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
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21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
27 #define U (1 + ((BR_MAX_RSA_FACTOR + 30) / 31))
29 /* see bearssl_rsa.h */
31 br_rsa_i31_private(unsigned char *x
, const br_rsa_private_key
*sk
)
33 const unsigned char *p
, *q
;
36 uint32_t *mp
, *mq
, *s1
, *s2
, *t1
, *t2
, *t3
;
41 * All our temporary buffers are from the tmp[] array.
43 * The mp, mq, s1, s2, t1 and t2 buffers are large enough to
44 * contain a RSA factor. The t3 buffer can contain a complete
45 * RSA modulus. t3 shares its storage space with s2, s1 and t1,
46 * in that order (this is important, see below).
57 * Compute the actual lengths (in bytes) of p and q, and check
58 * that they fit within our stack buffers.
62 while (plen
> 0 && *p
== 0) {
68 while (qlen
> 0 && *q
== 0) {
72 if (plen
> (BR_MAX_RSA_FACTOR
>> 3)
73 || qlen
> (BR_MAX_RSA_FACTOR
>> 3))
81 br_i31_decode(mp
, p
, plen
);
82 br_i31_decode(mq
, q
, qlen
);
85 * Compute signature length (in bytes).
87 xlen
= (sk
->n_bitlen
+ 7) >> 3;
90 * Compute s1 = x^dp mod p.
92 p0i
= br_i31_ninv31(mp
[1]);
93 br_i31_decode_reduce(s1
, x
, xlen
, mp
);
94 br_i31_modpow(s1
, sk
->dp
, sk
->dplen
, mp
, p0i
, t1
, t2
);
97 * Compute s2 = x^dq mod q.
99 q0i
= br_i31_ninv31(mq
[1]);
100 br_i31_decode_reduce(s2
, x
, xlen
, mq
);
101 br_i31_modpow(s2
, sk
->dq
, sk
->dqlen
, mq
, q0i
, t1
, t2
);
105 * h = (s1 - s2)*(1/q) mod p
106 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
107 * unclear about whether p may be lower than q (some existing,
108 * widely deployed implementations of RSA don't tolerate p < q),
109 * but we want to support that occurrence, so we need to use the
110 * reduction function.
112 * Since we use br_i31_decode_reduce() for iq (purportedly, the
113 * inverse of q modulo p), we also tolerate improperly large
114 * values for this parameter.
116 br_i31_reduce(t2
, s2
, mp
);
117 br_i31_add(s1
, mp
, br_i31_sub(s1
, t2
, 1));
118 br_i31_to_monty(s1
, mp
);
119 br_i31_decode_reduce(t1
, sk
->iq
, sk
->iqlen
, mp
);
120 br_i31_montymul(t2
, s1
, t1
, mp
, p0i
);
123 * h is now in t2. We compute the final result:
125 * All these operations are non-modular.
127 * We need mq, s2 and t2. We use the t3 buffer as destination.
128 * The buffers mp, s1 and t1 are no longer needed. Moreover,
129 * the first step is to copy s2 into the destination buffer t3.
130 * We thus arranged for t3 to actually share space with s2, and
131 * to be followed by the space formerly used by s1 and t1.
133 br_i31_mulacc(t3
, mq
, t2
);
136 * Encode the result. Since we already checked the value of xlen,
137 * we can just use it right away.
139 br_i31_encode(x
, xlen
, t3
);
142 * The only error conditions remaining at that point are invalid
143 * values for p and q (even integers).
145 return p0i
& q0i
& 1;