207 lines
6.6 KiB
C
207 lines
6.6 KiB
C
// Originally written by Bodo Moeller for the OpenSSL project.
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// Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
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// Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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//
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// The elliptic curve binary polynomial software is originally written by
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// Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
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// Laboratories.
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// SPDX-License-Identifier: Apache-2.0
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#include <openssl/ec.h>
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#include <assert.h>
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#include <string.h>
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#include <openssl/bn.h>
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#include <openssl/err.h>
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#include <openssl/mem.h>
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#include <openssl/thread.h>
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#include "internal.h"
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#include "../bn/internal.h"
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#include "../../internal.h"
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// This file implements the wNAF-based interleaving multi-exponentiation method
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// at:
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// http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
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// http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
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void ec_compute_wNAF(int8_t *out, const EC_SCALAR *scalar, size_t bits, int w) {
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// 'int8_t' can represent integers with absolute values less than 2^7.
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assert(0 < w && w <= 7);
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assert(bits != 0);
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int bit = 1 << w; // 2^w, at most 128
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int next_bit = bit << 1; // 2^(w+1), at most 256
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int mask = next_bit - 1; // at most 255
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int window_val = scalar->words[0] & mask;
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for (size_t j = 0; j < bits + 1; j++) {
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assert(0 <= window_val && window_val <= next_bit);
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int digit = 0;
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if (window_val & 1) {
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assert(0 < window_val && window_val < next_bit);
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if (window_val & bit) {
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digit = window_val - next_bit;
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// We know -next_bit < digit < 0 and window_val - digit = next_bit.
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// modified wNAF
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if (j + w + 1 >= bits) {
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// special case for generating modified wNAFs:
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// no new bits will be added into window_val,
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// so using a positive digit here will decrease
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// the total length of the representation
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digit = window_val & (mask >> 1);
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// We know 0 < digit < bit and window_val - digit = bit.
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}
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} else {
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digit = window_val;
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// We know 0 < digit < bit and window_val - digit = 0.
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}
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window_val -= digit;
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// Now window_val is 0 or 2^(w+1) in standard wNAF generation.
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// For modified window NAFs, it may also be 2^w.
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//
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// See the comments above for the derivation of each of these bounds.
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assert(window_val == 0 || window_val == next_bit || window_val == bit);
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assert(-bit < digit && digit < bit);
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// window_val was odd, so digit is also odd.
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assert(digit & 1);
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}
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out[j] = digit;
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// Incorporate the next bit. Previously, |window_val| <= |next_bit|, so if
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// we shift and add at most one copy of |bit|, this will continue to hold
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// afterwards.
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window_val >>= 1;
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const size_t bits_per_word = sizeof(scalar->words[0]) * 8;
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const size_t num_words = (bits + bits_per_word - 1) / bits_per_word;
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window_val += bit * bn_is_bit_set_words(scalar->words, num_words, j + w + 1);
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assert(window_val <= next_bit);
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}
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// bits + 1 entries should be sufficient to consume all bits.
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assert(window_val == 0);
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}
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// compute_precomp sets |out[i]| to (2*i+1)*p, for i from 0 to |len|.
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static void compute_precomp(const EC_GROUP *group, EC_JACOBIAN *out,
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const EC_JACOBIAN *p, size_t len) {
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ec_GFp_simple_point_copy(&out[0], p);
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EC_JACOBIAN two_p;
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ec_GFp_mont_dbl(group, &two_p, p);
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for (size_t i = 1; i < len; i++) {
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ec_GFp_mont_add(group, &out[i], &out[i - 1], &two_p);
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}
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}
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static void lookup_precomp(const EC_GROUP *group, EC_JACOBIAN *out,
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const EC_JACOBIAN *precomp, int digit) {
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if (digit < 0) {
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digit = -digit;
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ec_GFp_simple_point_copy(out, &precomp[digit >> 1]);
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ec_GFp_simple_invert(group, out);
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} else {
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ec_GFp_simple_point_copy(out, &precomp[digit >> 1]);
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}
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}
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// EC_WNAF_WINDOW_BITS is the window size to use for |ec_GFp_mont_mul_public|.
