2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
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27 #if BR_INT128 || BR_UMUL128
29 #define U (2 + ((BR_MAX_RSA_FACTOR + 30) / 31))
30 #define TLEN (4 * U) /* TLEN is counted in 64-bit words */
32 /* see bearssl_rsa.h */
34 br_rsa_i62_private(unsigned char *x, const br_rsa_private_key *sk)
36 const unsigned char *p, *q;
43 uint32_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
47 * Compute the actual lengths of p and q, in bytes.
48 * These lengths are not considered secret (we cannot really hide
49 * them anyway in constant-time code).
53 while (plen > 0 && *p == 0) {
59 while (qlen > 0 && *q == 0) {
65 * Compute the maximum factor length, in words.
67 z = (long)(plen > qlen ? plen : qlen) << 3;
75 * Convert size to 62-bit words.
77 fwlen = (fwlen + 1) >> 1;
80 * We need to fit at least 6 values in the stack buffer.
82 if (6 * fwlen > TLEN) {
87 * Compute signature length (in bytes).
89 xlen = (sk->n_bitlen + 7) >> 3;
95 br_i31_decode(mq, q, qlen);
100 t1 = (uint32_t *)(tmp + fwlen);
101 br_i31_decode(t1, p, plen);
104 * Compute the modulus (product of the two factors), to compare
105 * it with the source value. We use br_i31_mulacc(), since it's
106 * already used later on.
108 t2 = (uint32_t *)(tmp + 2 * fwlen);
109 br_i31_zero(t2, mq[0]);
110 br_i31_mulacc(t2, mq, t1);
113 * We encode the modulus into bytes, to perform the comparison
114 * with bytes. We know that the product length, in bytes, is
116 * The comparison actually computes the carry when subtracting
117 * the modulus from the source value; that carry must be 1 for
118 * a value in the correct range. We keep it in r, which is our
119 * accumulator for the error code.
121 t3 = (uint32_t *)(tmp + 4 * fwlen);
122 br_i31_encode(t3, xlen, t2);
129 wn = ((unsigned char *)t3)[u];
131 r = ((wx - (wn + r)) >> 8) & 1;
135 * Move the decoded p to another temporary buffer.
137 mp = (uint32_t *)(tmp + 2 * fwlen);
138 memmove(mp, t1, 2 * fwlen * sizeof *t1);
141 * Compute s2 = x^dq mod q.
143 q0i = br_i31_ninv31(mq[1]);
144 s2 = (uint32_t *)(tmp + fwlen);
145 br_i31_decode_reduce(s2, x, xlen, mq);
146 r &= br_i62_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
147 tmp + 3 * fwlen, TLEN - 3 * fwlen);
150 * Compute s1 = x^dp mod p.
152 p0i = br_i31_ninv31(mp[1]);
153 s1 = (uint32_t *)(tmp + 3 * fwlen);
154 br_i31_decode_reduce(s1, x, xlen, mp);
155 r &= br_i62_modpow_opt(s1, sk->dp, sk->dplen, mp, p0i,
156 tmp + 4 * fwlen, TLEN - 4 * fwlen);
160 * h = (s1 - s2)*(1/q) mod p
161 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
162 * unclear about whether p may be lower than q (some existing,
163 * widely deployed implementations of RSA don't tolerate p < q),
164 * but we want to support that occurrence, so we need to use the
165 * reduction function.
167 * Since we use br_i31_decode_reduce() for iq (purportedly, the
168 * inverse of q modulo p), we also tolerate improperly large
169 * values for this parameter.
171 t1 = (uint32_t *)(tmp + 4 * fwlen);
172 t2 = (uint32_t *)(tmp + 5 * fwlen);
173 br_i31_reduce(t2, s2, mp);
174 br_i31_add(s1, mp, br_i31_sub(s1, t2, 1));
175 br_i31_to_monty(s1, mp);
176 br_i31_decode_reduce(t1, sk->iq, sk->iqlen, mp);
177 br_i31_montymul(t2, s1, t1, mp, p0i);
180 * h is now in t2. We compute the final result:
182 * All these operations are non-modular.
184 * We need mq, s2 and t2. We use the t3 buffer as destination.
185 * The buffers mp, s1 and t1 are no longer needed, so we can
186 * reuse them for t3. Moreover, the first step of the computation
187 * is to copy s2 into t3, after which s2 is not needed. Right
188 * now, mq is in slot 0, s2 is in slot 1, and t2 is in slot 5.
189 * Therefore, we have ample room for t3 by simply using s2.
192 br_i31_mulacc(t3, mq, t2);
195 * Encode the result. Since we already checked the value of xlen,
196 * we can just use it right away.
198 br_i31_encode(x, xlen, t3);
201 * The only error conditions remaining at that point are invalid
202 * values for p and q (even integers).
204 return p0i & q0i & r;
207 /* see bearssl_rsa.h */
209 br_rsa_i62_private_get(void)
211 return &br_rsa_i62_private;
216 /* see bearssl_rsa.h */
218 br_rsa_i62_private_get(void)