/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. 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.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``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 THE AUTHOR OR CONTRIBUTORS 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.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.] */
#include <openssl/rsa.h>
#include <assert.h>
#include <limits.h>
#include <string.h>
#include <openssl/bn.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include <openssl/thread.h>
#include <openssl/type_check.h>
#include "internal.h"
#include "../bn/internal.h"
#include "../../internal.h"
#include "../delocate.h"
static int check_modulus_and_exponent_sizes(const RSA *rsa) {
unsigned rsa_bits = BN_num_bits(rsa->n);
if (rsa_bits > 16 * 1024) {
OPENSSL_PUT_ERROR(RSA, RSA_R_MODULUS_TOO_LARGE);
return 0;
}
// Mitigate DoS attacks by limiting the exponent size. 33 bits was chosen as
// the limit based on the recommendations in [1] and [2]. Windows CryptoAPI
// doesn't support values larger than 32 bits [3], so it is unlikely that
// exponents larger than 32 bits are being used for anything Windows commonly
// does.
//
// [1] https://www.imperialviolet.org/2012/03/16/rsae.html
// [2] https://www.imperialviolet.org/2012/03/17/rsados.html
// [3] https://msdn.microsoft.com/en-us/library/aa387685(VS.85).aspx
static const unsigned kMaxExponentBits = 33;
if (BN_num_bits(rsa->e) > kMaxExponentBits) {
OPENSSL_PUT_ERROR(RSA, RSA_R_BAD_E_VALUE);
return 0;
}
// Verify |n > e|. Comparing |rsa_bits| to |kMaxExponentBits| is a small
// shortcut to comparing |n| and |e| directly. In reality, |kMaxExponentBits|
// is much smaller than the minimum RSA key size that any application should
// accept.
if (rsa_bits <= kMaxExponentBits) {
OPENSSL_PUT_ERROR(RSA, RSA_R_KEY_SIZE_TOO_SMALL);
return 0;
}
assert(BN_ucmp(rsa->n, rsa->e) > 0);
return 1;
}
size_t rsa_default_size(const RSA *rsa) {
return BN_num_bytes(rsa->n);
}
int RSA_encrypt(RSA *rsa, size_t *out_len, uint8_t *out, size_t max_out,
const uint8_t *in, size_t in_len, int padding) {
if (rsa->n == NULL || rsa->e == NULL) {
OPENSSL_PUT_ERROR(RSA, RSA_R_VALUE_MISSING);
return 0;
}
const unsigned rsa_size = RSA_size(rsa);
BIGNUM *f, *result;
uint8_t *buf = NULL;
BN_CTX *ctx = NULL;
int i, ret = 0;
if (max_out < rsa_size) {
OPENSSL_PUT_ERROR(RSA, RSA_R_OUTPUT_BUFFER_TOO_SMALL);
return 0;
}
if (!check_modulus_and_exponent_sizes(rsa)) {
return 0;
}
ctx = BN_CTX_new();
if (ctx == NULL) {
goto err;
}
BN_CTX_start(ctx);
f = BN_CTX_get(ctx);
result = BN_CTX_get(ctx);
buf = OPENSSL_malloc(rsa_size);
if (!f || !result || !buf) {
OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE);
goto err;
}
switch (padding) {
case RSA_PKCS1_PADDING:
i = RSA_padding_add_PKCS1_type_2(buf, rsa_size, in, in_len);
break;
case RSA_PKCS1_OAEP_PADDING:
// Use the default parameters: SHA-1 for both hashes and no label.
i = RSA_padding_add_PKCS1_OAEP_mgf1(buf, rsa_size, in, in_len,
NULL, 0, NULL, NULL);
break;
case RSA_NO_PADDING:
i = RSA_padding_add_none(buf, rsa_size, in, in_len);
break;
default:
OPENSSL_PUT_ERROR(RSA, RSA_R_UNKNOWN_PADDING_TYPE);
goto err;
}
if (i <= 0) {
goto err;
}
if (BN_bin2bn(buf, rsa_size, f) == NULL) {
goto err;
}
if (BN_ucmp(f, rsa->n) >= 0) {
// usually the padding functions would catch this
OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_TOO_LARGE);
goto err;
}
if (!BN_MONT_CTX_set_locked(&rsa->mont_n, &rsa->lock, rsa->n, ctx) ||
!BN_mod_exp_mont(result, f, rsa->e, rsa->n, ctx, rsa->mont_n)) {
goto err;
}
// put in leading 0 bytes if the number is less than the length of the
// modulus
if (!BN_bn2bin_padded(out, rsa_size, result)) {
OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR);
goto err;
}
*out_len = rsa_size;
ret = 1;
err:
if (ctx != NULL) {
BN_CTX_end(ctx);
BN_CTX_free(ctx);
}
OPENSSL_free(buf);
return ret;
}
// MAX_BLINDINGS_PER_RSA defines the maximum number of cached BN_BLINDINGs per
// RSA*. Then this limit is exceeded, BN_BLINDING objects will be created and
// destroyed as needed.
