Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1 | /* Originally written by Bodo Moeller for the OpenSSL project. |
| 2 | * ==================================================================== |
| 3 | * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. |
| 4 | * |
| 5 | * Redistribution and use in source and binary forms, with or without |
| 6 | * modification, are permitted provided that the following conditions |
| 7 | * are met: |
| 8 | * |
| 9 | * 1. Redistributions of source code must retain the above copyright |
| 10 | * notice, this list of conditions and the following disclaimer. |
| 11 | * |
| 12 | * 2. Redistributions in binary form must reproduce the above copyright |
| 13 | * notice, this list of conditions and the following disclaimer in |
| 14 | * the documentation and/or other materials provided with the |
| 15 | * distribution. |
| 16 | * |
| 17 | * 3. All advertising materials mentioning features or use of this |
| 18 | * software must display the following acknowledgment: |
| 19 | * "This product includes software developed by the OpenSSL Project |
| 20 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| 21 | * |
| 22 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| 23 | * endorse or promote products derived from this software without |
| 24 | * prior written permission. For written permission, please contact |
| 25 | * openssl-core@openssl.org. |
| 26 | * |
| 27 | * 5. Products derived from this software may not be called "OpenSSL" |
| 28 | * nor may "OpenSSL" appear in their names without prior written |
| 29 | * permission of the OpenSSL Project. |
| 30 | * |
| 31 | * 6. Redistributions of any form whatsoever must retain the following |
| 32 | * acknowledgment: |
| 33 | * "This product includes software developed by the OpenSSL Project |
| 34 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| 35 | * |
| 36 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| 37 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 38 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| 39 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| 40 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 41 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| 42 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| 43 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 44 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| 45 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 46 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| 47 | * OF THE POSSIBILITY OF SUCH DAMAGE. |
| 48 | * ==================================================================== |
| 49 | * |
| 50 | * This product includes cryptographic software written by Eric Young |
| 51 | * (eay@cryptsoft.com). This product includes software written by Tim |
| 52 | * Hudson (tjh@cryptsoft.com). |
| 53 | * |
| 54 | */ |
| 55 | /* ==================================================================== |
| 56 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. |
| 57 | * |
| 58 | * Portions of the attached software ("Contribution") are developed by |
| 59 | * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. |
| 60 | * |
| 61 | * The Contribution is licensed pursuant to the OpenSSL open source |
| 62 | * license provided above. |
| 63 | * |
| 64 | * The elliptic curve binary polynomial software is originally written by |
| 65 | * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems |
| 66 | * Laboratories. */ |
| 67 | |
| 68 | #include <openssl/ec.h> |
| 69 | |
| 70 | #include <string.h> |
| 71 | |
| 72 | #include <openssl/bn.h> |
| 73 | #include <openssl/err.h> |
| 74 | #include <openssl/mem.h> |
| 75 | |
| 76 | #include "internal.h" |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 77 | #include "../internal.h" |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 78 | |
| 79 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 80 | /* Most method functions in this file are designed to work with non-trivial |
| 81 | * representations of field elements if necessary (see ecp_mont.c): while |
| 82 | * standard modular addition and subtraction are used, the field_mul and |
| 83 | * field_sqr methods will be used for multiplication, and field_encode and |
| 84 | * field_decode (if defined) will be used for converting between |
| 85 | * representations. |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 86 | * |
| 87 | * Functions here specifically assume that if a non-trivial representation is |
| 88 | * used, it is a Montgomery representation (i.e. 'encoding' means multiplying |
| 89 | * by some factor R). */ |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 90 | |
| 91 | int ec_GFp_simple_group_init(EC_GROUP *group) { |
| 92 | BN_init(&group->field); |
| 93 | BN_init(&group->a); |
| 94 | BN_init(&group->b); |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 95 | BN_init(&group->one); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 96 | group->a_is_minus3 = 0; |
| 97 | return 1; |
| 98 | } |
| 99 | |
| 100 | void ec_GFp_simple_group_finish(EC_GROUP *group) { |
| 101 | BN_free(&group->field); |
| 102 | BN_free(&group->a); |
| 103 | BN_free(&group->b); |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 104 | BN_free(&group->one); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 105 | } |
| 106 | |
| 107 | int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) { |
| 108 | if (!BN_copy(&dest->field, &src->field) || |
| 109 | !BN_copy(&dest->a, &src->a) || |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 110 | !BN_copy(&dest->b, &src->b) || |
| 111 | !BN_copy(&dest->one, &src->one)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 112 | return 0; |
| 113 | } |
| 114 | |
| 115 | dest->a_is_minus3 = src->a_is_minus3; |
| 116 | return 1; |
| 117 | } |
| 118 | |
| 119 | int ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p, |
| 120 | const BIGNUM *a, const BIGNUM *b, |
| 121 | BN_CTX *ctx) { |
| 122 | int ret = 0; |
| 123 | BN_CTX *new_ctx = NULL; |
| 124 | BIGNUM *tmp_a; |
| 125 | |
| 126 | /* p must be a prime > 3 */ |
| 127 | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 128 | OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FIELD); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 129 | return 0; |
| 130 | } |
| 131 | |
| 132 | if (ctx == NULL) { |
| 133 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 134 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 135 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 136 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 137 | } |
