Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1 | /* Originally written by Bodo Moeller and Nils Larsch 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 <openssl/bn.h> |
| 71 | #include <openssl/err.h> |
| 72 | #include <openssl/mem.h> |
| 73 | |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 74 | #include "../bn/internal.h" |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame^] | 75 | #include "../delocate.h" |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 76 | #include "internal.h" |
| 77 | |
| 78 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 79 | int ec_GFp_mont_group_init(EC_GROUP *group) { |
| 80 | int ok; |
| 81 | |
| 82 | ok = ec_GFp_simple_group_init(group); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 83 | group->mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 84 | return ok; |
| 85 | } |
| 86 | |
| 87 | void ec_GFp_mont_group_finish(EC_GROUP *group) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 88 | BN_MONT_CTX_free(group->mont); |
| 89 | group->mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 90 | ec_GFp_simple_group_finish(group); |
| 91 | } |
| 92 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 93 | int ec_GFp_mont_group_copy(EC_GROUP *dest, const EC_GROUP *src) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 94 | BN_MONT_CTX_free(dest->mont); |
| 95 | dest->mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 96 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 97 | if (!ec_GFp_simple_group_copy(dest, src)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 98 | return 0; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 99 | } |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 100 | |
| 101 | if (src->mont != NULL) { |
| 102 | dest->mont = BN_MONT_CTX_new(); |
| 103 | if (dest->mont == NULL) { |
| 104 | return 0; |
| 105 | } |
| 106 | if (!BN_MONT_CTX_copy(dest->mont, src->mont)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 107 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 108 | } |
| 109 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 110 | |
| 111 | return 1; |
| 112 | |
| 113 | err: |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 114 | BN_MONT_CTX_free(dest->mont); |
| 115 | dest->mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 116 | return 0; |
| 117 | } |
| 118 | |
| 119 | int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, |
| 120 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { |
| 121 | BN_CTX *new_ctx = NULL; |
| 122 | BN_MONT_CTX *mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 123 | int ret = 0; |
| 124 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 125 | BN_MONT_CTX_free(group->mont); |
| 126 | group->mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 127 | |
| 128 | if (ctx == NULL) { |
| 129 | ctx = new_ctx = BN_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 130 | if (ctx == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 131 | return 0; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 132 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 133 | } |
| 134 | |
| 135 | mont = BN_MONT_CTX_new(); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 136 | if (mont == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 137 | goto err; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 138 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 139 | if (!BN_MONT_CTX_set(mont, p, ctx)) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 140 | OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 141 | goto err; |
| 142 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 143 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 144 | group->mont = mont; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 145 | mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 146 | |
| 147 | ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); |
| 148 | |
| 149 | if (!ret) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 150 | BN_MONT_CTX_free(group->mont); |
| 151 | group->mont = NULL; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 152 | } |
| 153 | |
| 154 | err: |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 155 | BN_CTX_free(new_ctx); |
| 156 | BN_MONT_CTX_free(mont); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 157 | return ret; |
| 158 | } |
| 159 | |
| 160 | int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
| 161 | const BIGNUM *b, BN_CTX *ctx) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 162 | if (group->mont == NULL) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 163 | OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 164 | return 0; |
| 165 | } |
| 166 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 167 | return BN_mod_mul_montgomery(r, a, b, group->mont, ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 168 | } |
| 169 | |
| 170 | int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
| 171 | BN_CTX *ctx) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 172 | if (group->mont == NULL) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 173 | OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 174 | return 0; |
| 175 | } |
| 176 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 177 | return BN_mod_mul_montgomery(r, a, a, group->mont, ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 178 | } |
| 179 | |
| 180 | int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
