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 /* 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 #include #include #include #include #include #include "internal.h" #include "../internal.h" /* This file implements the wNAF-based interleaving multi-exponentation method * (); * */ /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'. * This is an array r[] of values that are either zero or odd with an * absolute value less than 2^w satisfying * scalar = \sum_j r[j]*2^j * where at most one of any w+1 consecutive digits is non-zero * with the exception that the most significant digit may be only * w-1 zeros away from that next non-zero digit. */ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) { int window_val; int ok = 0; signed char *r = NULL; int sign = 1; int bit, next_bit, mask; size_t len = 0, j; if (BN_is_zero(scalar)) { r = OPENSSL_malloc(1); if (!r) { OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); goto err; } r[0] = 0; *ret_len = 1; return r; } if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */ { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); goto err; } bit = 1 << w; /* at most 128 */ next_bit = bit << 1; /* at most 256 */ mask = next_bit - 1; /* at most 255 */ if (BN_is_negative(scalar)) { sign = -1; } if (scalar->d == NULL || scalar->top == 0) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); goto err; } len = BN_num_bits(scalar); r = OPENSSL_malloc( len + 1); /* modified wNAF may be one digit longer than binary representation * (*ret_len will be set to the actual length, i.e. at most * BN_num_bits(scalar) + 1) */ if (r == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); goto err; } window_val = scalar->d[0] & mask; j = 0; while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */ { int digit = 0; /* 0 <= window_val <= 2^(w+1) */ if (window_val & 1) { /* 0 < window_val < 2^(w+1) */ if (window_val & bit) { digit = window_val - next_bit; /* -2^w < digit < 0 */ #if 1 /* modified wNAF */ if (j + w + 1 >= len) { /* 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); /* 0 < digit < 2^w */ } #endif } else { digit = window_val; /* 0 < digit < 2^w */ } if (digit <= -bit || digit >= bit || !(digit & 1)) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); goto err; } 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 */ if (window_val != 0 && window_val != next_bit && window_val != bit) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); goto err; } } r[j++] = sign * digit; window_val >>= 1; window_val += bit * BN_is_bit_set(scalar, j + w); if (window_val > next_bit) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); goto err; } } if (j > len + 1) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); goto err; } len = j; ok = 1; err: if (!ok) { OPENSSL_free(r); r = NULL; } if (ok) { *ret_len = len; } return r; } /* TODO: table should be optimised for the wNAF-based implementation, * sometimes smaller windows will give better performance * (thus the boundaries should be increased) */ #define EC_window_bits_for_scalar_size(b) \ ((size_t)((b) >= 2000 ? 6 : (b) >= 800 ? 5 : (b) >= 300 \ ? 4 \ : (b) >= 70 ? 3 : (b) >= 20 \ ? 2 \ : 1)) int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; const EC_POINT *generator = NULL; EC_POINT *tmp = NULL; size_t total_num; size_t i, j; int k; int r_is_inverted = 0; int r_is_at_infinity = 1; size_t *wsize = NULL; /* individual window sizes */ signed char **wNAF = NULL; /* individual wNAFs */ size_t *wNAF_len = NULL; size_t max_len = 0; size_t num_val; EC_POINT **val = NULL; /* precomputation */ EC_POINT **v; EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */ int ret = 0; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { goto err; } } /* TODO: This function used to take |points| and |scalars| as arrays of * |num| elements. The code below should be simplified to work in terms of |p| * and |p_scalar|. */ size_t num = p != NULL ? 