| 138 | |
| 139 | BN_CTX_start(ctx); |
| 140 | tmp_a = BN_CTX_get(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 141 | if (tmp_a == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 142 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 143 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 144 | |
| 145 | /* group->field */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 146 | if (!BN_copy(&group->field, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 147 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 148 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 149 | BN_set_negative(&group->field, 0); |
| 150 | |
| 151 | /* group->a */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 152 | if (!BN_nnmod(tmp_a, a, p, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 153 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 154 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 155 | if (group->meth->field_encode) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 156 | if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 157 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 158 | } |
| 159 | } else if (!BN_copy(&group->a, tmp_a)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 160 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 161 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 162 | |
| 163 | /* group->b */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 164 | if (!BN_nnmod(&group->b, b, p, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 165 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 166 | } |
| 167 | if (group->meth->field_encode && |
| 168 | !group->meth->field_encode(group, &group->b, &group->b, ctx)) { |
| 169 | goto err; |
| 170 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 171 | |
| 172 | /* group->a_is_minus3 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 173 | if (!BN_add_word(tmp_a, 3)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 174 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 175 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 176 | group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); |
| 177 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 178 | if (group->meth->field_encode != NULL) { |
| 179 | if (!group->meth->field_encode(group, &group->one, BN_value_one(), ctx)) { |
| 180 | goto err; |
| 181 | } |
| 182 | } else if (!BN_copy(&group->one, BN_value_one())) { |
| 183 | goto err; |
| 184 | } |
| 185 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 186 | ret = 1; |
| 187 | |
| 188 | err: |
| 189 | BN_CTX_end(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 190 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 191 | return ret; |
| 192 | } |
| 193 | |
| 194 | int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, |
| 195 | BIGNUM *b, BN_CTX *ctx) { |
| 196 | int ret = 0; |
| 197 | BN_CTX *new_ctx = NULL; |
| 198 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 199 | if (p != NULL && !BN_copy(p, &group->field)) { |
| 200 | return 0; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 201 | } |
| 202 | |
| 203 | if (a != NULL || b != NULL) { |
| 204 | if (group->meth->field_decode) { |
| 205 | if (ctx == NULL) { |
| 206 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 207 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 208 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 209 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 210 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 211 | if (a != NULL && !group->meth->field_decode(group, a, &group->a, ctx)) { |
| 212 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 213 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 214 | if (b != NULL && !group->meth->field_decode(group, b, &group->b, ctx)) { |
| 215 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 216 | } |
| 217 | } else { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 218 | if (a != NULL && !BN_copy(a, &group->a)) { |
| 219 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 220 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 221 | if (b != NULL && !BN_copy(b, &group->b)) { |
| 222 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 223 | } |
| 224 | } |
| 225 | } |
| 226 | |
| 227 | ret = 1; |
| 228 | |
| 229 | err: |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 230 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 231 | return ret; |
| 232 | } |
| 233 | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 234 | unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *group) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 235 | return BN_num_bits(&group->field); |
| 236 | } |
| 237 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 238 | int ec_GFp_simple_point_init(EC_POINT *point) { |
| 239 | BN_init(&point->X); |
| 240 | BN_init(&point->Y); |
| 241 | BN_init(&point->Z); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 242 | |
| 243 | return 1; |
| 244 | } |
| 245 | |
| 246 | void ec_GFp_simple_point_finish(EC_POINT *point) { |
| 247 | BN_free(&point->X); |
| 248 | BN_free(&point->Y); |
| 249 | BN_free(&point->Z); |
| 250 | } |
| 251 | |
| 252 | void ec_GFp_simple_point_clear_finish(EC_POINT *point) { |
| 253 | BN_clear_free(&point->X); |
| 254 | BN_clear_free(&point->Y); |
| 255 | BN_clear_free(&point->Z); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 256 | } |
| 257 | |
| 258 | int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 259 | if (!BN_copy(&dest->X, &src->X) || |
| 260 | !BN_copy(&dest->Y, &src->Y) || |
| 261 | !BN_copy(&dest->Z, &src->Z)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 262 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 263 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 264 | |
| 265 | return 1; |
| 266 | } |
| 267 | |
| 268 | int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, |
| 269 | EC_POINT *point) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 270 | BN_zero(&point->Z); |
| 271 | return 1; |
| 272 | } |
| 273 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 274 | static int set_Jprojective_coordinate_GFp(const EC_GROUP *group, BIGNUM *out, |
| 275 | const BIGNUM *in, BN_CTX *ctx) { |
| 276 | if (in == NULL) { |
| 277 | return 1; |
| 278 | } |
| 279 | if (BN_is_negative(in) || |
| 280 | BN_cmp(in, &group->field) >= 0) { |
| 281 | OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE); |
| 282 | return 0; |
| 283 | } |
