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

src/rsa/rsa_i15_priv.c

@@ -0,0 +1,146 @@
+/*
+ * 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 U   (1 + ((BR_MAX_RSA_FACTOR + 14) / 15))
+
+/* see bearssl_rsa.h */
+uint32_t
+br_rsa_i15_private(unsigned char *x, const br_rsa_private_key *sk)
+{
+	const unsigned char *p, *q;
+	size_t plen, qlen;
+	uint16_t tmp[6 * U];
+	uint16_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
+	uint16_t p0i, q0i;
+	size_t xlen;
+
+	/*
+	 * All our temporary buffers are from the tmp[] array.
+	 *
+	 * The mp, mq, s1, s2, t1 and t2 buffers are large enough to
+	 * contain a RSA factor. The t3 buffer can contain a complete
+	 * RSA modulus. t3 shares its storage space with s2, s1 and t1,
+	 * in that order (this is important, see below).
+	 */
+	mq = tmp;
+	mp = tmp + U;
+	t2 = tmp + 2 * U;
+	s2 = tmp + 3 * U;
+	s1 = tmp + 4 * U;
+	t1 = tmp + 5 * U;
+	t3 = s2;
+
+	/*
+	 * Compute the actual lengths (in bytes) of p and q, and check
+	 * that they fit within our stack buffers.
+	 */
+	p = sk->p;
+	plen = sk->plen;
+	while (plen > 0 && *p == 0) {
+		p ++;
+		plen --;
+	}
+	q = sk->q;
+	qlen = sk->qlen;
+	while (qlen > 0 && *q == 0) {
+		q ++;
+		qlen --;
+	}
+	if (plen > (BR_MAX_RSA_FACTOR >> 3)
+		|| qlen > (BR_MAX_RSA_FACTOR >> 3))
+	{
+		return 0;
+	}
+
+	/*
+	 * Decode p and q.
+	 */
+	br_i15_decode(mp, p, plen);
+	br_i15_decode(mq, q, qlen);
+
+	/*
+	 * Compute signature length (in bytes).
+	 */
+	xlen = (sk->n_bitlen + 7) >> 3;
+
+	/*
+	 * Compute s1 = x^dp mod p.
+	 */
+	p0i = br_i15_ninv15(mp[1]);
+	br_i15_decode_reduce(s1, x, xlen, mp);
+	br_i15_modpow(s1, sk->dp, sk->dplen, mp, p0i, t1, t2);
+
+	/*
+	 * Compute s2 = x^dq mod q.
+	 */
+	q0i = br_i15_ninv15(mq[1]);
+	br_i15_decode_reduce(s2, x, xlen, mq);
+	br_i15_modpow(s2, sk->dq, sk->dqlen, mq, q0i, t1, t2);
+
+	/*
+	 * Compute:
+	 *   h = (s1 - s2)*(1/q) mod p
+	 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
+	 * unclear about whether p may be lower than q (some existing,
+	 * widely deployed implementations of RSA don't tolerate p < q),
+	 * but we want to support that occurrence, so we need to use the
+	 * reduction function.
+	 *
+	 * Since we use br_i15_decode_reduce() for iq (purportedly, the
+	 * inverse of q modulo p), we also tolerate improperly large
+	 * values for this parameter.
+	 */
+	br_i15_reduce(t2, s2, mp);
+	br_i15_add(s1, mp, br_i15_sub(s1, t2, 1));
+	br_i15_to_monty(s1, mp);
+	br_i15_decode_reduce(t1, sk->iq, sk->iqlen, mp);
+	br_i15_montymul(t2, s1, t1, mp, p0i);
+
+	/*
+	 * h is now in t2. We compute the final result:
+	 *   s = s2 + q*h
+	 * All these operations are non-modular.
+	 *
+	 * We need mq, s2 and t2. We use the t3 buffer as destination.
+	 * The buffers mp, s1 and t1 are no longer needed. Moreover,
+	 * the first step is to copy s2 into the destination buffer t3.
+	 * We thus arranged for t3 to actually share space with s2, and
+	 * to be followed by the space formerly used by s1 and t1.
+	 */
+	br_i15_mulacc(t3, mq, t2);
+
+	/*
+	 * Encode the result. Since we already checked the value of xlen,
+	 * we can just use it right away.
+	 */
+	br_i15_encode(x, xlen, t3);
+
+	/*
+	 * The only error conditions remaining at that point are invalid
+	 * values for p and q (even integers).
+	 */
+	return p0i & q0i & 1;
+}