/*
* Copyright (c) 2016 Thomas Pornin
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "inner.h"
#define U (2 + ((BR_MAX_RSA_FACTOR + 30) / 31))
#define TLEN (8 * U)
/* see bearssl_rsa.h */
uint32_t
br_rsa_i31_private(unsigned char *x, const br_rsa_private_key *sk)
{
const unsigned char *p, *q;
size_t plen, qlen;
size_t fwlen;
uint32_t p0i, q0i;
size_t xlen, u;
uint32_t tmp[1 + TLEN];
long z;
uint32_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
uint32_t r;
/*
* Compute the actual lengths of p and q, in bytes.
* These lengths are not considered secret (we cannot really hide
* them anyway in constant-time code).
*/
p = sk->p;
plen = sk->plen;
while (plen > 0 && *p == 0) {
p ++;
plen --;
}
q = sk->q;
qlen = sk->qlen;
while (qlen > 0 && *q == 0) {
q ++;
qlen --;
}
/*
* Compute the maximum factor length, in words.
*/
z = (long)(plen > qlen ? plen : qlen) << 3;
fwlen = 1;
while (z > 0) {
z -= 31;
fwlen ++;
}
/*
* Round up the word length to an even number.
*/
fwlen += (fwlen & 1);
/*
* We need to fit at least 6 values in the stack buffer.
*/
if (6 * fwlen > TLEN) {
return 0;
}
/*
* Compute modulus length (in bytes).
*/
xlen = (sk->n_bitlen + 7) >> 3;
/*
* Decode q.
*/
mq = tmp;
br_i31_decode(mq, q, qlen);
/*
* Decode p.
*/
t1 = mq + fwlen;
br_i31_decode(t1, p, plen);
/*
* Compute the modulus (product of the two factors), to compare
* it with the source value. We use br_i31_mulacc(), since it's
* already used later on.
*/
t2 = mq + 2 * fwlen;
br_i31_zero(t2, mq[0]);
br_i31_mulacc(t2, mq, t1);
/*
* We encode the modulus into bytes, to perform the comparison
* with bytes. We know that the product length, in bytes, is
* exactly xlen.
* The comparison actually computes the carry when subtracting
* the modulus from the source value; that carry must be 1 for
* a value in the correct range. We keep it in r, which is our
* accumulator for the error code.
*/
t3 = mq + 4 * fwlen;
br_i31_encode(t3, xlen, t2);
u = xlen;
r = 0;
while (u > 0) {
uint32_t wn, wx;
u --;
wn = ((unsigned char *)t3)[u];
wx = x[u];
r = ((wx - (wn + r)) >> 8) & 1;
}
/*
* Move the decoded p to another temporary buffer.
*/
mp = mq + 2 * fwlen;
memmove(mp, t1, fwlen * sizeof *t1);
/*
* Compute s2 = x^dq mod q.
*/
q0i = br_i31_ninv31(mq[1]);
s2 = mq + fwlen;
br_i31_decode_reduce(s2, x, xlen, mq);
r &= br_i31_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
mq + 3 * fwlen, TLEN - 3 * fwlen);
/*
* Compute s1 = x^dp mod p.
*/
p0i = br_i31_ninv31(mp[1]);
s1 = mq + 3 * fwlen;
br_i31_decode_reduce(s1, x, xlen, mp);
r &= br_i31_modpow_opt(s1, sk->dp, sk->dplen, mp, p0i,
mq + 4 * fwlen, TLEN - 4 * fwlen);
/*
* Compute:
* h = (s1 - s2)*(1/q) mod p
* s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
* unclear about whether p may be lower than q (some existing,
* widely deployed implementations of RSA don't tolerate p < q),
* but we want to support that occurrence, so we need to use the
* reduction function.
*
* Since we use br_i31_decode_reduce() for iq (purportedly, the
* inverse of q modulo p), we also tolerate improperly large
* values for this parameter.
*/
t1 = mq + 4 * fwlen;
t2 = mq + 5 * fwlen;
br_i31_reduce(t2, s2, mp);
br_i31_add(s1, mp, br_i31_sub(s1, t2, 1));
br_i31_to_monty(s1, mp);
br_i31_decode_reduce(t1, sk->iq, sk->iqlen, mp);
br_i31_montymul(t2, s1, t1, mp, p0i);
/*
* h is now in t2. We compute the final result:
* s = s2 + q*h
* All these operations are non-modular.
*
* We need mq, s2 and t2. We use the t3 buffer as destination.
* The buffers mp, s1 and t1 are no longer needed, so we can
* reuse them for t3. Moreover, the first step of the computation
* is to copy s2 into t3, after which s2 is not needed. Right
* now, mq is in slot 0, s2 is in slot 1, and t2 is in slot 5.
* Therefore, we have ample room for t3 by simply using s2.
*/
t3 = s2;
br_i31_mulacc(t3, mq, t2);
/*
* Encode the result. Since we already checked the value of xlen,
* we can just use it right away.
*/
br_i31_encode(x, xlen, t3);
/*
* The only error conditions remaining at that point are invalid
* values for p and q (even integers).
*/
return p0i & q0i & r;
}