| 284 | if (group->meth->field_encode) { |
| 285 | return group->meth->field_encode(group, out, in, ctx); |
| 286 | } |
| 287 | return BN_copy(out, in) != NULL; |
| 288 | } |
| 289 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 290 | int ec_GFp_simple_set_Jprojective_coordinates_GFp( |
| 291 | const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, |
| 292 | const BIGNUM *z, BN_CTX *ctx) { |
| 293 | BN_CTX *new_ctx = NULL; |
| 294 | int ret = 0; |
| 295 | |
| 296 | if (ctx == NULL) { |
| 297 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 298 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 299 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 300 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 301 | } |
| 302 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 303 | if (!set_Jprojective_coordinate_GFp(group, &point->X, x, ctx) || |
| 304 | !set_Jprojective_coordinate_GFp(group, &point->Y, y, ctx) || |
| 305 | !set_Jprojective_coordinate_GFp(group, &point->Z, z, ctx)) { |
| 306 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 307 | } |
| 308 | |
| 309 | ret = 1; |
| 310 | |
| 311 | err: |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 312 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 313 | return ret; |
| 314 | } |
| 315 | |
| 316 | int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, |
| 317 | const EC_POINT *point, |
| 318 | BIGNUM *x, BIGNUM *y, |
| 319 | BIGNUM *z, BN_CTX *ctx) { |
| 320 | BN_CTX *new_ctx = NULL; |
| 321 | int ret = 0; |
| 322 | |
| 323 | if (group->meth->field_decode != 0) { |
| 324 | if (ctx == NULL) { |
| 325 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 326 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 327 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 328 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 329 | } |
| 330 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 331 | if (x != NULL && !group->meth->field_decode(group, x, &point->X, ctx)) { |
| 332 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 333 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 334 | if (y != NULL && !group->meth->field_decode(group, y, &point->Y, ctx)) { |
| 335 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 336 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 337 | if (z != NULL && !group->meth->field_decode(group, z, &point->Z, ctx)) { |
| 338 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 339 | } |
| 340 | } else { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 341 | if (x != NULL && !BN_copy(x, &point->X)) { |
| 342 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 343 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 344 | if (y != NULL && !BN_copy(y, &point->Y)) { |
| 345 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 346 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 347 | if (z != NULL && !BN_copy(z, &point->Z)) { |
| 348 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 349 | } |
| 350 | } |
| 351 | |
| 352 | ret = 1; |
| 353 | |
| 354 | err: |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 355 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 356 | return ret; |
| 357 | } |
| 358 | |
| 359 | int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, |
| 360 | EC_POINT *point, const BIGNUM *x, |
| 361 | const BIGNUM *y, BN_CTX *ctx) { |
| 362 | if (x == NULL || y == NULL) { |
| 363 | /* unlike for projective coordinates, we do not tolerate this */ |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 364 | OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 365 | return 0; |
| 366 | } |
| 367 | |
| 368 | return ec_point_set_Jprojective_coordinates_GFp(group, point, x, y, |
| 369 | BN_value_one(), ctx); |
| 370 | } |
| 371 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 372 | int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
| 373 | const EC_POINT *b, BN_CTX *ctx) { |
| 374 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, |
| 375 | BN_CTX *); |
| 376 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| 377 | const BIGNUM *p; |
| 378 | BN_CTX *new_ctx = NULL; |
| 379 | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; |
| 380 | int ret = 0; |
| 381 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 382 | if (a == b) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 383 | return EC_POINT_dbl(group, r, a, ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 384 | } |
| 385 | if (EC_POINT_is_at_infinity(group, a)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 386 | return EC_POINT_copy(r, b); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 387 | } |
| 388 | if (EC_POINT_is_at_infinity(group, b)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 389 | return EC_POINT_copy(r, a); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 390 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 391 | |
| 392 | field_mul = group->meth->field_mul; |
| 393 | field_sqr = group->meth->field_sqr; |
| 394 | p = &group->field; |
| 395 | |
| 396 | if (ctx == NULL) { |
| 397 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 398 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 399 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 400 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 401 | } |
| 402 | |
| 403 | BN_CTX_start(ctx); |
| 404 | n0 = BN_CTX_get(ctx); |
| 405 | n1 = BN_CTX_get(ctx); |
| 406 | n2 = BN_CTX_get(ctx); |
| 407 | n3 = BN_CTX_get(ctx); |
| 408 | n4 = BN_CTX_get(ctx); |
| 409 | n5 = BN_CTX_get(ctx); |
| 410 | n6 = BN_CTX_get(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 411 | if (n6 == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 412 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 413 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 414 | |
| 415 | /* Note that in this function we must not read components of 'a' or 'b' |
| 416 | * once we have written the corresponding components of 'r'. |
| 417 | * ('r' might be one of 'a' or 'b'.) |
| 418 | */ |
| 419 | |
| 420 | /* n1, n2 */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 421 | int b_Z_is_one = BN_cmp(&b->Z, &group->one) == 0; |
| 422 | |
| 423 | if (b_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 424 | if (!BN_copy(n1, &a->X) || !BN_copy(n2, &a->Y)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 425 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 426 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 427 | /* n1 = X_a */ |
| 428 | /* n2 = Y_a */ |
