/* rsa.c
**
** Copyright 2012, 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"
#include "mincrypt/sha256.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 modpow(const RSAPublicKey* key,
uint8_t* inout) {
uint32_t a[RSANUMWORDS];
uint32_t aR[RSANUMWORDS];
uint32_t aaR[RSANUMWORDS];
uint32_t* aaa = 0;
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;
}
if (key->exponent == 65537) {
aaa = aaR; // Re-use location.
montMul(key, aR, a, key->rr); // aR = a * RR / R mod M
for (i = 0; i < 16; i += 2) {
montMul(key, aaR, aR, aR); // aaR = aR * aR / R mod M
montMul(key, aR, aaR, aaR); // aR = aaR * aaR / R mod M
}
montMul(key, aaa, aR, a); // aaa = aR * a / R mod M
} else if (key->exponent == 3) {
aaa = aR; // Re-use location.
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 sha_padding[RSANUMBYTES] = {
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,
// 20 bytes of hash go here.
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
};
*/
// SHA-1 of PKCS1.5 signature sha_padding for 2048 bit, as above.
// At the location of the bytes of the hash all 00 are hashed.
static const uint8_t kExpectedPadShaRsa2048[SHA_DIGEST_SIZE] = {
0xdc, 0xbd, 0xbe, 0x42, 0xd5, 0xf5, 0xa7, 0x2e,
0x6e, 0xfc, 0xf5, 0x5d, 0xaf, 0x9d, 0xea, 0x68,
0x7c, 0xfb, 0xf1, 0x67
};
/*
static const uint8_t sha256_padding[RSANUMBYTES] = {
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, 0x00, 0x30, 0x31, 0x30,
0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65,
0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20,
// 32 bytes of hash go here.
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
};
*/
// SHA-256 of PKCS1.5 signature sha256_padding for 2048 bit, as above.
// At the location of the bytes of the hash all 00 are hashed.
static const uint8_t kExpectedPadSha256Rsa2048[SHA256_DIGEST_SIZE] = {
0xab, 0x28, 0x8d, 0x8a, 0xd7, 0xd9, 0x59, 0x92,
0xba, 0xcc, 0xf8, 0x67, 0x20, 0xe1, 0x15, 0x2e,
0x39, 0x8d, 0x80, 0x36, 0xd6, 0x6f, 0xf0, 0xfd,
0x90, 0xe8, 0x7d, 0x8b, 0xe1, 0x7c, 0x87, 0x59,
};
// Verify a 2048-bit RSA PKCS1.5 signature against an expected hash.
// Both e=3 and e=65537 are supported. hash_len may be
// SHA_DIGEST_SIZE (== 20) to indicate a SHA-1 hash, or
// SHA256_DIGEST_SIZE (== 32) to indicate a SHA-256 hash. No other
// values are supported.
//
// Returns 1 on successful verification, 0 on failure.
int RSA_verify(const RSAPublicKey *key,
const uint8_t *signature,
const int len,
const uint8_t *hash,
const int hash_len) {
uint8_t buf[RSANUMBYTES];
int i;
const uint8_t* padding_hash;
if (key->len != RSANUMWORDS) {
return 0; // Wrong key passed in.
}
if (len != sizeof(buf)) {
return 0; // Wrong input length.
}
if (hash_len != SHA_DIGEST_SIZE &&
hash_len != SHA256_DIGEST_SIZE) {
return 0; // Unsupported hash.
}
if (key->exponent != 3 && key->exponent != 65537) {
return 0; // Unsupported exponent.
}
for (i = 0; i < len; ++i) { // Copy input to local workspace.
buf[i] = signature[i];
}
modpow(key, buf); // In-place exponentiation.
// Xor sha portion, so it all becomes 00 iff equal.
for (i = len - hash_len; i < len; ++i) {
buf[i] ^= *hash++;
}
// Hash resulting buf, in-place.
switch (hash_len) {
case SHA_DIGEST_SIZE:
padding_hash = kExpectedPadShaRsa2048;
SHA_hash(buf, len, buf);
break;
case SHA256_DIGEST_SIZE:
padding_hash = kExpectedPadSha256Rsa2048;
SHA256_hash(buf, len, buf);
break;
default:
return 0;
}
// Compare against expected hash value.
for (i = 0; i < hash_len; ++i) {
if (buf[i] != padding_hash[i]) {
return 0;
}
}
return 1; // All checked out OK.
}