1/*
2 * Copyright (c) 2016 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#if BR_INT128 || BR_UMUL128
28
29#define U      (2 + ((BR_MAX_RSA_FACTOR + 30) / 31))
30#define TLEN   (4 * U)  /* TLEN is counted in 64-bit words */
31
32/* see bearssl_rsa.h */
33uint32_t
34br_rsa_i62_private(unsigned char *x, const br_rsa_private_key *sk)
35{
36	const unsigned char *p, *q;
37	size_t plen, qlen;
38	size_t fwlen;
39	uint32_t p0i, q0i;
40	size_t xlen, u;
41	uint64_t tmp[TLEN];
42	long z;
43	uint32_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
44	uint32_t r;
45
46	/*
47	 * Compute the actual lengths of p and q, in bytes.
48	 * These lengths are not considered secret (we cannot really hide
49	 * them anyway in constant-time code).
50	 */
51	p = sk->p;
52	plen = sk->plen;
53	while (plen > 0 && *p == 0) {
54		p ++;
55		plen --;
56	}
57	q = sk->q;
58	qlen = sk->qlen;
59	while (qlen > 0 && *q == 0) {
60		q ++;
61		qlen --;
62	}
63
64	/*
65	 * Compute the maximum factor length, in words.
66	 */
67	z = (long)(plen > qlen ? plen : qlen) << 3;
68	fwlen = 1;
69	while (z > 0) {
70		z -= 31;
71		fwlen ++;
72	}
73
74	/*
75	 * Convert size to 62-bit words.
76	 */
77	fwlen = (fwlen + 1) >> 1;
78
79	/*
80	 * We need to fit at least 6 values in the stack buffer.
81	 */
82	if (6 * fwlen > TLEN) {
83		return 0;
84	}
85
86	/*
87	 * Compute signature length (in bytes).
88	 */
89	xlen = (sk->n_bitlen + 7) >> 3;
90
91	/*
92	 * Decode q.
93	 */
94	mq = (uint32_t *)tmp;
95	br_i31_decode(mq, q, qlen);
96
97	/*
98	 * Decode p.
99	 */
100	t1 = (uint32_t *)(tmp + fwlen);
101	br_i31_decode(t1, p, plen);
102
103	/*
104	 * Compute the modulus (product of the two factors), to compare
105	 * it with the source value. We use br_i31_mulacc(), since it's
106	 * already used later on.
107	 */
108	t2 = (uint32_t *)(tmp + 2 * fwlen);
109	br_i31_zero(t2, mq[0]);
110	br_i31_mulacc(t2, mq, t1);
111
112	/*
113	 * We encode the modulus into bytes, to perform the comparison
114	 * with bytes. We know that the product length, in bytes, is
115	 * exactly xlen.
116	 * The comparison actually computes the carry when subtracting
117	 * the modulus from the source value; that carry must be 1 for
118	 * a value in the correct range. We keep it in r, which is our
119	 * accumulator for the error code.
120	 */
121	t3 = (uint32_t *)(tmp + 4 * fwlen);
122	br_i31_encode(t3, xlen, t2);
123	u = xlen;
124	r = 0;
125	while (u > 0) {
126		uint32_t wn, wx;
127
128		u --;
129		wn = ((unsigned char *)t3)[u];
130		wx = x[u];
131		r = ((wx - (wn + r)) >> 8) & 1;
132	}
133
134	/*
135	 * Move the decoded p to another temporary buffer.
136	 */
137	mp = (uint32_t *)(tmp + 2 * fwlen);
138	memmove(mp, t1, 2 * fwlen * sizeof *t1);
139
140	/*
141	 * Compute s2 = x^dq mod q.
142	 */
143	q0i = br_i31_ninv31(mq[1]);
144	s2 = (uint32_t *)(tmp + fwlen);
145	br_i31_decode_reduce(s2, x, xlen, mq);
146	r &= br_i62_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
147		tmp + 3 * fwlen, TLEN - 3 * fwlen);
148
149	/*
150	 * Compute s1 = x^dp mod p.
151	 */
152	p0i = br_i31_ninv31(mp[1]);
153	s1 = (uint32_t *)(tmp + 3 * fwlen);
154	br_i31_decode_reduce(s1, x, xlen, mp);
155	r &= br_i62_modpow_opt(s1, sk->dp, sk->dplen, mp, p0i,
156		tmp + 4 * fwlen, TLEN - 4 * fwlen);
157
158	/*
159	 * Compute:
160	 *   h = (s1 - s2)*(1/q) mod p
161	 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
162	 * unclear about whether p may be lower than q (some existing,
163	 * widely deployed implementations of RSA don't tolerate p < q),
164	 * but we want to support that occurrence, so we need to use the
165	 * reduction function.
166	 *
167	 * Since we use br_i31_decode_reduce() for iq (purportedly, the
168	 * inverse of q modulo p), we also tolerate improperly large
169	 * values for this parameter.
170	 */
171	t1 = (uint32_t *)(tmp + 4 * fwlen);
172	t2 = (uint32_t *)(tmp + 5 * fwlen);
173	br_i31_reduce(t2, s2, mp);
174	br_i31_add(s1, mp, br_i31_sub(s1, t2, 1));
175	br_i31_to_monty(s1, mp);
176	br_i31_decode_reduce(t1, sk->iq, sk->iqlen, mp);
177	br_i31_montymul(t2, s1, t1, mp, p0i);
178
179	/*
180	 * h is now in t2. We compute the final result:
181	 *   s = s2 + q*h
182	 * All these operations are non-modular.
183	 *
184	 * We need mq, s2 and t2. We use the t3 buffer as destination.
185	 * The buffers mp, s1 and t1 are no longer needed, so we can
186	 * reuse them for t3. Moreover, the first step of the computation
187	 * is to copy s2 into t3, after which s2 is not needed. Right
188	 * now, mq is in slot 0, s2 is in slot 1, and t2 is in slot 5.
189	 * Therefore, we have ample room for t3 by simply using s2.
190	 */
191	t3 = s2;
192	br_i31_mulacc(t3, mq, t2);
193
194	/*
195	 * Encode the result. Since we already checked the value of xlen,
196	 * we can just use it right away.
197	 */
198	br_i31_encode(x, xlen, t3);
199
200	/*
201	 * The only error conditions remaining at that point are invalid
202	 * values for p and q (even integers).
203	 */
204	return p0i & q0i & r;
205}
206
207/* see bearssl_rsa.h */
208br_rsa_private
209br_rsa_i62_private_get(void)
210{
211	return &br_rsa_i62_private;
212}
213
214#else
215
216/* see bearssl_rsa.h */
217br_rsa_private
218br_rsa_i62_private_get(void)
219{
220	return 0;
221}
222
223#endif
224