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/* Copyright (c) 2014 The Chromium OS Authors. All rights reserved.
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
/*
* Implementation of RSA signature verification which uses a pre-processed key
* for computation.
*/
#include "rsa.h"
#include "sha256.h"
#include "util.h"
/**
* a[] -= mod
*/
static void sub_mod(const struct rsa_public_key *key, uint32_t *a)
{
int64_t A = 0;
uint32_t i;
for (i = 0; i < RSANUMWORDS; ++i) {
A += (uint64_t)a[i] - key->n[i];
a[i] = (uint32_t)A;
A >>= 32;
}
}
/**
* Return a[] >= mod
*/
static int ge_mod(const struct rsa_public_key *key, const uint32_t *a)
{
uint32_t i;
for (i = RSANUMWORDS; 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 mont_mul_add(const struct rsa_public_key *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;
uint32_t i;
for (i = 1; i < RSANUMWORDS; ++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)
sub_mod(key, c);
}
/**
* Montgomery c[] = a[] * b[] / R % mod
*/
static void mont_mul(const struct rsa_public_key *key,
uint32_t *c,
const uint32_t *a,
const uint32_t *b)
{
uint32_t i;
for (i = 0; i < RSANUMWORDS; ++i)
c[i] = 0;
for (i = 0; i < RSANUMWORDS; ++i)
mont_mul_add(key, c, a[i], b);
}
/**
* In-place public exponentiation.
*
* @param key Key to use in signing
* @param inout Input and output big-endian byte array
* @param workbuf32 Work buffer; caller must verify this is
* 3 x RSANUMWORDS elements long.
*/
static void mod_pow_F4(const struct rsa_public_key *key, uint8_t *inout,
uint32_t *workbuf32)
{
uint32_t *a = workbuf32;
uint32_t *a_r = a + RSANUMWORDS;
uint32_t *aa_r = a_r + RSANUMWORDS;
uint32_t *aaa = aa_r; /* Re-use location. */
int i;
/* Convert from big endian byte array to little endian word array. */
for (i = 0; i < RSANUMWORDS; ++i) {
uint32_t tmp =
(inout[((RSANUMWORDS - 1 - i) * 4) + 0] << 24) |
(inout[((RSANUMWORDS - 1 - i) * 4) + 1] << 16) |
(inout[((RSANUMWORDS - 1 - i) * 4) + 2] << 8) |
(inout[((RSANUMWORDS - 1 - i) * 4) + 3] << 0);
a[i] = tmp;
}
mont_mul(key, a_r, a, key->rr); /* a_r = a * RR / R mod M */
for (i = 0; i < 16; i += 2) {
mont_mul(key, aa_r, a_r, a_r); /* aa_r = a_r * a_r / R mod M */
mont_mul(key, a_r, aa_r, aa_r);/* a_r = aa_r * aa_r / R mod M */
}
mont_mul(key, aaa, a_r, a); /* aaa = a_r * a / R mod M */
/* Make sure aaa < mod; aaa is at most 1x mod too large. */
if (ge_mod(key, aaa))
sub_mod(key, aaa);
/* Convert to bigendian byte array */
for (i = RSANUMWORDS - 1; i >= 0; --i) {
uint32_t tmp = aaa[i];
*inout++ = (uint8_t)(tmp >> 24);
*inout++ = (uint8_t)(tmp >> 16);
*inout++ = (uint8_t)(tmp >> 8);
*inout++ = (uint8_t)(tmp >> 0);
}
}
/*
* PKCS#1 padding (from the RSA PKCS#1 v2.1 standard)
*
* The DER-encoded padding is defined as follows :
* 0x00 || 0x01 || PS || 0x00 || T
*
* T: DER Encoded DigestInfo value which depends on the hash function used,
* for SHA-256:
* (0x)30 31 30 0d 06 09 60 86 48 01 65 03 04 02 01 05 00 04 20 || H.
*
* Length(T) = 51 octets for SHA-256
*
* PS: octet string consisting of {Length(RSA Key) - Length(T) - 3} 0xFF
*/
static const uint8_t sha256_tail[] = {
0x00, 0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60,
0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01,
0x05, 0x00, 0x04, 0x20
};
#define PKCS_PAD_SIZE (RSANUMBYTES - SHA256_DIGEST_SIZE)
/**
* Check PKCS#1 padding bytes
*
* @param sig Signature to verify
* @return 0 if the padding is correct.
*/
static int check_padding(const uint8_t *sig)
{
uint8_t *ptr = (uint8_t *)sig;
int result = 0;
int i;
/* First 2 bytes are always 0x00 0x01 */
result |= *ptr++ ^ 0x00;
result |= *ptr++ ^ 0x01;
/* Then 0xff bytes until the tail */
for (i = 0; i < PKCS_PAD_SIZE - sizeof(sha256_tail) - 2; i++)
result |= *ptr++ ^ 0xff;
/* Check the tail. */
result |= memcmp(ptr, sha256_tail, sizeof(sha256_tail));
return !!result;
}
/*
* Verify a SHA256WithRSA PKCS#1 v1.5 signature against an expected
* SHA256 hash.
*
* @param key RSA public key
* @param signature RSA signature
* @param sha SHA-256 digest of the content to verify
* @param workbuf32 Work buffer; caller must verify this is
* 3 x RSANUMWORDS elements long.
* @return 0 on failure, 1 on success.
*/
int rsa_verify(const struct rsa_public_key *key, const uint8_t *signature,
const uint8_t *sha, uint32_t *workbuf32)
{
uint8_t buf[RSANUMBYTES];
/* Copy input to local workspace. */
memcpy(buf, signature, RSANUMBYTES);
mod_pow_F4(key, buf, workbuf32); /* In-place exponentiation. */
/* Check the PKCS#1 padding */
if (check_padding(buf) != 0)
return 0;
/* Check the digest. */
if (memcmp(buf + PKCS_PAD_SIZE, sha, SHA256_DIGEST_SIZE) != 0)
return 0;
return 1; /* All checked out OK. */
}
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