1 : 0; const EC_POINT **points = p != NULL ? &p : NULL; const BIGNUM **scalars = p != NULL ? &p_scalar : NULL; total_num = num; if (g_scalar != NULL) { generator = EC_GROUP_get0_generator(group); if (generator == NULL) { OPENSSL_PUT_ERROR(EC, EC_R_UNDEFINED_GENERATOR); goto err; } ++total_num; /* treat 'g_scalar' like 'num'-th element of 'scalars' */ } wsize = OPENSSL_malloc(total_num * sizeof wsize[0]); wNAF_len = OPENSSL_malloc(total_num * sizeof wNAF_len[0]); wNAF = OPENSSL_malloc((total_num + 1) * sizeof wNAF[0]); /* includes space for pivot */ val_sub = OPENSSL_malloc(total_num * sizeof val_sub[0]); /* Ensure wNAF is initialised in case we end up going to err. */ if (wNAF) { wNAF[0] = NULL; /* preliminary pivot */ } if (!wsize || !wNAF_len || !wNAF || !val_sub) { OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); goto err; } /* num_val will be the total number of temporarily precomputed points */ num_val = 0; for (i = 0; i < total_num; i++) { size_t bits; bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(g_scalar); wsize[i] = EC_window_bits_for_scalar_size(bits); num_val += (size_t)1 << (wsize[i] - 1); wNAF[i + 1] = NULL; /* make sure we always have a pivot */ wNAF[i] = compute_wNAF((i < num ? scalars[i] : g_scalar), wsize[i], &wNAF_len[i]); if (wNAF[i] == NULL) { goto err; } if (wNAF_len[i] > max_len) { max_len = wNAF_len[i]; } } /* All points we precompute now go into a single array 'val'. 'val_sub[i]' is * a pointer to the subarray for the i-th point. */ val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); if (val == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); goto err; } val[num_val] = NULL; /* pivot element */ /* allocate points for precomputation */ v = val; for (i = 0; i < total_num; i++) { val_sub[i] = v; for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { *v = EC_POINT_new(group); if (*v == NULL) { goto err; } v++; } } if (!(v == val + num_val)) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); goto err; } if (!(tmp = EC_POINT_new(group))) { goto err; } /* prepare precomputed values: * val_sub[i][0] := points[i] * val_sub[i][1] := 3 * points[i] * val_sub[i][2] := 5 * points[i] * ... */ for (i = 0; i < total_num; i++) { if (i < num) { if (!EC_POINT_copy(val_sub[i][0], points[i])) { goto err; } } else if (!EC_POINT_copy(val_sub[i][0], generator)) { goto err; } if (wsize[i] > 1) { if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) { goto err; } for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) { goto err; } } } } #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ if (!EC_POINTs_make_affine(group, num_val, val, ctx)) { goto err; } #endif r_is_at_infinity = 1; for (k = max_len - 1; k >= 0; k--) { if (!r_is_at_infinity && !EC_POINT_dbl(group, r, r, ctx)) { goto err; } for (i = 0; i < total_num; i++) { if (wNAF_len[i] > (size_t)k) { int digit = wNAF[i][k]; int is_neg; if (digit) { is_neg = digit < 0; if (is_neg) { digit = -digit; } if (is_neg != r_is_inverted) { if (!r_is_at_infinity && !EC_POINT_invert(group, r, ctx)) { goto err; } r_is_inverted = !r_is_inverted; } /* digit > 0 */ if (r_is_at_infinity) { if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) { goto err; } r_is_at_infinity = 0; } else { if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) { goto err; } } } } } } if (r_is_at_infinity) { if (!EC_POINT_set_to_infinity(group, r)) { goto err; } } else if (r_is_inverted && !EC_POINT_invert(group, r, ctx)) { goto err; } ret = 1; err: BN_CTX_free(new_ctx); EC_POINT_free(tmp); OPENSSL_free(wsize); OPENSSL_free(wNAF_len); if (wNAF != NULL) { signed char **w; for (w = wNAF; *w != NULL; w++) { OPENSSL_free(*w); } OPENSSL_free(wNAF); } if (val != NULL) { for (v = val; *v != NULL; v++) { EC_POINT_clear_free(*v); } OPENSSL_free(val); } OPENSSL_free(val_sub); return ret; }