#define MAX_BLINDINGS_PER_RSA 1024
// rsa_blinding_get returns a BN_BLINDING to use with |rsa|. It does this by
// allocating one of the cached BN_BLINDING objects in |rsa->blindings|. If
// none are free, the cache will be extended by a extra element and the new
// BN_BLINDING is returned.
//
// On success, the index of the assigned BN_BLINDING is written to
// |*index_used| and must be passed to |rsa_blinding_release| when finished.
static BN_BLINDING *rsa_blinding_get(RSA *rsa, unsigned *index_used,
BN_CTX *ctx) {
assert(ctx != NULL);
assert(rsa->mont_n != NULL);
BN_BLINDING *ret = NULL;
BN_BLINDING **new_blindings;
uint8_t *new_blindings_inuse;
char overflow = 0;
CRYPTO_MUTEX_lock_write(&rsa->lock);
unsigned i;
for (i = 0; i < rsa->num_blindings; i++) {
if (rsa->blindings_inuse[i] == 0) {
rsa->blindings_inuse[i] = 1;
ret = rsa->blindings[i];
*index_used = i;
break;
}
}
if (ret != NULL) {
CRYPTO_MUTEX_unlock_write(&rsa->lock);
return ret;
}
overflow = rsa->num_blindings >= MAX_BLINDINGS_PER_RSA;
// We didn't find a free BN_BLINDING to use so increase the length of
// the arrays by one and use the newly created element.
CRYPTO_MUTEX_unlock_write(&rsa->lock);
ret = BN_BLINDING_new();
if (ret == NULL) {
return NULL;
}
if (overflow) {
// We cannot add any more cached BN_BLINDINGs so we use |ret|
// and mark it for destruction in |rsa_blinding_release|.
*index_used = MAX_BLINDINGS_PER_RSA;
return ret;
}
CRYPTO_MUTEX_lock_write(&rsa->lock);
new_blindings =
OPENSSL_malloc(sizeof(BN_BLINDING *) * (rsa->num_blindings + 1));
if (new_blindings == NULL) {
goto err1;
}
OPENSSL_memcpy(new_blindings, rsa->blindings,
sizeof(BN_BLINDING *) * rsa->num_blindings);
new_blindings[rsa->num_blindings] = ret;
new_blindings_inuse = OPENSSL_malloc(rsa->num_blindings + 1);
if (new_blindings_inuse == NULL) {
goto err2;
}
OPENSSL_memcpy(new_blindings_inuse, rsa->blindings_inuse, rsa->num_blindings);
new_blindings_inuse[rsa->num_blindings] = 1;
*index_used = rsa->num_blindings;
OPENSSL_free(rsa->blindings);
rsa->blindings = new_blindings;
OPENSSL_free(rsa->blindings_inuse);
rsa->blindings_inuse = new_blindings_inuse;
rsa->num_blindings++;
CRYPTO_MUTEX_unlock_write(&rsa->lock);
return ret;
err2:
OPENSSL_free(new_blindings);
err1:
CRYPTO_MUTEX_unlock_write(&rsa->lock);
BN_BLINDING_free(ret);
return NULL;
}
// rsa_blinding_release marks the cached BN_BLINDING at the given index as free
// for other threads to use.
static void rsa_blinding_release(RSA *rsa, BN_BLINDING *blinding,
unsigned blinding_index) {
if (blinding_index == MAX_BLINDINGS_PER_RSA) {
// This blinding wasn't cached.