| 429 | } else { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 430 | if (!field_sqr(group, n0, &b->Z, ctx) || |
| 431 | !field_mul(group, n1, &a->X, n0, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 432 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 433 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 434 | /* n1 = X_a * Z_b^2 */ |
| 435 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 436 | if (!field_mul(group, n0, n0, &b->Z, ctx) || |
| 437 | !field_mul(group, n2, &a->Y, n0, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 438 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 439 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 440 | /* n2 = Y_a * Z_b^3 */ |
| 441 | } |
| 442 | |
| 443 | /* n3, n4 */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 444 | int a_Z_is_one = BN_cmp(&a->Z, &group->one) == 0; |
| 445 | if (a_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 446 | if (!BN_copy(n3, &b->X) || !BN_copy(n4, &b->Y)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 447 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 448 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 449 | /* n3 = X_b */ |
| 450 | /* n4 = Y_b */ |
| 451 | } else { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 452 | if (!field_sqr(group, n0, &a->Z, ctx) || |
| 453 | !field_mul(group, n3, &b->X, n0, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 454 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 455 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 456 | /* n3 = X_b * Z_a^2 */ |
| 457 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 458 | if (!field_mul(group, n0, n0, &a->Z, ctx) || |
| 459 | !field_mul(group, n4, &b->Y, n0, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 460 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 461 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 462 | /* n4 = Y_b * Z_a^3 */ |
| 463 | } |
| 464 | |
| 465 | /* n5, n6 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 466 | if (!BN_mod_sub_quick(n5, n1, n3, p) || |
| 467 | !BN_mod_sub_quick(n6, n2, n4, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 468 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 469 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 470 | /* n5 = n1 - n3 */ |
| 471 | /* n6 = n2 - n4 */ |
| 472 | |
| 473 | if (BN_is_zero(n5)) { |
| 474 | if (BN_is_zero(n6)) { |
| 475 | /* a is the same point as b */ |
| 476 | BN_CTX_end(ctx); |
| 477 | ret = EC_POINT_dbl(group, r, a, ctx); |
| 478 | ctx = NULL; |
| 479 | goto end; |
| 480 | } else { |
| 481 | /* a is the inverse of b */ |
| 482 | BN_zero(&r->Z); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 483 | ret = 1; |
| 484 | goto end; |
| 485 | } |
| 486 | } |
| 487 | |
| 488 | /* 'n7', 'n8' */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 489 | if (!BN_mod_add_quick(n1, n1, n3, p) || |
| 490 | !BN_mod_add_quick(n2, n2, n4, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 491 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 492 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 493 | /* 'n7' = n1 + n3 */ |
| 494 | /* 'n8' = n2 + n4 */ |
| 495 | |
| 496 | /* Z_r */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 497 | if (a_Z_is_one && b_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 498 | if (!BN_copy(&r->Z, n5)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 499 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 500 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 501 | } else { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 502 | if (a_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 503 | if (!BN_copy(n0, &b->Z)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 504 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 505 | } |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 506 | } else if (b_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 507 | if (!BN_copy(n0, &a->Z)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 508 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 509 | } |
| 510 | } else if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 511 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 512 | } |
| 513 | if (!field_mul(group, &r->Z, n0, n5, ctx)) { |
| 514 | goto end; |
| 515 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 516 | } |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 517 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 518 | /* Z_r = Z_a * Z_b * n5 */ |
| 519 | |
| 520 | /* X_r */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 521 | if (!field_sqr(group, n0, n6, ctx) || |
| 522 | !field_sqr(group, n4, n5, ctx) || |
| 523 | !field_mul(group, n3, n1, n4, ctx) || |
| 524 | !BN_mod_sub_quick(&r->X, n0, n3, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 525 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 526 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 527 | /* X_r = n6^2 - n5^2 * 'n7' */ |
| 528 | |
| 529 | /* 'n9' */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 530 | if (!BN_mod_lshift1_quick(n0, &r->X, p) || |
| 531 | !BN_mod_sub_quick(n0, n3, n0, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 532 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 533 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 534 | /* n9 = n5^2 * 'n7' - 2 * X_r */ |
| 535 | |
| 536 | /* Y_r */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 537 | if (!field_mul(group, n0, n0, n6, ctx) || |
| 538 | !field_mul(group, n5, n4, n5, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 539 | goto end; /* now n5 is n5^3 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 540 | } |
| 541 | if (!field_mul(group, n1, n2, n5, ctx) || |
| 542 | !BN_mod_sub_quick(n0, n0, n1, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 543 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 544 | } |
| 545 | if (BN_is_odd(n0) && !BN_add(n0, n0, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 546 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 547 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 548 | /* now 0 <= n0 < 2*p, and n0 is even */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 549 | if (!BN_rshift1(&r->Y, n0)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 550 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 551 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 552 | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ |
| 553 | |
| 554 | ret = 1; |
| 555 | |