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#define EC_WNAF_WINDOW_BITS 4
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// EC_WNAF_TABLE_SIZE is the table size to use for |ec_GFp_mont_mul_public|.
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#define EC_WNAF_TABLE_SIZE (1 << (EC_WNAF_WINDOW_BITS - 1))
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// EC_WNAF_STACK is the number of points worth of data to stack-allocate and
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// avoid a malloc.
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#define EC_WNAF_STACK 3
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int ec_GFp_mont_mul_public_batch(const EC_GROUP *group, EC_JACOBIAN *r,
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const EC_SCALAR *g_scalar,
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const EC_JACOBIAN *points,
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const EC_SCALAR *scalars, size_t num) {
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size_t bits = EC_GROUP_order_bits(group);
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size_t wNAF_len = bits + 1;
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int ret = 0;
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int8_t wNAF_stack[EC_WNAF_STACK][EC_MAX_BYTES * 8 + 1];
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int8_t (*wNAF_alloc)[EC_MAX_BYTES * 8 + 1] = NULL;
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int8_t (*wNAF)[EC_MAX_BYTES * 8 + 1];
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EC_JACOBIAN precomp_stack[EC_WNAF_STACK][EC_WNAF_TABLE_SIZE];
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EC_JACOBIAN (*precomp_alloc)[EC_WNAF_TABLE_SIZE] = NULL;
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EC_JACOBIAN (*precomp)[EC_WNAF_TABLE_SIZE];
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if (num <= EC_WNAF_STACK) {
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wNAF = wNAF_stack;
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precomp = precomp_stack;
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} else {
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wNAF_alloc = OPENSSL_calloc(num, sizeof(wNAF_alloc[0]));
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precomp_alloc = OPENSSL_calloc(num, sizeof(precomp_alloc[0]));
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if (wNAF_alloc == NULL || precomp_alloc == NULL) {
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goto err;
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}
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wNAF = wNAF_alloc;
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precomp = precomp_alloc;
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}
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int8_t g_wNAF[EC_MAX_BYTES * 8 + 1];
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EC_JACOBIAN g_precomp[EC_WNAF_TABLE_SIZE];
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assert(wNAF_len <= OPENSSL_ARRAY_SIZE(g_wNAF));
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const EC_JACOBIAN *g = &group->generator.raw;
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if (g_scalar != NULL) {
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ec_compute_wNAF(g_wNAF, g_scalar, bits, EC_WNAF_WINDOW_BITS);
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compute_precomp(group, g_precomp, g, EC_WNAF_TABLE_SIZE);
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}
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for (size_t i = 0; i < num; i++) {
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assert(wNAF_len <= OPENSSL_ARRAY_SIZE(wNAF[i]));
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ec_compute_wNAF(wNAF[i], &scalars[i], bits, EC_WNAF_WINDOW_BITS);
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compute_precomp(group, precomp[i], &points[i], EC_WNAF_TABLE_SIZE);
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}
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EC_JACOBIAN tmp;
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int r_is_at_infinity = 1;
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for (size_t k = wNAF_len - 1; k < wNAF_len; k--) {
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if (!r_is_at_infinity) {
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ec_GFp_mont_dbl(group, r, r);
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}
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if (g_scalar != NULL && g_wNAF[k] != 0) {
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lookup_precomp(group, &tmp, g_precomp, g_wNAF[k]);
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if (r_is_at_infinity) {
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ec_GFp_simple_point_copy(r, &tmp);
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r_is_at_infinity = 0;
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} else {
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ec_GFp_mont_add(group, r, r, &tmp);
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}
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}
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for (size_t i = 0; i < num; i++) {
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if (wNAF[i][k] != 0) {
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lookup_precomp(group, &tmp, precomp[i], wNAF[i][k]);
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if (r_is_at_infinity) {
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ec_GFp_simple_point_copy(r, &tmp);
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r_is_at_infinity = 0;
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} else {
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ec_GFp_mont_add(group, r, r, &tmp);
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}
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}
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}
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}
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if (r_is_at_infinity) {
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ec_GFp_simple_point_set_to_infinity(group, r);
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}
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ret = 1;
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err:
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OPENSSL_free(wNAF_alloc);
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OPENSSL_free(precomp_alloc);
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return ret;
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}
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