BN_BLINDING_free(blinding);
return;
}
CRYPTO_MUTEX_lock_write(&rsa->lock);
rsa->blindings_inuse[blinding_index] = 0;
CRYPTO_MUTEX_unlock_write(&rsa->lock);
}
// signing
int rsa_default_sign_raw(RSA *rsa, size_t *out_len, uint8_t *out,
size_t max_out, const uint8_t *in, size_t in_len,
int padding) {
const unsigned rsa_size = RSA_size(rsa);
uint8_t *buf = NULL;
int i, ret = 0;
if (max_out < rsa_size) {
OPENSSL_PUT_ERROR(RSA, RSA_R_OUTPUT_BUFFER_TOO_SMALL);
return 0;
}
buf = OPENSSL_malloc(rsa_size);
if (buf == NULL) {
OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE);
goto err;
}
switch (padding) {
case RSA_PKCS1_PADDING:
i = RSA_padding_add_PKCS1_type_1(buf, rsa_size, in, in_len);
break;
case RSA_NO_PADDING:
i = RSA_padding_add_none(buf, rsa_size, in, in_len);
break;
default:
OPENSSL_PUT_ERROR(RSA, RSA_R_UNKNOWN_PADDING_TYPE);
goto err;
}
if (i <= 0) {
goto err;
}
if (!RSA_private_transform(rsa, out, buf, rsa_size)) {
goto err;
}
*out_len = rsa_size;
ret = 1;
err:
OPENSSL_free(buf);
return ret;
}
int rsa_default_decrypt(RSA *rsa, size_t *out_len, uint8_t *out, size_t max_out,
const uint8_t *in, size_t in_len, int padding) {
const unsigned rsa_size = RSA_size(rsa);
uint8_t *buf = NULL;
int ret = 0;
if (max_out < rsa_size) {
OPENSSL_PUT_ERROR(RSA, RSA_R_OUTPUT_BUFFER_TOO_SMALL);
return 0;
}
if (padding == RSA_NO_PADDING) {
buf = out;
} else {
// Allocate a temporary buffer to hold the padded plaintext.
buf = OPENSSL_malloc(rsa_size);
if (buf == NULL) {
OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE);
goto err;
}
}
if (in_len != rsa_size) {
OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_LEN_NOT_EQUAL_TO_MOD_LEN);
goto err;
}
if (!RSA_private_transform(rsa, buf, in, rsa_size)) {
goto err;
}
switch (padding) {
case RSA_PKCS1_PADDING:
ret =
RSA_padding_check_PKCS1_type_2(out, out_len, rsa_size, buf, rsa_size);
break;
case RSA_PKCS1_OAEP_PADDING:
// Use the default parameters: SHA-1 for both hashes and no label.
ret = RSA_padding_check_PKCS1_OAEP_mgf1(out, out_len, rsa_size, buf,
rsa_size, NULL, 0, NULL, NULL);
break;
case RSA_NO_PADDING:
*out_len = rsa_size;
ret = 1;
break;
default:
OPENSSL_PUT_ERROR(RSA, RSA_R_UNKNOWN_PADDING_TYPE);
goto err;
}
if (!ret) {
OPENSSL_PUT_ERROR(RSA, RSA_R_PADDING_CHECK_FAILED);
}
err:
if (padding != RSA_NO_PADDING) {
OPENSSL_free(buf);
}
return ret;
}
static int mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa, BN_CTX *ctx);
int RSA_verify_raw(RSA *rsa, size_t *out_len, uint8_t *out, size_t max_out,
const uint8_t *in, size_t in_len, int padding) {
if (rsa->n == NULL || rsa->e == NULL) {
OPENSSL_PUT_ERROR(RSA, RSA_R_VALUE_MISSING);
return 0;
}
const unsigned rsa_size = RSA_size(rsa);
BIGNUM *f, *result;
if (max_out < rsa_size) {
OPENSSL_PUT_ERROR(RSA, RSA_R_OUTPUT_BUFFER_TOO_SMALL);
return 0;
}
if (in_len != rsa_size) {
OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_LEN_NOT_EQUAL_TO_MOD_LEN);
return 0;
}
if (!check_modulus_and_exponent_sizes(rsa)) {
return 0;
}
BN_CTX *ctx = BN_CTX_new();
if (ctx == NULL) {
return 0;
}
int ret = 0;
uint8_t *buf = NULL;
BN_CTX_start(ctx);
f = BN_CTX_get(ctx);
result = BN_CTX_get(ctx);
if (f == NULL || result == NULL) {
OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE);
goto err;
}
if (padding == RSA_NO_PADDING) {
buf = out;
} else {
// Allocate a temporary buffer to hold the padded plaintext.