| 556 | end: |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 557 | if (ctx) { |
| 558 | /* otherwise we already called BN_CTX_end */ |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 559 | BN_CTX_end(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 560 | } |
| 561 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 562 | return ret; |
| 563 | } |
| 564 | |
| 565 | int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
| 566 | BN_CTX *ctx) { |
| 567 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, |
| 568 | BN_CTX *); |
| 569 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| 570 | const BIGNUM *p; |
| 571 | BN_CTX *new_ctx = NULL; |
| 572 | BIGNUM *n0, *n1, *n2, *n3; |
| 573 | int ret = 0; |
| 574 | |
| 575 | if (EC_POINT_is_at_infinity(group, a)) { |
| 576 | BN_zero(&r->Z); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 577 | return 1; |
| 578 | } |
| 579 | |
| 580 | field_mul = group->meth->field_mul; |
| 581 | field_sqr = group->meth->field_sqr; |
| 582 | p = &group->field; |
| 583 | |
| 584 | if (ctx == NULL) { |
| 585 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 586 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 587 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 588 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 589 | } |
| 590 | |
| 591 | BN_CTX_start(ctx); |
| 592 | n0 = BN_CTX_get(ctx); |
| 593 | n1 = BN_CTX_get(ctx); |
| 594 | n2 = BN_CTX_get(ctx); |
| 595 | n3 = BN_CTX_get(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 596 | if (n3 == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 597 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 598 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 599 | |
| 600 | /* Note that in this function we must not read components of 'a' |
| 601 | * once we have written the corresponding components of 'r'. |
| 602 | * ('r' might the same as 'a'.) |
| 603 | */ |
| 604 | |
| 605 | /* n1 */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 606 | if (BN_cmp(&a->Z, &group->one) == 0) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 607 | if (!field_sqr(group, n0, &a->X, ctx) || |
| 608 | !BN_mod_lshift1_quick(n1, n0, p) || |
| 609 | !BN_mod_add_quick(n0, n0, n1, p) || |
| 610 | !BN_mod_add_quick(n1, n0, &group->a, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 611 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 612 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 613 | /* n1 = 3 * X_a^2 + a_curve */ |
| 614 | } else if (group->a_is_minus3) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 615 | if (!field_sqr(group, n1, &a->Z, ctx) || |
| 616 | !BN_mod_add_quick(n0, &a->X, n1, p) || |
| 617 | !BN_mod_sub_quick(n2, &a->X, n1, p) || |
| 618 | !field_mul(group, n1, n0, n2, ctx) || |
| 619 | !BN_mod_lshift1_quick(n0, n1, p) || |
| 620 | !BN_mod_add_quick(n1, n0, n1, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 621 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 622 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 623 | /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) |
| 624 | * = 3 * X_a^2 - 3 * Z_a^4 */ |
| 625 | } else { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 626 | if (!field_sqr(group, n0, &a->X, ctx) || |
| 627 | !BN_mod_lshift1_quick(n1, n0, p) || |
| 628 | !BN_mod_add_quick(n0, n0, n1, p) || |
| 629 | !field_sqr(group, n1, &a->Z, ctx) || |
| 630 | !field_sqr(group, n1, n1, ctx) || |
| 631 | !field_mul(group, n1, n1, &group->a, ctx) || |
| 632 | !BN_mod_add_quick(n1, n1, n0, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 633 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 634 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 635 | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ |
| 636 | } |
| 637 | |
| 638 | /* Z_r */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 639 | if (BN_cmp(&a->Z, &group->one) == 0) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 640 | if (!BN_copy(n0, &a->Y)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 641 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 642 | } |
| 643 | } else if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 644 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 645 | } |
| 646 | if (!BN_mod_lshift1_quick(&r->Z, n0, p)) { |
| 647 | goto err; |
| 648 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 649 | /* Z_r = 2 * Y_a * Z_a */ |
| 650 | |
| 651 | /* n2 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 652 | if (!field_sqr(group, n3, &a->Y, ctx) || |
| 653 | !field_mul(group, n2, &a->X, n3, ctx) || |
| 654 | !BN_mod_lshift_quick(n2, n2, 2, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 655 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 656 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 657 | /* n2 = 4 * X_a * Y_a^2 */ |
| 658 | |
| 659 | /* X_r */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 660 | if (!BN_mod_lshift1_quick(n0, n2, p) || |
| 661 | !field_sqr(group, &r->X, n1, ctx) || |
| 662 | !BN_mod_sub_quick(&r->X, &r->X, n0, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 663 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 664 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 665 | /* X_r = n1^2 - 2 * n2 */ |
| 666 | |
| 667 | /* n3 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 668 | if (!field_sqr(group, n0, n3, ctx) || |
| 669 | !BN_mod_lshift_quick(n3, n0, 3, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 670 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 671 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 672 | /* n3 = 8 * Y_a^4 */ |
| 673 | |
| 674 | /* Y_r */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 675 | if (!BN_mod_sub_quick(n0, n2, &r->X, p) || |
| 676 | !field_mul(group, n0, n1, n0, ctx) || |
| 677 | !BN_mod_sub_quick(&r->Y, n0, n3, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 678 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 679 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 680 | /* Y_r = n1 * (n2 - X_r) - n3 */ |
| 681 | |
| 682 | ret = 1; |
| 683 | |
| 684 | err: |
| 685 | BN_CTX_end(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 686 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 687 | return ret; |
| 688 | } |
| 689 | |
| 690 | int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 691 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 692 | /* point is its own inverse */ |
| 693 | return 1; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 694 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 695 | |
