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
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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 + 14) / 15))
30 /* see bearssl_rsa.h */
32 br_rsa_i15_private(unsigned char *x
, const br_rsa_private_key
*sk
)
34 const unsigned char *p
, *q
;
39 uint16_t tmp
[1 + TLEN
];
41 uint16_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;
72 * Round up the word length to an even number.
77 * We need to fit at least 6 values in the stack buffer.
79 if (6 * fwlen
> TLEN
) {
84 * Compute signature length (in bytes).
86 xlen
= (sk
->n_bitlen
+ 7) >> 3;
89 * Ensure 32-bit alignment for value words.
92 if (((uintptr_t)mq
& 2) == 0) {
99 br_i15_decode(mq
, q
, qlen
);
105 br_i15_decode(t1
, p
, plen
);
108 * Compute the modulus (product of the two factors), to compare
109 * it with the source value. We use br_i15_mulacc(), since it's
110 * already used later on.
113 br_i15_zero(t2
, mq
[0]);
114 br_i15_mulacc(t2
, mq
, t1
);
117 * We encode the modulus into bytes, to perform the comparison
118 * with bytes. We know that the product length, in bytes, is
120 * The comparison actually computes the carry when subtracting
121 * the modulus from the source value; that carry must be 1 for
122 * a value in the correct range. We keep it in r, which is our
123 * accumulator for the error code.
126 br_i15_encode(t3
, xlen
, t2
);
133 wn
= ((unsigned char *)t3
)[u
];
135 r
= ((wx
- (wn
+ r
)) >> 8) & 1;
139 * Move the decoded p to another temporary buffer.
142 memmove(mp
, t1
, fwlen
* sizeof *t1
);
145 * Compute s2 = x^dq mod q.
147 q0i
= br_i15_ninv15(mq
[1]);
149 br_i15_decode_reduce(s2
, x
, xlen
, mq
);
150 r
&= br_i15_modpow_opt(s2
, sk
->dq
, sk
->dqlen
, mq
, q0i
,
151 mq
+ 3 * fwlen
, TLEN
- 3 * fwlen
);
154 * Compute s1 = x^dq mod q.
156 p0i
= br_i15_ninv15(mp
[1]);
158 br_i15_decode_reduce(s1
, x
, xlen
, mp
);
159 r
&= br_i15_modpow_opt(s1
, sk
->dp
, sk
->dplen
, mp
, p0i
,
160 mq
+ 4 * fwlen
, TLEN
- 4 * fwlen
);
164 * h = (s1 - s2)*(1/q) mod p
165 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
166 * unclear about whether p may be lower than q (some existing,
167 * widely deployed implementations of RSA don't tolerate p < q),
168 * but we want to support that occurrence, so we need to use the
169 * reduction function.
171 * Since we use br_i15_decode_reduce() for iq (purportedly, the
172 * inverse of q modulo p), we also tolerate improperly large
173 * values for this parameter.
177 br_i15_reduce(t2
, s2
, mp
);
178 br_i15_add(s1
, mp
, br_i15_sub(s1
, t2
, 1));
179 br_i15_to_monty(s1
, mp
);
180 br_i15_decode_reduce(t1
, sk
->iq
, sk
->iqlen
, mp
);
181 br_i15_montymul(t2
, s1
, t1
, mp
, p0i
);
184 * h is now in t2. We compute the final result:
186 * All these operations are non-modular.
188 * We need mq, s2 and t2. We use the t3 buffer as destination.
189 * The buffers mp, s1 and t1 are no longer needed, so we can
190 * reuse them for t3. Moreover, the first step of the computation
191 * is to copy s2 into t3, after which s2 is not needed. Right
192 * now, mq is in slot 0, s2 is in slot 1, and t2 in slot 5.
193 * Therefore, we have ample room for t3 by simply using s2.
196 br_i15_mulacc(t3
, mq
, t2
);
199 * Encode the result. Since we already checked the value of xlen,
200 * we can just use it right away.
202 br_i15_encode(x
, xlen
, t3
);
205 * The only error conditions remaining at that point are invalid
206 * values for p and q (even integers).
208 return p0i
& q0i
& r
;