buf = OPENSSL_malloc(rsa_size);
if (buf == NULL) {
OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE);
goto err;
}
}
if (BN_bin2bn(in, in_len, f) == NULL) {
goto err;
}
if (BN_ucmp(f, rsa->n) >= 0) {
OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_TOO_LARGE);
goto err;
}
if (!BN_MONT_CTX_set_locked(&rsa->mont_n, &rsa->lock, rsa->n, ctx) ||
!BN_mod_exp_mont(result, f, rsa->e, rsa->n, ctx, rsa->mont_n)) {
goto err;
}
if (!BN_bn2bin_padded(buf, rsa_size, result)) {
OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR);
goto err;
}
switch (padding) {
case RSA_PKCS1_PADDING:
ret =
RSA_padding_check_PKCS1_type_1(out, out_len, rsa_size, buf, rsa_size);
break;
case RSA_NO_PADDING:
ret = 1;
*out_len = rsa_size;
break;
default:
OPENSSL_PUT_ERROR(RSA, RSA_R_UNKNOWN_PADDING_TYPE);
goto err;
}
if (!ret) {
OPENSSL_PUT_ERROR(RSA, RSA_R_PADDING_CHECK_FAILED);
goto err;
}
err:
BN_CTX_end(ctx);
BN_CTX_free(ctx);
if (buf != out) {
OPENSSL_free(buf);
}
return ret;
}
int rsa_default_private_transform(RSA *rsa, uint8_t *out, const uint8_t *in,
size_t len) {
if (rsa->n == NULL || rsa->d == NULL) {
OPENSSL_PUT_ERROR(RSA, RSA_R_VALUE_MISSING);
return 0;
}
BIGNUM *f, *result;
BN_CTX *ctx = NULL;
unsigned blinding_index = 0;
BN_BLINDING *blinding = NULL;
int ret = 0;
ctx = BN_CTX_new();
if (ctx == NULL) {
goto err;
}
BN_CTX_start(ctx);
f = BN_CTX_get(ctx);
result = BN_CTX_get(ctx);
if (f == NULL || result == NULL) {
OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE);
goto err;
}
if (BN_bin2bn(in, len, f) == NULL) {
goto err;
}
if (BN_ucmp(f, rsa->n) >= 0) {
// Usually the padding functions would catch this.
OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_TOO_LARGE);
goto err;
}
if (!BN_MONT_CTX_set_locked(&rsa->mont_n, &rsa->lock, rsa->n, ctx)) {
OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR);
goto err;
}
const int do_blinding = (rsa->flags & RSA_FLAG_NO_BLINDING) == 0;
if (rsa->e == NULL && do_blinding) {
// We cannot do blinding or verification without |e|, and continuing without
// those countermeasures is dangerous. However, the Java/Android RSA API
// requires support for keys where only |d| and |n| (and not |e|) are known.
// The callers that require that bad behavior set |RSA_FLAG_NO_BLINDING|.
OPENSSL_PUT_ERROR(RSA, RSA_R_NO_PUBLIC_EXPONENT);
goto err;
}
if (do_blinding) {
blinding = rsa_blinding_get(rsa, &blinding_index, ctx);
if (blinding == NULL) {
OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR);
goto err;
}
if (!BN_BLINDING_convert(f, blinding, rsa->e, rsa->mont_n, ctx)) {
goto err;
}
}
if (rsa->p != NULL && rsa->q != NULL && rsa->e != NULL && rsa->dmp1 != NULL &&
rsa->dmq1 != NULL && rsa->iqmp != NULL) {
if (!mod_exp(result, f, rsa, ctx)) {
goto err;
}
} else if (!BN_mod_exp_mont_consttime(result, f, rsa->d, rsa->n, ctx,
rsa->mont_n)) {
goto err;
}
// Verify the result to protect against fault attacks as described in the
// 1997 paper "On the Importance of Checking Cryptographic Protocols for
// Faults" by Dan Boneh, Richard A. DeMillo, and Richard J. Lipton. Some
// implementations do this only when the CRT is used, but we do it in all
// cases. Section 6 of the aforementioned paper describes an attack that
// works when the CRT isn't used. That attack is much less likely to succeed
// than the CRT attack, but there have likely been improvements since 1997.
//
// This check is cheap assuming |e| is small; it almost always is.
if (rsa->e != NULL) {
BIGNUM *vrfy = BN_CTX_get(ctx);
if (vrfy == NULL ||
!BN_mod_exp_mont(vrfy, result, rsa->e, rsa->n, ctx, rsa->mont_n) ||
!BN_equal_consttime(vrfy, f)) {
OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR);
goto err;
}
}
if (do_blinding &&
!BN_BLINDING_invert(result, blinding, rsa->mont_n, ctx)) {
goto err;
}
if (!BN_bn2bin_padded(out, len, result)) {
OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR);
goto err;
}
ret = 1;
err:
if (ctx != NULL) {
BN_CTX_end(ctx);
BN_CTX_free(ctx);
}
if (blinding != NULL) {
rsa_blinding_release(rsa, blinding, blinding_index);
}
return ret;
}
// mod_montgomery sets |r| to |I| mod |p|. |I| must already be fully reduced
// modulo |p| times |q|. It returns one on success and zero on error.
static int mod_montgomery(BIGNUM *r, const BIGNUM *I, const BIGNUM *p,
const BN_MONT_CTX *mont_p, const BIGNUM *q,
BN_CTX *ctx) {
// Reducing in constant-time with Montgomery reduction requires I <= p * R. We
// have I < p * q, so this follows if q < R. In particular, this always holds
// if p and q are the same size, which is true for any RSA keys we or anyone
// sane generates. For other keys, we fall back to |BN_mod|.
if (!bn_less_than_montgomery_R(q, mont_p)) {
return BN_mod(r, I, p, ctx);
}
if (// Reduce mod p with Montgomery reduction. This computes I * R^-1 mod p.