| 696 | return BN_usub(&point->Y, &group->field, &point->Y); |
| 697 | } |
| 698 | |
| 699 | int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 700 | return BN_is_zero(&point->Z); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 701 | } |
| 702 | |
| 703 | int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, |
| 704 | BN_CTX *ctx) { |
| 705 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, |
| 706 | BN_CTX *); |
| 707 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| 708 | const BIGNUM *p; |
| 709 | BN_CTX *new_ctx = NULL; |
| 710 | BIGNUM *rh, *tmp, *Z4, *Z6; |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 711 | int ret = 0; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 712 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 713 | if (EC_POINT_is_at_infinity(group, point)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 714 | return 1; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 715 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 716 | |
| 717 | field_mul = group->meth->field_mul; |
| 718 | field_sqr = group->meth->field_sqr; |
| 719 | p = &group->field; |
| 720 | |
| 721 | if (ctx == NULL) { |
| 722 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 723 | if (ctx == NULL) { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 724 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 725 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 726 | } |
| 727 | |
| 728 | BN_CTX_start(ctx); |
| 729 | rh = BN_CTX_get(ctx); |
| 730 | tmp = BN_CTX_get(ctx); |
| 731 | Z4 = BN_CTX_get(ctx); |
| 732 | Z6 = BN_CTX_get(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 733 | if (Z6 == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 734 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 735 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 736 | |
| 737 | /* We have a curve defined by a Weierstrass equation |
| 738 | * y^2 = x^3 + a*x + b. |
| 739 | * The point to consider is given in Jacobian projective coordinates |
| 740 | * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). |
| 741 | * Substituting this and multiplying by Z^6 transforms the above equation |
| 742 | * into |
| 743 | * Y^2 = X^3 + a*X*Z^4 + b*Z^6. |
| 744 | * To test this, we add up the right-hand side in 'rh'. |
| 745 | */ |
| 746 | |
| 747 | /* rh := X^2 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 748 | if (!field_sqr(group, rh, &point->X, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 749 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 750 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 751 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 752 | if (BN_cmp(&point->Z, &group->one) != 0) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 753 | if (!field_sqr(group, tmp, &point->Z, ctx) || |
| 754 | !field_sqr(group, Z4, tmp, ctx) || |
| 755 | !field_mul(group, Z6, Z4, tmp, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 756 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 757 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 758 | |
| 759 | /* rh := (rh + a*Z^4)*X */ |
| 760 | if (group->a_is_minus3) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 761 | if (!BN_mod_lshift1_quick(tmp, Z4, p) || |
| 762 | !BN_mod_add_quick(tmp, tmp, Z4, p) || |
| 763 | !BN_mod_sub_quick(rh, rh, tmp, p) || |
| 764 | !field_mul(group, rh, rh, &point->X, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 765 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 766 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 767 | } else { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 768 | if (!field_mul(group, tmp, Z4, &group->a, ctx) || |
| 769 | !BN_mod_add_quick(rh, rh, tmp, p) || |
| 770 | !field_mul(group, rh, rh, &point->X, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 771 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 772 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 773 | } |
| 774 | |
| 775 | /* rh := rh + b*Z^6 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 776 | if (!field_mul(group, tmp, &group->b, Z6, ctx) || |
| 777 | !BN_mod_add_quick(rh, rh, tmp, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 778 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 779 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 780 | } else { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 781 | /* rh := (rh + a)*X */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 782 | if (!BN_mod_add_quick(rh, rh, &group->a, p) || |
| 783 | !field_mul(group, rh, rh, &point->X, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 784 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 785 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 786 | /* rh := rh + b */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 787 | if (!BN_mod_add_quick(rh, rh, &group->b, p)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 788 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 789 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 790 | } |
| 791 | |
| 792 | /* 'lh' := Y^2 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 793 | if (!field_sqr(group, tmp, &point->Y, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 794 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 795 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 796 | |
| 797 | ret = (0 == BN_ucmp(tmp, rh)); |
| 798 | |
| 799 | err: |
| 800 | BN_CTX_end(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 801 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 802 | return ret; |
| 803 | } |
| 804 | |
| 805 | int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, |
| 806 | const EC_POINT *b, BN_CTX *ctx) { |
| 807 | /* return values: |
| 808 | * -1 error |
| 809 | * 0 equal (in affine coordinates) |
| 810 | * 1 not equal |
| 811 | */ |
| 812 | |
| 813 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, |
| 814 | BN_CTX *); |
| 815 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| 816 | BN_CTX *new_ctx = NULL; |
| 817 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; |
| 818 | const BIGNUM *tmp1_, *tmp2_; |
| 819 | int ret = -1; |
| 820 | |
| 821 | if (EC_POINT_is_at_infinity(group, a)) { |
| 822 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; |
| 823 | } |
| 824 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 825 | if (EC_POINT_is_at_infinity(group, b)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 826 | return 1; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 827 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 828 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 829 | int a_Z_is_one = BN_cmp(&a->Z, &group->one) == 0; |
