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/* 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.]
*/
/* ====================================================================
* Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
*
* 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 above 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 acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED 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 OpenSSL PROJECT OR
* ITS 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.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com). */
#if defined(_MSC_VER)
#pragma warning(push, 3)
#endif
#include <limits.h>
#include <string.h>
#if defined(_MSC_VER)
#pragma warning(pop)
#endif
#include <GFp/mem.h>
#include "internal.h"
#include "../../internal.h"
#include "../../limbs/limbs.h"
// Prototypes to avoid -Wmissing-prototypes warnings.
int GFp_BN_mod_exp_mont_consttime(BN_ULONG rr[], const BN_ULONG a_mont[],
const BN_ULONG p[], const BN_ULONG one_mont[],
const BN_ULONG n[], size_t num_limbs,
const BN_ULONG n0[BN_MONT_CTX_N0_LIMBS]);
#if defined(OPENSSL_X86_64)
#define OPENSSL_BN_ASM_MONT5
void GFp_bn_mul_mont_gather5(BN_ULONG rp[], const BN_ULONG ap[],
const BN_ULONG table[], const BN_ULONG np[],
const BN_ULONG n0[], int num, int power);
void GFp_bn_scatter5(const BN_ULONG inp[], size_t num, BN_ULONG table[],
size_t power);
void GFp_bn_gather5(BN_ULONG out[], size_t num, const BN_ULONG table[],
size_t power);
void GFp_bn_power5(BN_ULONG rp[], const BN_ULONG ap[], const BN_ULONG table[],
const BN_ULONG np[], const BN_ULONG n0[], int num,
int power);
int GFp_bn_from_montgomery(BN_ULONG rp[], const BN_ULONG ap[],
const BN_ULONG *not_used, const BN_ULONG np[],
const BN_ULONG n0[], int num);
#else
// GFp_BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
// layout so that accessing any of these table values shows the same access
// pattern as far as cache lines are concerned. The following functions are
// used to transfer a BIGNUM from/to that table.
static void copy_to_prebuf(const BN_ULONG b[], int top, BN_ULONG table[],
int idx, int window) {
int i, j;
const int width = 1 << window;
for (i = 0, j = idx; i < top; i++, j += width) {
table[j] = b[i];
}
}
static void copy_from_prebuf(BN_ULONG b[], int top, const BN_ULONG buf[], int idx,
int window) {
int i, j;
const int width = 1 << window;
volatile const BN_ULONG *table = (volatile const BN_ULONG *)buf;
if (window <= 3) {
for (i = 0; i < top; i++, table += width) {
BN_ULONG acc = 0;
for (j = 0; j < width; j++) {
acc |= table[j] & ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
}
b[i] = acc;
}
} else {
int xstride = 1 << (window - 2);
BN_ULONG y0, y1, y2, y3;
i = idx >> (window - 2); // equivalent of idx / xstride
idx &= xstride - 1; // equivalent of idx % xstride
y0 = (BN_ULONG)0 - (constant_time_eq_int(i, 0) & 1);
y1 = (BN_ULONG)0 - (constant_time_eq_int(i, 1) & 1);
y2 = (BN_ULONG)0 - (constant_time_eq_int(i, 2) & 1);
y3 = (BN_ULONG)0 - (constant_time_eq_int(i, 3) & 1);
for (i = 0; i < top; i++, table += width) {
BN_ULONG acc = 0;
for (j = 0; j < xstride; j++) {
acc |= ((table[j + 0 * xstride] & y0) | (table[j + 1 * xstride] & y1) |
(table[j + 2 * xstride] & y2) | (table[j + 3 * xstride] & y3)) &
((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
}
b[i] = acc;
}
}
}
#endif
// GFp_BN_mod_exp_mont_consttime is based on the assumption that the L1 data cache
// line width of the target processor is at least the following value.
#define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH (64)
#define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK \
(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
#if !defined(OPENSSL_X86_64)
// Window sizes optimized for fixed window size modular exponentiation
// algorithm (GFp_BN_mod_exp_mont_consttime).
//
// To achieve the security goals of GFp_BN_mod_exp_mont_consttime, the maximum
// size of the window must not exceed
// log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
//
// Window size thresholds are defined for cache line sizes of 32 and 64, cache
// line sizes where log_2(32)=5 and log_2(64)=6 respectively. A window size of
// 7 should only be used on processors that have a 128 byte or greater cache
// line size.