!BN_from_montgomery(r, I, mont_p, ctx) ||
// Multiply by R^2 and do another Montgomery reduction to compute
// I * R^-1 * R^2 * R^-1 = I mod p.
!BN_to_montgomery(r, r, mont_p, ctx)) {
return 0;
}
// By precomputing R^3 mod p (normally |BN_MONT_CTX| only uses R^2 mod p) and
// adjusting the API for |BN_mod_exp_mont_consttime|, we could instead compute
// I * R mod p here and save a reduction per prime. But this would require
// changing the RSAZ code and may not be worth it.
return 1;
}
static int mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa, BN_CTX *ctx) {
assert(ctx != NULL);
assert(rsa->n != NULL);
assert(rsa->e != NULL);
assert(rsa->d != NULL);
assert(rsa->p != NULL);
assert(rsa->q != NULL);
assert(rsa->dmp1 != NULL);
assert(rsa->dmq1 != NULL);
assert(rsa->iqmp != NULL);
BIGNUM *r1, *m1, *vrfy;
int ret = 0;
BN_CTX_start(ctx);
r1 = BN_CTX_get(ctx);
m1 = BN_CTX_get(ctx);
vrfy = BN_CTX_get(ctx);
if (r1 == NULL ||
m1 == NULL ||
vrfy == NULL) {
goto err;
}
if (!BN_MONT_CTX_set_locked(&rsa->mont_p, &rsa->lock, rsa->p, ctx) ||
!BN_MONT_CTX_set_locked(&rsa->mont_q, &rsa->lock, rsa->q, ctx)) {
goto err;
}
if (!BN_MONT_CTX_set_locked(&rsa->mont_n, &rsa->lock, rsa->n, ctx)) {
goto err;
}
// This is a pre-condition for |mod_montgomery|. It was already checked by the
// caller.
assert(BN_ucmp(I, rsa->n) < 0);
// compute I mod q
if (!mod_montgomery(r1, I, rsa->q, rsa->mont_q, rsa->p, ctx)) {
goto err;
}
// compute r1^dmq1 mod q
if (!BN_mod_exp_mont_consttime(m1, r1, rsa->dmq1, rsa->q, ctx, rsa->mont_q)) {
goto err;
}
// compute I mod p
if (!mod_montgomery(r1, I, rsa->p, rsa->mont_p, rsa->q, ctx)) {
goto err;
}
// compute r1^dmp1 mod p
if (!BN_mod_exp_mont_consttime(r0, r1, rsa->dmp1, rsa->p, ctx, rsa->mont_p)) {
goto err;
}
// TODO(davidben): The code below is not constant-time, even ignoring
// |bn_correct_top|. To fix this:
//
// 1. Canonicalize keys on p > q. (p > q for keys we generate, but not ones we
// import.) We have exposed structs, but we can generalize the
// |BN_MONT_CTX_set_locked| trick to do a one-time canonicalization of the
// private key where we optionally swap p and q (re-computing iqmp if
// necessary) and fill in mont_*. This removes the p < q case below.
//
// 2. Compute r0 - m1 (mod p) in constant-time. With (1) done, this is just a
// constant-time modular subtraction. It should be doable with
// |bn_sub_words| and a select on the borrow bit.
//
// 3. When computing mont_*, additionally compute iqmp_mont, iqmp in
// Montgomery form. The |BN_mul| and |BN_mod| pair can then be replaced
// with |BN_mod_mul_montgomery|.
if (!BN_sub(r0, r0, m1)) {
goto err;
}
// This will help stop the size of r0 increasing, which does
// affect the multiply if it optimised for a power of 2 size
if (BN_is_negative(r0)) {
if (!BN_add(r0, r0, rsa->p)) {
goto err;
}
}
if (!BN_mul(r1, r0, rsa->iqmp, ctx)) {
goto err;
}
if (!BN_mod(r0, r1, rsa->p, ctx)) {
goto err;
}
// If p < q it is occasionally possible for the correction of
// adding 'p' if r0 is negative above to leave the result still
// negative. This can break the private key operations: the following
// second correction should *always* correct this rare occurrence.
