2 * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
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:
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
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
27 #define U (1 + ((BR_MAX_RSA_FACTOR + 14) / 15))
32 print_int(const char *name, const uint16_t *x)
34 extern int printf(const char *fmt, ...);
35 unsigned char tmp[1000];
38 len = (x[0] - (x[0] >> 4) + 7) >> 3;
39 br_i15_encode(tmp, len, x);
40 printf("%s = ", name);
41 for (u = 0; u < len; u ++) {
42 printf("%02X", tmp[u]);
48 /* see bearssl_rsa.h */
50 br_rsa_i15_private(unsigned char *x
, const br_rsa_private_key
*sk
)
52 const unsigned char *p
, *q
;
59 uint16_t *mp
, *mq
, *s1
, *s2
, *t1
, *t2
, *t3
;
63 * Compute the actual lengths of p and q, in bytes.
64 * These lengths are not considered secret (we cannot really hide
65 * them anyway in constant-time code).
69 while (plen
> 0 && *p
== 0) {
75 while (qlen
> 0 && *q
== 0) {
81 * Compute the maximum factor length, in words.
83 z
= (long)(plen
> qlen
? plen
: qlen
) << 3;
91 * We need to fit at least 6 values in the stack buffer.
93 if (6 * fwlen
> TLEN
) {
98 * Compute signature length (in bytes).
100 xlen
= (sk
->n_bitlen
+ 7) >> 3;
106 br_i15_decode(mq
, q
, qlen
);
109 * Compute s2 = x^dq mod q.
111 q0i
= br_i15_ninv15(mq
[1]);
113 br_i15_decode_reduce(s2
, x
, xlen
, mq
);
114 r
= br_i15_modpow_opt(s2
, sk
->dq
, sk
->dqlen
, mq
, q0i
,
115 tmp
+ 2 * fwlen
, TLEN
- 2 * fwlen
);
120 mp
= tmp
+ 2 * fwlen
;
121 br_i15_decode(mp
, p
, plen
);
124 * Compute s1 = x^dq mod q.
126 p0i
= br_i15_ninv15(mp
[1]);
127 s1
= tmp
+ 3 * fwlen
;
128 br_i15_decode_reduce(s1
, x
, xlen
, mp
);
129 r
&= br_i15_modpow_opt(s1
, sk
->dp
, sk
->dplen
, mp
, p0i
,
130 tmp
+ 4 * fwlen
, TLEN
- 4 * fwlen
);
134 * h = (s1 - s2)*(1/q) mod p
135 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
136 * unclear about whether p may be lower than q (some existing,
137 * widely deployed implementations of RSA don't tolerate p < q),
138 * but we want to support that occurrence, so we need to use the
139 * reduction function.
141 * Since we use br_i15_decode_reduce() for iq (purportedly, the
142 * inverse of q modulo p), we also tolerate improperly large
143 * values for this parameter.
145 t1
= tmp
+ 4 * fwlen
;
146 t2
= tmp
+ 5 * fwlen
;
147 br_i15_reduce(t2
, s2
, mp
);
148 br_i15_add(s1
, mp
, br_i15_sub(s1
, t2
, 1));
149 br_i15_to_monty(s1
, mp
);
150 br_i15_decode_reduce(t1
, sk
->iq
, sk
->iqlen
, mp
);
151 br_i15_montymul(t2
, s1
, t1
, mp
, p0i
);
154 * h is now in t2. We compute the final result:
156 * All these operations are non-modular.
158 * We need mq, s2 and t2. We use the t3 buffer as destination.
159 * The buffers mp, s1 and t1 are no longer needed, so we can
160 * reuse them for t3. Moreover, the first step of the computation
161 * is to copy s2 into t3, after which s2 is not needed. Right
162 * now, mq is in slot 0, s2 is in slot 1, and t2 in slot 5.
163 * Therefore, we have ample room for t3 by simply using s2.
166 br_i15_mulacc(t3
, mq
, t2
);
169 * Encode the result. Since we already checked the value of xlen,
170 * we can just use it right away.
172 br_i15_encode(x
, xlen
, t3
);
175 * The only error conditions remaining at that point are invalid
176 * values for p and q (even integers).
178 return p0i
& q0i
& r
;