/* Originally written by Bodo Moeller for the OpenSSL project.
* ====================================================================
* 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).
*
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the OpenSSL open source
* license provided above.
*
* The elliptic curve binary polynomial software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
* Laboratories. */
#include <openssl/ec.h>
#include <assert.h>
#include <string.h>
#include <openssl/bn.h>
#include <openssl/err.h>
#include <openssl/thread.h>
#include "internal.h"
#include "../bn/internal.h"
#include "../../internal.h"
// This file implements the wNAF-based interleaving multi-exponentiation method
// at:
// http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
// http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
void ec_compute_wNAF(const EC_GROUP *group, int8_t *out,
const EC_SCALAR *scalar, size_t bits, int w) {
// 'int8_t' can represent integers with absolute values less than 2^7.
assert(0 < w && w <= 7);
assert(bits != 0);
int bit = 1 << w; // 2^w, at most 128
int next_bit = bit << 1; // 2^(w+1), at most 256
int mask = next_bit - 1; // at most 255
int window_val = scalar->words[0] & mask;
for (size_t j = 0; j < bits + 1; j++) {
assert(0 <= window_val && window_val <= next_bit);
int digit = 0;
if (window_val & 1) {
assert(0 < window_val && window_val < next_bit);
if (window_val & bit) {
digit = window_val - next_bit;
// We know -next_bit < digit < 0 and window_val - digit = next_bit.
// modified wNAF
if (j + w + 1 >= bits) {
// special case for generating modified wNAFs:
// no new bits will be added into window_val,
// so using a positive digit here will decrease
// the total length of the representation
digit = window_val & (mask >> 1);
// We know 0 < digit < bit and window_val - digit = bit.
}
} else {
digit = window_val;
// We know 0 < digit < bit and window_val - digit = 0.
}
window_val -= digit;
// Now window_val is 0 or 2^(w+1) in standard wNAF generation.
// For modified window NAFs, it may also be 2^w.
//
// See the comments above for the derivation of each of these bounds.
assert(window_val == 0 || window_val == next_bit || window_val == bit);
assert(-bit < digit && digit < bit);
// window_val was odd, so digit is also odd.
assert(digit & 1);
}
out[j] = digit;
// Incorporate the next bit. Previously, |window_val| <= |next_bit|, so if
// we shift and add at most one copy of |bit|, this will continue to hold
// afterwards.
window_val >>= 1;
window_val +=
bit * bn_is_bit_set_words(scalar->words, group->order.width, j + w + 1);
assert(window_val <= next_bit);
}
// bits + 1 entries should be sufficient to consume all bits.
assert(window_val == 0);
}
// compute_precomp sets |out[i]| to (2*i+1)*p, for i from 0 to |len|.
static void compute_precomp(const EC_GROUP *group, EC_RAW_POINT *out,
const EC_RAW_POINT *p, size_t len) {
ec_GFp_simple_point_copy(&out[0], p);
EC_RAW_POINT two_p;
ec_GFp_mont_dbl(group, &two_p, p);
for (size_t i = 1; i < len; i++) {
ec_GFp_mont_add(group, &out[i], &out[i - 1], &two_p);
}
}
static void lookup_precomp(const EC_GROUP *group, EC_RAW_POINT *out,
const EC_RAW_POINT *precomp, int digit) {
if (digit < 0) {
digit = -digit;
ec_GFp_simple_point_copy(out, &precomp[digit >> 1]);
ec_GFp_simple_invert(group, out);
} else {
ec_GFp_simple_point_copy(out, &precomp[digit >> 1]);
}
}
// EC_WNAF_WINDOW_BITS is the window size to use for |ec_GFp_mont_mul_public|.
#define EC_WNAF_WINDOW_BITS 4
// EC_WNAF_TABLE_SIZE is the table size to use for |ec_GFp_mont_mul_public|.
#define EC_WNAF_TABLE_SIZE (1 << (EC_WNAF_WINDOW_BITS - 1))
void ec_GFp_mont_mul_public(const EC_GROUP *group, EC_RAW_POINT *r,
const EC_SCALAR *g_scalar, const EC_RAW_POINT *p,
const EC_SCALAR *p_scalar) {
size_t bits = BN_num_bits(&group->order);
size_t wNAF_len = bits + 1;
int8_t g_wNAF[EC_MAX_BYTES * 8 + 1];
EC_RAW_POINT g_precomp[EC_WNAF_TABLE_SIZE];
assert(wNAF_len <= OPENSSL_ARRAY_SIZE(g_wNAF));
const EC_RAW_POINT *g = &group->generator->raw;
ec_compute_wNAF(group, g_wNAF, g_scalar, bits, EC_WNAF_WINDOW_BITS);
compute_precomp(group, g_precomp, g, EC_WNAF_TABLE_SIZE);
int8_t p_wNAF[EC_MAX_BYTES * 8 + 1];
EC_RAW_POINT p_precomp[EC_WNAF_TABLE_SIZE];
assert(wNAF_len <= OPENSSL_ARRAY_SIZE(p_wNAF));
ec_compute_wNAF(group, p_wNAF, p_scalar, bits, EC_WNAF_WINDOW_BITS);
compute_precomp(group, p_precomp, p, EC_WNAF_TABLE_SIZE);
EC_RAW_POINT tmp;
int r_is_at_infinity = 1;
for (size_t k = wNAF_len - 1; k < wNAF_len; k--) {
if (!r_is_at_infinity) {
ec_GFp_mont_dbl(group, r, r);
}
if (g_wNAF[k] != 0) {
lookup_precomp(group, &tmp, g_precomp, g_wNAF[k]);
if (r_is_at_infinity) {
ec_GFp_simple_point_copy(r, &tmp);
r_is_at_infinity = 0;
} else {
ec_GFp_mont_add(group, r, r, &tmp);
}
}
if (p_wNAF[k] != 0) {
lookup_precomp(group, &tmp, p_precomp, p_wNAF[k]);
if (r_is_at_infinity) {
ec_GFp_simple_point_copy(r, &tmp);
r_is_at_infinity = 0;
} else {
ec_GFp_mont_add(group, r, r, &tmp);
}
}
}
if (r_is_at_infinity) {
ec_GFp_simple_point_set_to_infinity(group, r);
}
}