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
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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 modulus length (in bytes).
87 xlen
= (sk
->n_bitlen
+ 7) >> 3;
93 br_i31_decode(mq
, q
, qlen
);
99 br_i31_decode(t1
, p
, plen
);
102 * Compute the modulus (product of the two factors), to compare
103 * it with the source value. We use br_i31_mulacc(), since it's
104 * already used later on.
107 br_i31_zero(t2
, mq
[0]);
108 br_i31_mulacc(t2
, mq
, t1
);
111 * We encode the modulus into bytes, to perform the comparison
112 * with bytes. We know that the product length, in bytes, is
114 * The comparison actually computes the carry when subtracting
115 * the modulus from the source value; that carry must be 1 for
116 * a value in the correct range. We keep it in r, which is our
117 * accumulator for the error code.
120 br_i31_encode(t3
, xlen
, t2
);
127 wn
= ((unsigned char *)t3
)[u
];
129 r
= ((wx
- (wn
+ r
)) >> 8) & 1;
133 * Move the decoded p to another temporary buffer.
136 memmove(mp
, t1
, fwlen
* sizeof *t1
);
139 * Compute s2 = x^dq mod q.
141 q0i
= br_i31_ninv31(mq
[1]);
143 br_i31_decode_reduce(s2
, x
, xlen
, mq
);
144 r
&= br_i31_modpow_opt(s2
, sk
->dq
, sk
->dqlen
, mq
, q0i
,
145 mq
+ 3 * fwlen
, TLEN
- 3 * fwlen
);
148 * Compute s1 = x^dp mod p.
150 p0i
= br_i31_ninv31(mp
[1]);
152 br_i31_decode_reduce(s1
, x
, xlen
, mp
);
153 r
&= br_i31_modpow_opt(s1
, sk
->dp
, sk
->dplen
, mp
, p0i
,
154 mq
+ 4 * fwlen
, TLEN
- 4 * fwlen
);
158 * h = (s1 - s2)*(1/q) mod p
159 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
160 * unclear about whether p may be lower than q (some existing,
161 * widely deployed implementations of RSA don't tolerate p < q),
162 * but we want to support that occurrence, so we need to use the
163 * reduction function.
165 * Since we use br_i31_decode_reduce() for iq (purportedly, the
166 * inverse of q modulo p), we also tolerate improperly large
167 * values for this parameter.
171 br_i31_reduce(t2
, s2
, mp
);
172 br_i31_add(s1
, mp
, br_i31_sub(s1
, t2
, 1));
173 br_i31_to_monty(s1
, mp
);
174 br_i31_decode_reduce(t1
, sk
->iq
, sk
->iqlen
, mp
);
175 br_i31_montymul(t2
, s1
, t1
, mp
, p0i
);
178 * h is now in t2. We compute the final result:
180 * All these operations are non-modular.
182 * We need mq, s2 and t2. We use the t3 buffer as destination.
183 * The buffers mp, s1 and t1 are no longer needed, so we can
184 * reuse them for t3. Moreover, the first step of the computation
185 * is to copy s2 into t3, after which s2 is not needed. Right
186 * now, mq is in slot 0, s2 is in slot 1, and t2 is in slot 5.
187 * Therefore, we have ample room for t3 by simply using s2.
190 br_i31_mulacc(t3
, mq
, t2
);
193 * Encode the result. Since we already checked the value of xlen,
194 * we can just use it right away.
196 br_i31_encode(x
, xlen
, t3
);
199 * The only error conditions remaining at that point are invalid
200 * values for p and q (even integers).
202 return p0i
& q0i
& r
;