| /* 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 <string.h> |
| |
| #include <openssl/bn.h> |
| #include <openssl/err.h> |
| #include <openssl/mem.h> |
| #include <openssl/thread.h> |
| |
| #include "internal.h" |
| #include "../internal.h" |
| |
| |
| /* This file implements the wNAF-based interleaving multi-exponentation method |
| * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>); |
| * */ |
| |
| /* 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; |
| } |