// This will *never* happen with OpenSSL generated keys because
// they ensure p > q [steve]
if (BN_is_negative(r0)) {
if (!BN_add(r0, r0, rsa->p)) {
goto err;
}
}
if (!BN_mul(r1, r0, rsa->q, ctx)) {
goto err;
}
if (!BN_add(r0, r1, m1)) {
goto err;
}
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
static int ensure_bignum(BIGNUM **out) {
if (*out == NULL) {
*out = BN_new();
}
return *out != NULL;
}
// kBoringSSLRSASqrtTwo is the BIGNUM representation of ⌊2¹⁵³⁵×√2⌋. This is
// chosen to give enough precision for 3072-bit RSA, the largest key size FIPS
// specifies. Key sizes beyond this will round up.
//
// To verify this number, check that n² < 2³⁰⁷¹ < (n+1)², where n is value
// represented here. Note the components are listed in little-endian order. Here
// is some sample Python code to check:
//
// >>> TOBN = lambda a, b: a << 32 | b
// >>> l = [ <paste the contents of kSqrtTwo> ]
// >>> n = sum(a * 2**(64*i) for i, a in enumerate(l))
// >>> n**2 < 2**3071 < (n+1)**2
// True
const BN_ULONG kBoringSSLRSASqrtTwo[] = {
TOBN(0xdea06241, 0xf7aa81c2), TOBN(0xf6a1be3f, 0xca221307),
TOBN(0x332a5e9f, 0x7bda1ebf), TOBN(0x0104dc01, 0xfe32352f),
TOBN(0xb8cf341b, 0x6f8236c7), TOBN(0x4264dabc, 0xd528b651),
TOBN(0xf4d3a02c, 0xebc93e0c), TOBN(0x81394ab6, 0xd8fd0efd),
TOBN(0xeaa4a089, 0x9040ca4a), TOBN(0xf52f120f, 0x836e582e),
TOBN(0xcb2a6343, 0x31f3c84d), TOBN(0xc6d5a8a3, 0x8bb7e9dc),
TOBN(0x460abc72, 0x2f7c4e33), TOBN(0xcab1bc91, 0x1688458a),
TOBN(0x53059c60, 0x11bc337b), TOBN(0xd2202e87, 0x42af1f4e),
TOBN(0x78048736, 0x3dfa2768), TOBN(0x0f74a85e, 0x439c7b4a),
TOBN(0xa8b1fe6f, 0xdc83db39), TOBN(0x4afc8304, 0x3ab8a2c3),
TOBN(0xed17ac85, 0x83339915), TOBN(0x1d6f60ba, 0x893ba84c),
TOBN(0x597d89b3, 0x754abe9f), TOBN(0xb504f333, 0xf9de6484),
};
const size_t kBoringSSLRSASqrtTwoLen = OPENSSL_ARRAY_SIZE(kBoringSSLRSASqrtTwo);
int rsa_greater_than_pow2(const BIGNUM *b, int n) {
if (BN_is_negative(b) || n == INT_MAX) {
return 0;
}
int b_bits = BN_num_bits(b);
return b_bits > n + 1 || (b_bits == n + 1 && !BN_is_pow2(b));
}
// generate_prime sets |out| to a prime with length |bits| such that |out|-1 is
// relatively prime to |e|. If |p| is non-NULL, |out| will also not be close to
// |p|.
static int generate_prime(BIGNUM *out, int bits, const BIGNUM *e,
const BIGNUM *p, const BIGNUM *sqrt2, BN_CTX *ctx,
BN_GENCB *cb) {
if (bits < 128 || (bits % BN_BITS2) != 0) {
OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR);
return 0;
}
// See FIPS 186-4 appendix B.3.3, steps 4 and 5. Note |bits| here is nlen/2.
// Use the limit from steps 4.7 and 5.8 for most values of |e|. When |e| is 3,
// the 186-4 limit is too low, so we use a higher one. Note this case is not
// reachable from |RSA_generate_key_fips|.
if (bits >= INT_MAX/32) {
OPENSSL_PUT_ERROR(RSA, RSA_R_MODULUS_TOO_LARGE);
return 0;
}
int limit = BN_is_word(e, 3) ? bits * 32 : bits * 5;
int ret = 0, tries = 0, rand_tries = 0;
BN_CTX_start(ctx);
BIGNUM *tmp = BN_CTX_get(ctx);
if (tmp == NULL) {
goto err;
}
for (;;) {
// Generate a random number of length |bits| where the bottom bit is set
// (steps 4.2, 4.3, 5.2 and 5.3) and the top bit is set (implied by the
// bound checked below in steps 4.4 and 5.5).
if (!BN_rand(out, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD) ||
!BN_GENCB_call(cb, BN_GENCB_GENERATED, rand_tries++)) {
goto err;
}
if (p != NULL) {
// If |p| and |out| are too close, try again (step 5.4).
if (!BN_sub(tmp, out, p)) {
goto err;
}
BN_set_negative(tmp, 0);
if (!rsa_greater_than_pow2(tmp, bits - 100)) {
continue;
}
}
// If out < 2^(bits-1)×√2, try again (steps 4.4 and 5.5). This is equivalent
// to out <= ⌊2^(bits-1)×√2⌋, or out <= sqrt2 for FIPS key sizes.