| 830 | int b_Z_is_one = BN_cmp(&b->Z, &group->one) == 0; |
| 831 | |
| 832 | if (a_Z_is_one && b_Z_is_one) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 833 | return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; |
| 834 | } |
| 835 | |
| 836 | field_mul = group->meth->field_mul; |
| 837 | field_sqr = group->meth->field_sqr; |
| 838 | |
| 839 | if (ctx == NULL) { |
| 840 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 841 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 842 | return -1; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 843 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 844 | } |
| 845 | |
| 846 | BN_CTX_start(ctx); |
| 847 | tmp1 = BN_CTX_get(ctx); |
| 848 | tmp2 = BN_CTX_get(ctx); |
| 849 | Za23 = BN_CTX_get(ctx); |
| 850 | Zb23 = BN_CTX_get(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 851 | if (Zb23 == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 852 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 853 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 854 | |
| 855 | /* We have to decide whether |
| 856 | * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), |
| 857 | * or equivalently, whether |
| 858 | * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). |
| 859 | */ |
| 860 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 861 | if (!b_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 862 | if (!field_sqr(group, Zb23, &b->Z, ctx) || |
| 863 | !field_mul(group, tmp1, &a->X, Zb23, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 864 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 865 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 866 | tmp1_ = tmp1; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 867 | } else { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 868 | tmp1_ = &a->X; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 869 | } |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 870 | if (!a_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 871 | if (!field_sqr(group, Za23, &a->Z, ctx) || |
| 872 | !field_mul(group, tmp2, &b->X, Za23, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 873 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 874 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 875 | tmp2_ = tmp2; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 876 | } else { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 877 | tmp2_ = &b->X; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 878 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 879 | |
| 880 | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ |
| 881 | if (BN_cmp(tmp1_, tmp2_) != 0) { |
| 882 | ret = 1; /* points differ */ |
| 883 | goto end; |
| 884 | } |
| 885 | |
| 886 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 887 | if (!b_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 888 | if (!field_mul(group, Zb23, Zb23, &b->Z, ctx) || |
| 889 | !field_mul(group, tmp1, &a->Y, Zb23, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 890 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 891 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 892 | /* tmp1_ = tmp1 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 893 | } else { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 894 | tmp1_ = &a->Y; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 895 | } |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 896 | if (!a_Z_is_one) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 897 | if (!field_mul(group, Za23, Za23, &a->Z, ctx) || |
| 898 | !field_mul(group, tmp2, &b->Y, Za23, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 899 | goto end; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 900 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 901 | /* tmp2_ = tmp2 */ |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 902 | } else { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 903 | tmp2_ = &b->Y; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 904 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 905 | |
| 906 | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ |
| 907 | if (BN_cmp(tmp1_, tmp2_) != 0) { |
| 908 | ret = 1; /* points differ */ |
| 909 | goto end; |
| 910 | } |
| 911 | |
| 912 | /* points are equal */ |
| 913 | ret = 0; |
| 914 | |
| 915 | end: |
| 916 | BN_CTX_end(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 917 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 918 | return ret; |
| 919 | } |
| 920 | |
| 921 | int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, |
| 922 | BN_CTX *ctx) { |
| 923 | BN_CTX *new_ctx = NULL; |
| 924 | BIGNUM *x, *y; |
| 925 | int ret = 0; |
| 926 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 927 | if (BN_cmp(&point->Z, &group->one) == 0 || |
| 928 | EC_POINT_is_at_infinity(group, point)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 929 | return 1; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 930 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 931 | |
| 932 | if (ctx == NULL) { |
| 933 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 934 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 935 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 936 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 937 | } |
| 938 | |
| 939 | BN_CTX_start(ctx); |
| 940 | x = BN_CTX_get(ctx); |
| 941 | y = BN_CTX_get(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 942 | if (y == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 943 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 944 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 945 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 946 | if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx) || |
| 947 | !EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 948 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 949 | } |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 950 | if (BN_cmp(&point->Z, &group->one) != 0) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 951 | OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 952 | goto err; |
| 953 | } |
| 954 | |
| 955 | ret = 1; |
| 956 | |
| 957 | err: |
| 958 | BN_CTX_end(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 959 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 960 | return ret; |
