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 (at) 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 (at) cryptsoft.com). This product includes software written by Tim 52 * Hudson (tjh (at) 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 74 #include "../bn/internal.h" 75 #include "../delocate.h" 76 #include "internal.h" 77 78 79 int ec_GFp_mont_group_init(EC_GROUP *group) { 80 int ok; 81 82 ok = ec_GFp_simple_group_init(group); 83 group->mont = NULL; 84 return ok; 85 } 86 87 void ec_GFp_mont_group_finish(EC_GROUP *group) { 88 BN_MONT_CTX_free(group->mont); 89 group->mont = NULL; 90 ec_GFp_simple_group_finish(group); 91 } 92 93 int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, 94 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { 95 BN_CTX *new_ctx = NULL; 96 int ret = 0; 97 98 BN_MONT_CTX_free(group->mont); 99 group->mont = NULL; 100 101 if (ctx == NULL) { 102 ctx = new_ctx = BN_CTX_new(); 103 if (ctx == NULL) { 104 return 0; 105 } 106 } 107 108 group->mont = BN_MONT_CTX_new_for_modulus(p, ctx); 109 if (group->mont == NULL) { 110 OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); 111 goto err; 112 } 113 114 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); 115 116 if (!ret) { 117 BN_MONT_CTX_free(group->mont); 118 group->mont = NULL; 119 } 120 121 err: 122 BN_CTX_free(new_ctx); 123 return ret; 124 } 125 126 int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 127 const BIGNUM *b, BN_CTX *ctx) { 128 if (group->mont == NULL) { 129 OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED); 130 return 0; 131 } 132 133 return BN_mod_mul_montgomery(r, a, b, group->mont, ctx); 134 } 135 136 int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 137 BN_CTX *ctx) { 138 if (group->mont == NULL) { 139 OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED); 140 return 0; 141 } 142 143 return BN_mod_mul_montgomery(r, a, a, group->mont, ctx); 144 } 145 146 int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 147 BN_CTX *ctx) { 148 if (group->mont == NULL) { 149 OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED); 150 return 0; 151 } 152 153 return BN_to_montgomery(r, a, group->mont, ctx); 154 } 155 156 int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 157 BN_CTX *ctx) { 158 if (group->mont == NULL) { 159 OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED); 160 return 0; 161 } 162 163 return BN_from_montgomery(r, a, group->mont, ctx); 164 } 165 166 static int ec_GFp_mont_point_get_affine_coordinates(const EC_GROUP *group, 167 const EC_POINT *point, 168 BIGNUM *x, BIGNUM *y, 169 BN_CTX *ctx) { 170 if (EC_POINT_is_at_infinity(group, point)) { 171 OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); 172 return 0; 173 } 174 175 BN_CTX *new_ctx = NULL; 176 if (ctx == NULL) { 177 ctx = new_ctx = BN_CTX_new(); 178 if (ctx == NULL) { 179 return 0; 180 } 181 } 182 183 int ret = 0; 184 185 BN_CTX_start(ctx); 186 187 if (BN_cmp(&point->Z, &group->one) == 0) { 188 // |point| is already affine. 189 if (x != NULL && !BN_from_montgomery(x, &point->X, group->mont, ctx)) { 190 goto err; 191 } 192 if (y != NULL && !BN_from_montgomery(y, &point->Y, group->mont, ctx)) { 193 goto err; 194 } 195 } else { 196 // transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) 197 198 BIGNUM *Z_1 = BN_CTX_get(ctx); 199 BIGNUM *Z_2 = BN_CTX_get(ctx); 200 BIGNUM *Z_3 = BN_CTX_get(ctx); 201 if (Z_1 == NULL || 202 Z_2 == NULL || 203 Z_3 == NULL) { 204 goto err; 205 } 206 207 // The straightforward way to calculate the inverse of a Montgomery-encoded 208 // value where the result is Montgomery-encoded is: 209 // 210 // |BN_from_montgomery| + invert + |BN_to_montgomery|. 211 // 212 // This is equivalent, but more efficient, because |BN_from_montgomery| 213 // is more efficient (at least in theory) than |BN_to_montgomery|, since it 214 // doesn't have to do the multiplication before the reduction. 215 // 216 // Use Fermat's Little Theorem instead of |BN_mod_inverse_odd| since this 217 // inversion may be done as the final step of private key operations. 218 // Unfortunately, this is suboptimal for ECDSA verification. 219 if (!BN_from_montgomery(Z_1, &point->Z, group->mont, ctx) || 220 !BN_from_montgomery(Z_1, Z_1, group->mont, ctx) || 221 !bn_mod_inverse_prime(Z_1, Z_1, &group->field, ctx, group->mont)) { 222 goto err; 223 } 224 225 if (!BN_mod_mul_montgomery(Z_2, Z_1, Z_1, group->mont, ctx)) { 226 goto err; 227 } 228 229 // Instead of using |BN_from_montgomery| to convert the |x| coordinate 230 // and then calling |BN_from_montgomery| again to convert the |y| 231 // coordinate below, convert the common factor |Z_2| once now, saving one 232 // reduction. 233 if (!BN_from_montgomery(Z_2, Z_2, group->mont, ctx)) { 234 goto err; 235 } 236 237 if (x != NULL) { 238 if (!BN_mod_mul_montgomery(x, &point->X, Z_2, group->mont, ctx)) { 239 goto err; 240 } 241 } 242 243 if (y != NULL) { 244 if (!BN_mod_mul_montgomery(Z_3, Z_2, Z_1, group->mont, ctx) || 245 !BN_mod_mul_montgomery(y, &point->Y, Z_3, group->mont, ctx)) { 246 goto err; 247 } 248 } 249 } 250 251 ret = 1; 252 253 err: 254 BN_CTX_end(ctx); 255 BN_CTX_free(new_ctx); 256 return ret; 257 } 258 259 DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_mont_method) { 260 out->group_init = ec_GFp_mont_group_init; 261 out->group_finish = ec_GFp_mont_group_finish; 262 out->group_set_curve = ec_GFp_mont_group_set_curve; 263 out->point_get_affine_coordinates = ec_GFp_mont_point_get_affine_coordinates; 264 out->mul = ec_wNAF_mul /* XXX: Not constant time. */; 265 out->mul_public = ec_wNAF_mul; 266 out->field_mul = ec_GFp_mont_field_mul; 267 out->field_sqr = ec_GFp_mont_field_sqr; 268 out->field_encode = ec_GFp_mont_field_encode; 269 out->field_decode = ec_GFp_mont_field_decode; 270 } 271
