2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
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27 #define U (1 + (BR_MAX_RSA_FACTOR >> 5))
29 /* see bearssl_rsa.h */
31 br_rsa_i32_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;
42 * All our temporary buffers are from the tmp[] array.
44 * The mp, mq, s1, s2, t1 and t2 buffers are large enough to
45 * contain a RSA factor. The t3 buffer can contain a complete
46 * RSA modulus. t3 shares its storage space with s2, s1 and t1,
47 * in that order (this is important, see below).
58 * Compute the actual lengths (in bytes) of p and q, and check
59 * that they fit within our stack buffers.
63 while (plen > 0 && *p == 0) {
69 while (qlen > 0 && *q == 0) {
73 if (plen > (BR_MAX_RSA_FACTOR >> 3)
74 || qlen > (BR_MAX_RSA_FACTOR >> 3))
82 br_i32_decode(mp, p, plen);
83 br_i32_decode(mq, q, qlen);
86 * Recompute modulus, to compare with the source value.
88 br_i32_zero(t2, mp[0]);
89 br_i32_mulacc(t2, mp, mq);
90 xlen = (sk->n_bitlen + 7) >> 3;
91 br_i32_encode(t2 + 2 * U, xlen, t2);
98 wn = ((unsigned char *)(t2 + 2 * U))[u];
100 r = ((wx - (wn + r)) >> 8) & 1;
104 * Compute s1 = x^dp mod p.
106 p0i = br_i32_ninv32(mp[1]);
107 br_i32_decode_reduce(s1, x, xlen, mp);
108 br_i32_modpow(s1, sk->dp, sk->dplen, mp, p0i, t1, t2);
111 * Compute s2 = x^dq mod q.
113 q0i = br_i32_ninv32(mq[1]);
114 br_i32_decode_reduce(s2, x, xlen, mq);
115 br_i32_modpow(s2, sk->dq, sk->dqlen, mq, q0i, t1, t2);
119 * h = (s1 - s2)*(1/q) mod p
120 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
121 * unclear about whether p may be lower than q (some existing,
122 * widely deployed implementations of RSA don't tolerate p < q),
123 * but we want to support that occurrence, so we need to use the
124 * reduction function.
126 * Since we use br_i32_decode_reduce() for iq (purportedly, the
127 * inverse of q modulo p), we also tolerate improperly large
128 * values for this parameter.
130 br_i32_reduce(t2, s2, mp);
131 br_i32_add(s1, mp, br_i32_sub(s1, t2, 1));
132 br_i32_to_monty(s1, mp);
133 br_i32_decode_reduce(t1, sk->iq, sk->iqlen, mp);
134 br_i32_montymul(t2, s1, t1, mp, p0i);
137 * h is now in t2. We compute the final result:
139 * All these operations are non-modular.
141 * We need mq, s2 and t2. We use the t3 buffer as destination.
142 * The buffers mp, s1 and t1 are no longer needed. Moreover,
143 * the first step is to copy s2 into the destination buffer t3.
144 * We thus arranged for t3 to actually share space with s2, and
145 * to be followed by the space formerly used by s1 and t1.
147 br_i32_mulacc(t3, mq, t2);
150 * Encode the result. Since we already checked the value of xlen,
151 * we can just use it right away.
153 br_i32_encode(x, xlen, t3);
156 * The only error conditions remaining at that point are invalid
157 * values for p and q (even integers).
159 return p0i & q0i & r;