2 * Copyright (c) 2016 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 (2 + ((BR_MAX_RSA_FACTOR + 30) / 31))
30 /* see bearssl_rsa.h */
32 br_rsa_i31_private(unsigned char *x
, const br_rsa_private_key
*sk
)
34 const unsigned char *p
, *q
;
39 uint32_t tmp
[1 + TLEN
];
41 uint32_t *mp
, *mq
, *s1
, *s2
, *t1
, *t2
, *t3
;
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).
51 while (plen
> 0 && *p
== 0) {
57 while (qlen
> 0 && *q
== 0) {
63 * Compute the maximum factor length, in words.
65 z
= (long)(plen
> qlen
? plen
: qlen
) << 3;
73 * Round up the word length to an even number.
78 * We need to fit at least 6 values in the stack buffer.
80 if (6 * fwlen
> TLEN
) {
85 * Compute signature length (in bytes).
87 xlen
= (sk
->n_bitlen
+ 7) >> 3;
93 br_i31_decode(mq
, q
, qlen
);
96 * Compute s2 = x^dq mod q.
98 q0i
= br_i31_ninv31(mq
[1]);
100 br_i31_decode_reduce(s2
, x
, xlen
, mq
);
101 r
= br_i31_modpow_opt(s2
, sk
->dq
, sk
->dqlen
, mq
, q0i
,
102 mq
+ 2 * fwlen
, TLEN
- 2 * fwlen
);
108 br_i31_decode(mp
, p
, plen
);
111 * Compute s1 = x^dp mod p.
113 p0i
= br_i31_ninv31(mp
[1]);
115 br_i31_decode_reduce(s1
, x
, xlen
, mp
);
116 r
&= br_i31_modpow_opt(s1
, sk
->dp
, sk
->dplen
, mp
, p0i
,
117 mq
+ 4 * fwlen
, TLEN
- 4 * fwlen
);
121 * h = (s1 - s2)*(1/q) mod p
122 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
123 * unclear about whether p may be lower than q (some existing,
124 * widely deployed implementations of RSA don't tolerate p < q),
125 * but we want to support that occurrence, so we need to use the
126 * reduction function.
128 * Since we use br_i31_decode_reduce() for iq (purportedly, the
129 * inverse of q modulo p), we also tolerate improperly large
130 * values for this parameter.
134 br_i31_reduce(t2
, s2
, mp
);
135 br_i31_add(s1
, mp
, br_i31_sub(s1
, t2
, 1));
136 br_i31_to_monty(s1
, mp
);
137 br_i31_decode_reduce(t1
, sk
->iq
, sk
->iqlen
, mp
);
138 br_i31_montymul(t2
, s1
, t1
, mp
, p0i
);
141 * h is now in t2. We compute the final result:
143 * All these operations are non-modular.
145 * We need mq, s2 and t2. We use the t3 buffer as destination.
146 * The buffers mp, s1 and t1 are no longer needed, so we can
147 * reuse them for t3. Moreover, the first step of the computation
148 * is to copy s2 into t3, after which s2 is not needed. Right
149 * now, mq is in slot 0, s2 is in slot 1, and t2 is in slot 5.
150 * Therefore, we have ample room for t3 by simply using s2.
153 br_i31_mulacc(t3
, mq
, t2
);
156 * Encode the result. Since we already checked the value of xlen,
157 * we can just use it right away.
159 br_i31_encode(x
, xlen
, t3
);
162 * The only error conditions remaining at that point are invalid
163 * values for p and q (even integers).
165 return p0i
& q0i
& r
;