//
// For larger keys, the comparison is approximate, leaning towards
// retrying. That is, we reject a negligible fraction of primes that are
// within the FIPS bound, but we will never accept a prime outside the
// bound, ensuring the resulting RSA key is the right size.
if (!BN_less_than_consttime(sqrt2, out)) {
continue;
}
// Check gcd(out-1, e) is one (steps 4.5 and 5.6).
if (!BN_sub(tmp, out, BN_value_one()) ||
!BN_gcd(tmp, tmp, e, ctx)) {
goto err;
}
if (BN_is_one(tmp)) {
// Test |out| for primality (steps 4.5.1 and 5.6.1).
int is_probable_prime;
if (!BN_primality_test(&is_probable_prime, out, BN_prime_checks, ctx, 1,
cb)) {
goto err;
}
if (is_probable_prime) {
ret = 1;
goto err;
}
}
// If we've tried too many times to find a prime, abort (steps 4.7 and
// 5.8).
tries++;
if (tries >= limit) {
OPENSSL_PUT_ERROR(RSA, RSA_R_TOO_MANY_ITERATIONS);
goto err;
}
if (!BN_GENCB_call(cb, 2, tries)) {
goto err;
}
}
err:
BN_CTX_end(ctx);
return ret;
}
int RSA_generate_key_ex(RSA *rsa, int bits, BIGNUM *e_value, BN_GENCB *cb) {
// See FIPS 186-4 appendix B.3. This function implements a generalized version
// of the FIPS algorithm. |RSA_generate_key_fips| performs additional checks
// for FIPS-compliant key generation.
// Always generate RSA keys which are a multiple of 128 bits. Round |bits|
// down as needed.
bits &= ~127;
// Reject excessively small keys.
if (bits < 256) {
OPENSSL_PUT_ERROR(RSA, RSA_R_KEY_SIZE_TOO_SMALL);
return 0;
}
int ret = 0;
BN_CTX *ctx = BN_CTX_new();
if (ctx == NULL) {
goto bn_err;
}
BN_CTX_start(ctx);
BIGNUM *totient = BN_CTX_get(ctx);
BIGNUM *pm1 = BN_CTX_get(ctx);
BIGNUM *qm1 = BN_CTX_get(ctx);
BIGNUM *gcd = BN_CTX_get(ctx);
BIGNUM *sqrt2 = BN_CTX_get(ctx);
if (totient == NULL || pm1 == NULL || qm1 == NULL || gcd == NULL ||
sqrt2 == NULL) {
goto bn_err;
}
// We need the RSA components non-NULL.
if (!ensure_bignum(&rsa->n) ||
!ensure_bignum(&rsa->d) ||
!ensure_bignum(&rsa->e) ||
!ensure_bignum(&rsa->p) ||
!ensure_bignum(&rsa->q) ||
!ensure_bignum(&rsa->dmp1) ||
!ensure_bignum(&rsa->dmq1) ||
!ensure_bignum(&rsa->iqmp)) {
goto bn_err;
}
if (!BN_copy(rsa->e, e_value)) {
goto bn_err;
}
int prime_bits = bits / 2;
// Compute sqrt2 >= ⌊2^(prime_bits-1)×√2⌋.
if (!bn_set_words(sqrt2, kBoringSSLRSASqrtTwo, kBoringSSLRSASqrtTwoLen)) {
goto bn_err;
}
int sqrt2_bits = kBoringSSLRSASqrtTwoLen * BN_BITS2;
assert(sqrt2_bits == (int)BN_num_bits(sqrt2));
if (sqrt2_bits > prime_bits) {
// For key sizes up to 3072 (prime_bits = 1536), this is exactly
// ⌊2^(prime_bits-1)×√2⌋.
if (!BN_rshift(sqrt2, sqrt2, sqrt2_bits - prime_bits)) {
goto bn_err;
}
} else if (prime_bits > sqrt2_bits) {
// For key sizes beyond 3072, this is approximate. We err towards retrying
// to ensure our key is the right size and round up.