#if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
#define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
#elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
#define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
#endif
#endif // defined(OPENSSL_X86_64)
// Given a pointer value, compute the next address that is a cache line
// multiple.
#define MOD_EXP_CTIME_ALIGN(x_) \
((unsigned char *)(x_) + \
(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - \
(((uintptr_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
// This variant of GFp_BN_mod_exp_mont() uses fixed windows and the special
// precomputation memory layout to limit data-dependency to a minimum
// to protect secret exponents (cf. the hyper-threading timing attacks
// pointed out by Colin Percival,
// http://www.daemonology.net/hyperthreading-considered-harmful/).
//
// |p| must be positive. |a_mont| must in [0, m). |one_mont| must be
// the value 1 Montgomery-encoded and fully reduced (mod m).
//
// Assumes 0 < a_mont < n, 0 < p, 0 < p_bits.
int GFp_BN_mod_exp_mont_consttime(BN_ULONG rr[], const BN_ULONG a_mont[],
const BN_ULONG p[], const BN_ULONG one_mont[],
const BN_ULONG n[], size_t num_limbs,
const BN_ULONG n0[BN_MONT_CTX_N0_LIMBS]) {
int i, ret = 0, wvalue;
int numPowers;
unsigned char *powerbufFree = NULL;
int powerbufLen = 0;
const int top = (int)num_limbs;
if (!GFp_bn_mul_mont_check_num_limbs(num_limbs)) {
goto err;
}
// Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
// whether the top bits are zero.
int max_bits = (int)num_limbs * BN_BITS2;
int bits = max_bits;
assert(bits > 0);
// Get the window size to use with size of p.
#if defined(OPENSSL_BN_ASM_MONT5)
static const int window = 5;
// reserve space for n copy
powerbufLen += top * sizeof(n[0]);
#else
const int window = BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE;
#endif
// Allocate a buffer large enough to hold all of the pre-computed
// powers of am, am itself and tmp.
numPowers = 1 << window;
powerbufLen +=
sizeof(n[0]) *
(top * numPowers + ((2 * top) > numPowers ? (2 * top) : numPowers));
powerbufFree = malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
if (powerbufFree == NULL) {
goto err;
}
BN_ULONG *powerbuf = (BN_ULONG *)MOD_EXP_CTIME_ALIGN(powerbufFree);
// Lay down tmp and am right after powers table.
BN_ULONG *tmp = powerbuf + (top * numPowers);
BN_ULONG *am = tmp + top;
// Copy a^0 and a^1.
LIMBS_copy(tmp, one_mont, num_limbs);
LIMBS_copy(am, a_mont, num_limbs);
#if defined(OPENSSL_BN_ASM_MONT5)
// This optimization uses ideas from http://eprint.iacr.org/2011/239,
// specifically optimization of cache-timing attack countermeasures
// and pre-computation optimization.
{
BN_ULONG *np = am + top;
// copy n[] to improve cache locality
LIMBS_copy(np, n, num_limbs);
GFp_bn_scatter5(tmp, top, powerbuf, 0);
GFp_bn_scatter5(am, top, powerbuf, 1);
GFp_bn_mul_mont(tmp, am, am, np, n0, top);
GFp_bn_scatter5(tmp, top, powerbuf, 2);
// same as above, but uses squaring for 1/2 of operations
for (i = 4; i < 32; i *= 2) {
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
GFp_bn_scatter5(tmp, top, powerbuf, i);
}
for (i = 3; i < 8; i += 2) {
int j;
GFp_bn_mul_mont_gather5(tmp, am, powerbuf, np, n0, top, i - 1);
GFp_bn_scatter5(tmp, top, powerbuf, i);
for (j = 2 * i; j < 32; j *= 2) {
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
GFp_bn_scatter5(tmp, top, powerbuf, j);
}
}
for (; i < 16; i += 2) {
GFp_bn_mul_mont_gather5(tmp, am, powerbuf, np, n0, top, i - 1);
GFp_bn_scatter5(tmp, top, powerbuf, i);
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
GFp_bn_scatter5(tmp, top, powerbuf, 2 * i);
}
for (; i < 32; i += 2) {
GFp_bn_mul_mont_gather5(tmp, am, powerbuf, np, n0, top, i - 1);
GFp_bn_scatter5(tmp, top, powerbuf, i);
}
bits--;
for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) {
wvalue = (wvalue << 1) + GFp_bn_is_bit_set_words(p, num_limbs, bits);
}
GFp_bn_gather5(tmp, top, powerbuf, wvalue);
// At this point |bits| is 4 mod 5 and at least -1. (|bits| is the first bit
// that has not been read yet.)