| 961 | } |
| 962 | |
| 963 | int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, |
| 964 | EC_POINT *points[], BN_CTX *ctx) { |
| 965 | BN_CTX *new_ctx = NULL; |
| 966 | BIGNUM *tmp, *tmp_Z; |
| 967 | BIGNUM **prod_Z = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 968 | int ret = 0; |
| 969 | |
| 970 | if (num == 0) { |
| 971 | return 1; |
| 972 | } |
| 973 | |
| 974 | if (ctx == NULL) { |
| 975 | ctx = new_ctx = BN_CTX_new(); |
| 976 | if (ctx == NULL) { |
| 977 | return 0; |
| 978 | } |
| 979 | } |
| 980 | |
| 981 | BN_CTX_start(ctx); |
| 982 | tmp = BN_CTX_get(ctx); |
| 983 | tmp_Z = BN_CTX_get(ctx); |
| 984 | if (tmp == NULL || tmp_Z == NULL) { |
| 985 | goto err; |
| 986 | } |
| 987 | |
| 988 | prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0])); |
| 989 | if (prod_Z == NULL) { |
| 990 | goto err; |
| 991 | } |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 992 | OPENSSL_memset(prod_Z, 0, num * sizeof(prod_Z[0])); |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 993 | for (size_t i = 0; i < num; i++) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 994 | prod_Z[i] = BN_new(); |
| 995 | if (prod_Z[i] == NULL) { |
| 996 | goto err; |
| 997 | } |
| 998 | } |
| 999 | |
| 1000 | /* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, |
| 1001 | * skipping any zero-valued inputs (pretend that they're 1). */ |
| 1002 | |
| 1003 | if (!BN_is_zero(&points[0]->Z)) { |
| 1004 | if (!BN_copy(prod_Z[0], &points[0]->Z)) { |
| 1005 | goto err; |
| 1006 | } |
| 1007 | } else { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1008 | if (BN_copy(prod_Z[0], &group->one) == NULL) { |
| 1009 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1010 | } |
| 1011 | } |
| 1012 | |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 1013 | for (size_t i = 1; i < num; i++) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1014 | if (!BN_is_zero(&points[i]->Z)) { |
| 1015 | if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], |
| 1016 | &points[i]->Z, ctx)) { |
| 1017 | goto err; |
| 1018 | } |
| 1019 | } else { |
| 1020 | if (!BN_copy(prod_Z[i], prod_Z[i - 1])) { |
| 1021 | goto err; |
| 1022 | } |
| 1023 | } |
| 1024 | } |
| 1025 | |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 1026 | /* Now use a single explicit inversion to replace every non-zero points[i]->Z |
| 1027 | * by its inverse. We use |BN_mod_inverse_odd| instead of doing a constant- |
| 1028 | * time inversion using Fermat's Little Theorem because this function is |
| 1029 | * usually only used for converting multiples of a public key point to |
| 1030 | * affine, and a public key point isn't secret. If we were to use Fermat's |
| 1031 | * Little Theorem then the cost of the inversion would usually be so high |
| 1032 | * that converting the multiples to affine would be counterproductive. */ |
| 1033 | int no_inverse; |
| 1034 | if (!BN_mod_inverse_odd(tmp, &no_inverse, prod_Z[num - 1], &group->field, |
| 1035 | ctx)) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 1036 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1037 | goto err; |
| 1038 | } |
| 1039 | |
| 1040 | if (group->meth->field_encode != NULL) { |
| 1041 | /* In the Montgomery case, we just turned R*H (representing H) |
| 1042 | * into 1/(R*H), but we need R*(1/H) (representing 1/H); |
| 1043 | * i.e. we need to multiply by the Montgomery factor twice. */ |
| 1044 | if (!group->meth->field_encode(group, tmp, tmp, ctx) || |
| 1045 | !group->meth->field_encode(group, tmp, tmp, ctx)) { |
| 1046 | goto err; |
| 1047 | } |
| 1048 | } |
| 1049 | |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 1050 | for (size_t i = num - 1; i > 0; --i) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1051 | /* Loop invariant: tmp is the product of the inverses of |
| 1052 | * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */ |
| 1053 | if (BN_is_zero(&points[i]->Z)) { |
| 1054 | continue; |
| 1055 | } |
| 1056 | |
| 1057 | /* Set tmp_Z to the inverse of points[i]->Z (as product |
| 1058 | * of Z inverses 0 .. i, Z values 0 .. i - 1). */ |
| 1059 | if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx) || |
| 1060 | /* Update tmp to satisfy the loop invariant for i - 1. */ |
| 1061 | !group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx) || |
| 1062 | /* Replace points[i]->Z by its inverse. */ |
| 1063 | !BN_copy(&points[i]->Z, tmp_Z)) { |
| 1064 | goto err; |
| 1065 | } |
| 1066 | } |
| 1067 | |
| 1068 | /* Replace points[0]->Z by its inverse. */ |
| 1069 | if (!BN_is_zero(&points[0]->Z) && !BN_copy(&points[0]->Z, tmp)) { |
| 1070 | goto err; |
| 1071 | } |
| 1072 | |
| 1073 | /* Finally, fix up the X and Y coordinates for all points. */ |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 1074 | for (size_t i = 0; i < num; i++) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1075 | EC_POINT *p = points[i]; |
| 1076 | |
| 1077 | if (!BN_is_zero(&p->Z)) { |
| 1078 | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1). */ |
| 1079 | if (!group->meth->field_sqr(group, tmp, &p->Z, ctx) || |
| 1080 | !group->meth->field_mul(group, &p->X, &p->X, tmp, ctx) || |
| 1081 | !group->meth->field_mul(group, tmp, tmp, &p->Z, ctx) || |
| 1082 | !group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) { |
| 1083 | goto err; |
| 1084 | } |
| 1085 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 1086 | if (BN_copy(&p->Z, &group->one) == NULL) { |
| 1087 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1088 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1089 | } |
| 1090 | } |
| 1091 | |
| 1092 | ret = 1; |
| 1093 | |
| 1094 | err: |
| 1095 | BN_CTX_end(ctx); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 1096 | BN_CTX_free(new_ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1097 | if (prod_Z != NULL) { |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 1098 | for (size_t i = 0; i < num; i++) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1099 | if (prod_Z[i] == NULL) { |
| 1100 | break; |
| 1101 | } |
| 1102 | BN_clear_free(prod_Z[i]); |
| 1103 | } |
| 1104 | OPENSSL_free(prod_Z); |
| 1105 | } |
| 1106 | |
| 1107 | return ret; |
| 1108 | } |
| 1109 | |
| 1110 | int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
| 1111 | const BIGNUM *b, BN_CTX *ctx) { |
| 1112 | return BN_mod_mul(r, a, b, &group->field, ctx); |
| 1113 | } |
| 1114 | |
| 1115 | int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
| 1116 | BN_CTX *ctx) { |
| 1117 | return BN_mod_sqr(r, a, &group->field, ctx); |
| 1118 | } |