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/* rsa_e_3.c
**
** Copyright 2008, The Android Open Source Project
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions are met:
** * Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
** * Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in the
** documentation and/or other materials provided with the distribution.
** * Neither the name of Google Inc. nor the names of its contributors may
** be used to endorse or promote products derived from this software
** without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY Google Inc. ``AS IS'' AND ANY EXPRESS OR
** IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
** MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
** EVENT SHALL Google Inc. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
** SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
** PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
** OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
** WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
** OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
** ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "mincrypt/rsa.h"
#include "mincrypt/sha.h"
/* a[] -= mod */
static void subM(const RSAPublicKey *key, uint32_t *a) {
int64_t A = 0;
int i;
for (i = 0; i < key->len; ++i) {
A += (uint64_t)a[i] - key->n[i];
a[i] = (uint32_t)A;
A >>= 32;
}
}
/* return a[] >= mod */
static int geM(const RSAPublicKey *key, const uint32_t *a) {
int i;
for (i = key->len; i;) {
--i;
if (a[i] < key->n[i]) return 0;
if (a[i] > key->n[i]) return 1;
}
return 1; /* equal */
}
/* montgomery c[] += a * b[] / R % mod */
static void montMulAdd(const RSAPublicKey *key,
uint32_t* c,
const uint32_t a,
const uint32_t* b) {
uint64_t A = (uint64_t)a * b[0] + c[0];
uint32_t d0 = (uint32_t)A * key->n0inv;
uint64_t B = (uint64_t)d0 * key->n[0] + (uint32_t)A;
int i;
for (i = 1; i < key->len; ++i) {
A = (A >> 32) + (uint64_t)a * b[i] + c[i];
B = (B >> 32) + (uint64_t)d0 * key->n[i] + (uint32_t)A;
c[i - 1] = (uint32_t)B;
}
A = (A >> 32) + (B >> 32);
c[i - 1] = (uint32_t)A;
if (A >> 32) {
subM(key, c);
}
}
/* montgomery c[] = a[] * b[] / R % mod */
static void montMul(const RSAPublicKey *key,
uint32_t* c,
const uint32_t* a,
const uint32_t* b) {
int i;
for (i = 0; i < key->len; ++i) {
c[i] = 0;
}
for (i = 0; i < key->len; ++i) {
montMulAdd(key, c, a[i], b);
}
}
/* In-place public exponentiation.
** Input and output big-endian byte array in inout.
*/
static void modpow3(const RSAPublicKey *key,
uint8_t* inout) {
uint32_t a[RSANUMWORDS];
uint32_t aR[RSANUMWORDS];
uint32_t aaR[RSANUMWORDS];
uint32_t *aaa = aR; /* Re-use location. */
int i;
/* Convert from big endian byte array to little endian word array. */
for (i = 0; i < key->len; ++i) {
uint32_t tmp =
(inout[((key->len - 1 - i) * 4) + 0] << 24) |
(inout[((key->len - 1 - i) * 4) + 1] << 16) |
(inout[((key->len - 1 - i) * 4) + 2] << 8) |
(inout[((key->len - 1 - i) * 4) + 3] << 0);
a[i] = tmp;
}
montMul(key, aR, a, key->rr); /* aR = a * RR / R mod M */
montMul(key, aaR, aR, aR); /* aaR = aR * aR / R mod M */
montMul(key, aaa, aaR, a); /* aaa = aaR * a / R mod M */
/* Make sure aaa < mod; aaa is at most 1x mod too large. */
if (geM(key, aaa)) {
subM(key, aaa);
}
/* Convert to bigendian byte array */
for (i = key->len - 1; i >= 0; --i) {
uint32_t tmp = aaa[i];
*inout++ = tmp >> 24;
*inout++ = tmp >> 16;
*inout++ = tmp >> 8;
*inout++ = tmp >> 0;
}
}
/* Expected PKCS1.5 signature padding bytes, for a keytool RSA signature.
** Has the 0-length optional parameter encoded in the ASN1 (as opposed to the
** other flavor which omits the optional parameter entirely). This code does not
** accept signatures without the optional parameter.
*/
static const uint8_t padding[RSANUMBYTES - SHA_DIGEST_SIZE] = {
0x00,0x01,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x00,
0x30,0x21,0x30,0x09,0x06,0x05,0x2b,0x0e,0x03,0x02,0x1a,0x05,0x00,
0x04,0x14
};
/* Verify a 2048 bit RSA e=3 PKCS1.5 signature against an expected SHA-1 hash.
** Returns 0 on failure, 1 on success.
*/
int RSA_e_3_verify(const RSAPublicKey *key,
const uint8_t *signature,
const int len,
const uint8_t *sha) {
uint8_t buf[RSANUMBYTES];
int i;
if (key->len != RSANUMWORDS) {
return 0; /* Wrong key passed in. */
}
if (len != sizeof(buf)) {
return 0; /* Wrong input length. */
}
if (key->exponent != 3) {
return 0; // Wrong exponent.
}
for (i = 0; i < len; ++i) {
buf[i] = signature[i];
}
modpow3(key, buf);
/* Check pkcs1.5 padding bytes. */
for (i = 0; i < (int) sizeof(padding); ++i) {
if (buf[i] != padding[i]) {
return 0;
}
}
/* Check sha digest matches. */
for (; i < len; ++i) {
if (buf[i] != *sha++) {
return 0;
}
}
return 1;
}
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