| 181 | BN_CTX *ctx) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 182 | if (group->mont == NULL) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 183 | OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 184 | return 0; |
| 185 | } |
| 186 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 187 | return BN_to_montgomery(r, a, group->mont, ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 188 | } |
| 189 | |
| 190 | int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
| 191 | BN_CTX *ctx) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 192 | if (group->mont == NULL) { |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 193 | OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 194 | return 0; |
| 195 | } |
| 196 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 197 | return BN_from_montgomery(r, a, group->mont, ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 198 | } |
| 199 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 200 | static int ec_GFp_mont_point_get_affine_coordinates(const EC_GROUP *group, |
| 201 | const EC_POINT *point, |
| 202 | BIGNUM *x, BIGNUM *y, |
| 203 | BN_CTX *ctx) { |
| 204 | if (EC_POINT_is_at_infinity(group, point)) { |
| 205 | OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); |
| 206 | return 0; |
| 207 | } |
| 208 | |
| 209 | BN_CTX *new_ctx = NULL; |
| 210 | if (ctx == NULL) { |
| 211 | ctx = new_ctx = BN_CTX_new(); |
| 212 | if (ctx == NULL) { |
| 213 | return 0; |
| 214 | } |
| 215 | } |
| 216 | |
| 217 | int ret = 0; |
| 218 | |
| 219 | BN_CTX_start(ctx); |
| 220 | |
| 221 | if (BN_cmp(&point->Z, &group->one) == 0) { |
| 222 | /* |point| is already affine. */ |
| 223 | if (x != NULL && !BN_from_montgomery(x, &point->X, group->mont, ctx)) { |
| 224 | goto err; |
| 225 | } |
| 226 | if (y != NULL && !BN_from_montgomery(y, &point->Y, group->mont, ctx)) { |
| 227 | goto err; |
| 228 | } |
| 229 | } else { |
| 230 | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ |
| 231 | |
| 232 | BIGNUM *Z_1 = BN_CTX_get(ctx); |
| 233 | BIGNUM *Z_2 = BN_CTX_get(ctx); |
| 234 | BIGNUM *Z_3 = BN_CTX_get(ctx); |
| 235 | if (Z_1 == NULL || |
| 236 | Z_2 == NULL || |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 237 | Z_3 == NULL) { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 238 | goto err; |
| 239 | } |
| 240 | |
| 241 | /* The straightforward way to calculate the inverse of a Montgomery-encoded |
| 242 | * value where the result is Montgomery-encoded is: |
| 243 | * |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 244 | * |BN_from_montgomery| + invert + |BN_to_montgomery|. |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 245 | * |
| 246 | * This is equivalent, but more efficient, because |BN_from_montgomery| |
| 247 | * is more efficient (at least in theory) than |BN_to_montgomery|, since it |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 248 | * doesn't have to do the multiplication before the reduction. |
| 249 | * |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 250 | * Use Fermat's Little Theorem instead of |BN_mod_inverse_odd| since this |
| 251 | * inversion may be done as the final step of private key operations. |
| 252 | * Unfortunately, this is suboptimal for ECDSA verification. */ |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 253 | if (!BN_from_montgomery(Z_1, &point->Z, group->mont, ctx) || |
| 254 | !BN_from_montgomery(Z_1, Z_1, group->mont, ctx) || |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 255 | !bn_mod_inverse_prime(Z_1, Z_1, &group->field, ctx, group->mont)) { |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 256 | goto err; |
| 257 | } |
| 258 | |
| 259 | if (!BN_mod_mul_montgomery(Z_2, Z_1, Z_1, group->mont, ctx)) { |
| 260 | goto err; |
| 261 | } |
| 262 | |
| 263 | /* Instead of using |BN_from_montgomery| to convert the |x| coordinate |
| 264 | * and then calling |BN_from_montgomery| again to convert the |y| |
| 265 | * coordinate below, convert the common factor |Z_2| once now, saving one |
| 266 | * reduction. */ |
| 267 | if (!BN_from_montgomery(Z_2, Z_2, group->mont, ctx)) { |
| 268 | goto err; |
| 269 | } |
| 270 | |
| 271 | if (x != NULL) { |
| 272 | if (!BN_mod_mul_montgomery(x, &point->X, Z_2, group->mont, ctx)) { |
| 273 | goto err; |
| 274 | } |
| 275 | } |
| 276 | |
| 277 | if (y != NULL) { |
| 278 | if (!BN_mod_mul_montgomery(Z_3, Z_2, Z_1, group->mont, ctx) || |
| 279 | !BN_mod_mul_montgomery(y, &point->Y, Z_3, group->mont, ctx)) { |
| 280 | goto err; |
| 281 | } |
| 282 | } |
| 283 | } |
| 284 | |
| 285 | ret = 1; |
| 286 | |
| 287 | err: |
| 288 | BN_CTX_end(ctx); |
| 289 | BN_CTX_free(new_ctx); |
| 290 | return ret; |
| 291 | } |
| 292 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame^] | 293 | DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_mont_method) { |
| 294 | out->group_init = ec_GFp_mont_group_init; |
| 295 | out->group_finish = ec_GFp_mont_group_finish; |
| 296 | out->group_copy = ec_GFp_mont_group_copy; |
| 297 | out->group_set_curve = ec_GFp_mont_group_set_curve; |
| 298 | out->point_get_affine_coordinates = ec_GFp_mont_point_get_affine_coordinates; |
| 299 | out->mul = ec_wNAF_mul /* XXX: Not constant time. */; |
| 300 | out->field_mul = ec_GFp_mont_field_mul; |
| 301 | out->field_sqr = ec_GFp_mont_field_sqr; |
| 302 | out->field_encode = ec_GFp_mont_field_encode; |
| 303 | out->field_decode = ec_GFp_mont_field_decode; |
| 304 | } |