1/*
2 * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
11 *
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
14 *
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24
25#include "inner.h"
26
27#define U      (2 + ((BR_MAX_RSA_FACTOR + 14) / 15))
28#define TLEN   (8 * U)
29
30/* see bearssl_rsa.h */
31uint32_t
32br_rsa_i15_private(unsigned char *x, const br_rsa_private_key *sk)
33{
34	const unsigned char *p, *q;
35	size_t plen, qlen;
36	size_t fwlen;
37	uint16_t p0i, q0i;
38	size_t xlen, u;
39	uint16_t tmp[1 + TLEN];
40	long z;
41	uint16_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
42	uint32_t r;
43
44	/*
45	 * Compute the actual lengths of p and q, in bytes.
46	 * These lengths are not considered secret (we cannot really hide
47	 * them anyway in constant-time code).
48	 */
49	p = sk->p;
50	plen = sk->plen;
51	while (plen > 0 && *p == 0) {
52		p ++;
53		plen --;
54	}
55	q = sk->q;
56	qlen = sk->qlen;
57	while (qlen > 0 && *q == 0) {
58		q ++;
59		qlen --;
60	}
61
62	/*
63	 * Compute the maximum factor length, in words.
64	 */
65	z = (long)(plen > qlen ? plen : qlen) << 3;
66	fwlen = 1;
67	while (z > 0) {
68		z -= 15;
69		fwlen ++;
70	}
71	/*
72	 * Round up the word length to an even number.
73	 */
74	fwlen += (fwlen & 1);
75
76	/*
77	 * We need to fit at least 6 values in the stack buffer.
78	 */
79	if (6 * fwlen > TLEN) {
80		return 0;
81	}
82
83	/*
84	 * Compute signature length (in bytes).
85	 */
86	xlen = (sk->n_bitlen + 7) >> 3;
87
88	/*
89	 * Ensure 32-bit alignment for value words.
90	 */
91	mq = tmp;
92	if (((uintptr_t)mq & 2) == 0) {
93		mq ++;
94	}
95
96	/*
97	 * Decode q.
98	 */
99	br_i15_decode(mq, q, qlen);
100
101	/*
102	 * Decode p.
103	 */
104	t1 = mq + fwlen;
105	br_i15_decode(t1, p, plen);
106
107	/*
108	 * Compute the modulus (product of the two factors), to compare
109	 * it with the source value. We use br_i15_mulacc(), since it's
110	 * already used later on.
111	 */
112	t2 = mq + 2 * fwlen;
113	br_i15_zero(t2, mq[0]);
114	br_i15_mulacc(t2, mq, t1);
115
116	/*
117	 * We encode the modulus into bytes, to perform the comparison
118	 * with bytes. We know that the product length, in bytes, is
119	 * exactly xlen.
120	 * The comparison actually computes the carry when subtracting
121	 * the modulus from the source value; that carry must be 1 for
122	 * a value in the correct range. We keep it in r, which is our
123	 * accumulator for the error code.
124	 */
125	t3 = mq + 4 * fwlen;
126	br_i15_encode(t3, xlen, t2);
127	u = xlen;
128	r = 0;
129	while (u > 0) {
130		uint32_t wn, wx;
131
132		u --;
133		wn = ((unsigned char *)t3)[u];
134		wx = x[u];
135		r = ((wx - (wn + r)) >> 8) & 1;
136	}
137
138	/*
139	 * Move the decoded p to another temporary buffer.
140	 */
141	mp = mq + 2 * fwlen;
142	memmove(mp, t1, fwlen * sizeof *t1);
143
144	/*
145	 * Compute s2 = x^dq mod q.
146	 */
147	q0i = br_i15_ninv15(mq[1]);
148	s2 = mq + fwlen;
149	br_i15_decode_reduce(s2, x, xlen, mq);
150	r &= br_i15_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
151		mq + 3 * fwlen, TLEN - 3 * fwlen);
152
153	/*
154	 * Compute s1 = x^dq mod q.
155	 */
156	p0i = br_i15_ninv15(mp[1]);
157	s1 = mq + 3 * fwlen;
158	br_i15_decode_reduce(s1, x, xlen, mp);
159	r &= br_i15_modpow_opt(s1, sk->dp, sk->dplen, mp, p0i,
160		mq + 4 * fwlen, TLEN - 4 * fwlen);
161
162	/*
163	 * Compute:
164	 *   h = (s1 - s2)*(1/q) mod p
165	 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
166	 * unclear about whether p may be lower than q (some existing,
167	 * widely deployed implementations of RSA don't tolerate p < q),
168	 * but we want to support that occurrence, so we need to use the
169	 * reduction function.
170	 *
171	 * Since we use br_i15_decode_reduce() for iq (purportedly, the
172	 * inverse of q modulo p), we also tolerate improperly large
173	 * values for this parameter.
174	 */
175	t1 = mq + 4 * fwlen;
176	t2 = mq + 5 * fwlen;
177	br_i15_reduce(t2, s2, mp);
178	br_i15_add(s1, mp, br_i15_sub(s1, t2, 1));
179	br_i15_to_monty(s1, mp);
180	br_i15_decode_reduce(t1, sk->iq, sk->iqlen, mp);
181	br_i15_montymul(t2, s1, t1, mp, p0i);
182
183	/*
184	 * h is now in t2. We compute the final result:
185	 *   s = s2 + q*h
186	 * All these operations are non-modular.
187	 *
188	 * We need mq, s2 and t2. We use the t3 buffer as destination.
189	 * The buffers mp, s1 and t1 are no longer needed, so we can
190	 * reuse them for t3. Moreover, the first step of the computation
191	 * is to copy s2 into t3, after which s2 is not needed. Right
192	 * now, mq is in slot 0, s2 is in slot 1, and t2 in slot 5.
193	 * Therefore, we have ample room for t3 by simply using s2.
194	 */
195	t3 = s2;
196	br_i15_mulacc(t3, mq, t2);
197
198	/*
199	 * Encode the result. Since we already checked the value of xlen,
200	 * we can just use it right away.
201	 */
202	br_i15_encode(x, xlen, t3);
203
204	/*
205	 * The only error conditions remaining at that point are invalid
206	 * values for p and q (even integers).
207	 */
208	return p0i & q0i & r;
209}
210