2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
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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;