0];
+	br_i15_sub(r, n, br_i15_sub(r, n, 0) ^ 1);
+
+	/*
+	 * Compute 1/k in double-Montgomery representation. We do so by
+	 * first converting _from_ Montgomery representation (twice),
+	 * then using a modular exponentiation.
+	 */
+	br_i15_from_monty(k, n, n0i);
+	br_i15_from_monty(k, n, n0i);
+	memcpy(tt, cd->order, nlen);
+	tt[nlen - 1] -= 2;
+	br_i15_modpow(k, tt, nlen, n, n0i, t1, t2);
+
+	/*
+	 * Compute s = (m+xr)/k (mod n).
+	 * The k[] array contains R^2/k (double-Montgomery representation);
+	 * we thus can use direct Montgomery multiplications and conversions
+	 * from Montgomery, avoiding any call to br_i15_to_monty() (which
+	 * is slower).
+	 */
+	br_i15_from_monty(m, n, n0i);
+	br_i15_montymul(t1, x, r, n, n0i);
+	ctl = br_i15_add(t1, m, 1);
+	ctl |= br_i15_sub(t1, n, 0) ^ 1;
+	br_i15_sub(t1, n, ctl);
+	br_i15_montymul(s, t1, k, n, n0i);
+
+	/*
+	 * Encode r and s in the signature.
+	 */
+	br_i15_encode(sig, nlen, r);
+	br_i15_encode((unsigned char *)sig + nlen, nlen, s);
+	return nlen << 1;
+}