if (!BN_add_word(sqrt2, 1) ||
!BN_lshift(sqrt2, sqrt2, prime_bits - sqrt2_bits)) {
goto bn_err;
}
}
assert(prime_bits == (int)BN_num_bits(sqrt2));
do {
// Generate p and q, each of size |prime_bits|, using the steps outlined in
// appendix FIPS 186-4 appendix B.3.3.
if (!generate_prime(rsa->p, prime_bits, rsa->e, NULL, sqrt2, ctx, cb) ||
!BN_GENCB_call(cb, 3, 0) ||
!generate_prime(rsa->q, prime_bits, rsa->e, rsa->p, sqrt2, ctx, cb) ||
!BN_GENCB_call(cb, 3, 1)) {
goto bn_err;
}
if (BN_cmp(rsa->p, rsa->q) < 0) {
BIGNUM *tmp = rsa->p;
rsa->p = rsa->q;
rsa->q = tmp;
}
// Calculate d = e^(-1) (mod lcm(p-1, q-1)), per FIPS 186-4. This differs
// from typical RSA implementations which use (p-1)*(q-1).
//
// Note this means the size of d might reveal information about p-1 and
// q-1. However, we do operations with Chinese Remainder Theorem, so we only
// use d (mod p-1) and d (mod q-1) as exponents. Using a minimal totient
// does not affect those two values.
if (!BN_sub(pm1, rsa->p, BN_value_one()) ||
!BN_sub(qm1, rsa->q, BN_value_one()) ||
!BN_mul(totient, pm1, qm1, ctx) ||
!BN_gcd(gcd, pm1, qm1, ctx) ||
!BN_div(totient, NULL, totient, gcd, ctx) ||
!BN_mod_inverse(rsa->d, rsa->e, totient, ctx)) {
goto bn_err;
}
// Check that |rsa->d| > 2^|prime_bits| and try again if it fails. See
// appendix B.3.1's guidance on values for d.
} while (!rsa_greater_than_pow2(rsa->d, prime_bits));
if (// Calculate n.
!BN_mul(rsa->n, rsa->p, rsa->q, ctx) ||
// Calculate d mod (p-1).
!BN_mod(rsa->dmp1, rsa->d, pm1, ctx) ||
// Calculate d mod (q-1)
!BN_mod(rsa->dmq1, rsa->d, qm1, ctx)) {
goto bn_err;
}
// Sanity-check that |rsa->n| has the specified size. This is implied by
// |generate_prime|'s bounds.
if (BN_num_bits(rsa->n) != (unsigned)bits) {
OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR);
goto err;
}
// Calculate inverse of q mod p. Note that although RSA key generation is far
// from constant-time, |bn_mod_inverse_secret_prime| uses the same modular
// exponentation logic as in RSA private key operations and, if the RSAZ-1024
// code is enabled, will be optimized for common RSA prime sizes.
if (!BN_MONT_CTX_set_locked(&rsa->mont_p, &rsa->lock, rsa->p, ctx) ||
!bn_mod_inverse_secret_prime(rsa->iqmp, rsa->q, rsa->p, ctx,
rsa->mont_p)) {
goto bn_err;
}
// The key generation process is complex and thus error-prone. It could be
// disastrous to generate and then use a bad key so double-check that the key
// makes sense.
if (!RSA_check_key(rsa)) {
OPENSSL_PUT_ERROR(RSA, RSA_R_INTERNAL_ERROR);
goto err;
}
ret = 1;
bn_err:
if (!ret) {
OPENSSL_PUT_ERROR(RSA, ERR_LIB_BN);
}
err:
if (ctx != NULL) {
BN_CTX_end(ctx);
BN_CTX_free(ctx);
}
return ret;
}
int RSA_generate_key_fips(RSA *rsa, int bits, BN_GENCB *cb) {
// FIPS 186-4 allows 2048-bit and 3072-bit RSA keys (1024-bit and 1536-bit
// primes, respectively) with the prime generation method we use.
if (bits != 2048 && bits != 3072) {
OPENSSL_PUT_ERROR(RSA, RSA_R_BAD_RSA_PARAMETERS);
return 0;
}
BIGNUM *e = BN_new();
int ret = e != NULL &&
BN_set_word(e, RSA_F4) &&
RSA_generate_key_ex(rsa, bits, e, cb) &&
RSA_check_fips(rsa);
BN_free(e);
return ret;
}
DEFINE_METHOD_FUNCTION(RSA_METHOD, RSA_default_method) {
// All of the methods are NULL to make it easier for the compiler/linker to
// drop unused functions. The wrapper functions will select the appropriate
// |rsa_default_*| implementation.
OPENSSL_memset(out, 0, sizeof(RSA_METHOD));
out->common.is_static = 1;
}