assert(bits >= -1 && (bits == -1 || bits % 5 == 4));
// Scan the exponent one window at a time starting from the most
// significant bits.
if (top & 7) {
while (bits >= 0) {
for (wvalue = 0, i = 0; i < 5; i++, bits--) {
wvalue = (wvalue << 1) + GFp_bn_is_bit_set_words(p, num_limbs, bits);
}
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
GFp_bn_mul_mont_gather5(tmp, tmp, powerbuf, np, n0, top, wvalue);
}
} else {
const aliasing_uint8 *p_bytes = (const aliasing_uint8 *)p;
assert(bits < max_bits);
// |p = 0| has been handled as a special case, so |max_bits| is at least
// one word.
assert(max_bits >= 64);
// If the first bit to be read lands in the last byte, unroll the first
// iteration to avoid reading past the bounds of |p|. (After the first
// iteration, we are guaranteed to be past the last byte.) Note |bits|
// here is the top bit, inclusive.
if (bits - 4 >= max_bits - 8) {
// Read five bits from |bits-4| through |bits|, inclusive.
wvalue = p_bytes[num_limbs * sizeof(Limb) - 1];
wvalue >>= (bits - 4) & 7;
wvalue &= 0x1f;
bits -= 5;
GFp_bn_power5(tmp, tmp, powerbuf, np, n0, top, wvalue);
}
while (bits >= 0) {
// Read five bits from |bits-4| through |bits|, inclusive.
int first_bit = bits - 4;
uint16_t val;
// Assumes little-endian.
memcpy(&val, p_bytes + (first_bit >> 3), sizeof(val));
val >>= first_bit & 7;
val &= 0x1f;
bits -= 5;
GFp_bn_power5(tmp, tmp, powerbuf, np, n0, top, val);
}
}
if (!GFp_bn_from_montgomery(tmp, tmp, NULL, np, n0, top)) {
goto err;
}
}
#else
{
const BN_ULONG *np = n;
copy_to_prebuf(tmp, top, powerbuf, 0, window);
copy_to_prebuf(am, top, powerbuf, 1, window);
// If the window size is greater than 1, then calculate
// val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
// (even powers could instead be computed as (a^(i/2))^2
// to use the slight performance advantage of sqr over mul).
if (window > 1) {
GFp_bn_mul_mont(tmp, am, am, np, n0, top);
copy_to_prebuf(tmp, top, powerbuf, 2, window);
for (i = 3; i < numPowers; i++) {
// Calculate a^i = a^(i-1) * a
GFp_bn_mul_mont(tmp, am, tmp, np, n0, top);
copy_to_prebuf(tmp, top, powerbuf, i, window);
}
}
bits--;
for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) {
wvalue = (wvalue << 1) + GFp_bn_is_bit_set_words(p, num_limbs, bits);
}
copy_from_prebuf(tmp, top, powerbuf, wvalue, window);
// Scan the exponent one window at a time starting from the most
// significant bits.
while (bits >= 0) {
wvalue = 0; // The 'value' of the window
// Scan the window, squaring the result as we go
for (i = 0; i < window; i++, bits--) {
GFp_bn_mul_mont(tmp, tmp, tmp, np, n0, top);
wvalue = (wvalue << 1) + GFp_bn_is_bit_set_words(p, num_limbs, bits);
}
// Fetch the appropriate pre-computed value from the pre-buf */
copy_from_prebuf(am, top, powerbuf, wvalue, window);
// Multiply the result into the intermediate result */
GFp_bn_mul_mont(tmp, tmp, am, np, n0, top);
}
}
#endif
LIMBS_copy(rr, tmp, top);
ret = 1;
err:
OPENSSL_free(powerbufFree);
return (ret);
}