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 (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 #ifndef OPENSSL_HEADER_EC_INTERNAL_H 69 #define OPENSSL_HEADER_EC_INTERNAL_H 70 71 #include <openssl/base.h> 72 73 #include <openssl/bn.h> 74 #include <openssl/ex_data.h> 75 #include <openssl/thread.h> 76 77 #if defined(__cplusplus) 78 extern "C" { 79 #endif 80 81 82 struct ec_method_st { 83 int (*group_init)(EC_GROUP *); 84 void (*group_finish)(EC_GROUP *); 85 int (*group_copy)(EC_GROUP *, const EC_GROUP *); 86 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 87 const BIGNUM *b, BN_CTX *); 88 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *, 89 BIGNUM *x, BIGNUM *y, BN_CTX *); 90 91 /* Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar| 92 * are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null. 93 * Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar| 94 * and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is 95 * non-null. */ 96 int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, 97 const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx); 98 99 /* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that the 100 * same implementations of point operations can be used with different 101 * optimized implementations of expensive field operations: */ 102 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 103 const BIGNUM *b, BN_CTX *); 104 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 105 106 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 107 BN_CTX *); /* e.g. to Montgomery */ 108 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 109 BN_CTX *); /* e.g. from Montgomery */ 110 } /* EC_METHOD */; 111 112 extern const EC_METHOD EC_GFp_mont_method; 113 114 struct ec_group_st { 115 const EC_METHOD *meth; 116 117 EC_POINT *generator; 118 BIGNUM order; 119 120 int curve_name; /* optional NID for named curve */ 121 122 const BN_MONT_CTX *mont_data; /* data for ECDSA inverse */ 123 124 /* The following members are handled by the method functions, 125 * even if they appear generic */ 126 127 BIGNUM field; /* For curves over GF(p), this is the modulus. */ 128 129 BIGNUM a, b; /* Curve coefficients. */ 130 131 int a_is_minus3; /* enable optimized point arithmetics for special case */ 132 133 BN_MONT_CTX *mont; /* Montgomery structure. */ 134 135 BIGNUM one; /* The value one. */ 136 } /* EC_GROUP */; 137 138 struct ec_point_st { 139 const EC_METHOD *meth; 140 141 BIGNUM X; 142 BIGNUM Y; 143 BIGNUM Z; /* Jacobian projective coordinates: 144 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ 145 } /* EC_POINT */; 146 147 EC_GROUP *ec_group_new(const EC_METHOD *meth); 148 int ec_group_copy(EC_GROUP *dest, const EC_GROUP *src); 149 150 /* ec_group_get_mont_data returns a Montgomery context for operations in the 151 * scalar field of |group|. It may return NULL in the case that |group| is not 152 * a built-in group. */ 153 const BN_MONT_CTX *ec_group_get_mont_data(const EC_GROUP *group); 154 155 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, 156 const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx); 157 158 /* method functions in simple.c */ 159 int ec_GFp_simple_group_init(EC_GROUP *); 160 void ec_GFp_simple_group_finish(EC_GROUP *); 161 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); 162 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 163 const BIGNUM *b, BN_CTX *); 164 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 165 BIGNUM *b, BN_CTX *); 166 unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *); 167 int ec_GFp_simple_point_init(EC_POINT *); 168 void ec_GFp_simple_point_finish(EC_POINT *); 169 void ec_GFp_simple_point_clear_finish(EC_POINT *); 170 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 171 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 172 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *, 173 const BIGNUM *x, 174 const BIGNUM *y, 175 const BIGNUM *z, BN_CTX *); 176 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, 177 const EC_POINT *, BIGNUM *x, 178 BIGNUM *y, BIGNUM *z, 179 BN_CTX *); 180 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 181 const BIGNUM *x, const BIGNUM *y, 182 BN_CTX *); 183 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 184 const BIGNUM *x, int y_bit, 185 BN_CTX *); 186 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 187 const EC_POINT *b, BN_CTX *); 188 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 189 BN_CTX *); 190 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 191 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 192 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 193 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 194 BN_CTX *); 195 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 196 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, 197 EC_POINT * [], BN_CTX *); 198 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 199 const BIGNUM *b, BN_CTX *); 200 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 201 BN_CTX *); 202 203 /* method functions in montgomery.c */ 204 int ec_GFp_mont_group_init(EC_GROUP *); 205 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 206 const BIGNUM *b, BN_CTX *); 207 void ec_GFp_mont_group_finish(EC_GROUP *); 208 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); 209 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 210 const BIGNUM *b, BN_CTX *); 211 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 212 BN_CTX *); 213 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 214 BN_CTX *); 215 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 216 BN_CTX *); 217 218 int ec_point_set_Jprojective_coordinates_GFp(const EC_GROUP *group, 219 EC_POINT *point, const BIGNUM *x, 220 const BIGNUM *y, const BIGNUM *z, 221 BN_CTX *ctx); 222 223 void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in); 224 225 extern const EC_METHOD EC_GFp_nistp224_method; 226 extern const EC_METHOD EC_GFp_nistp256_method; 227 228 /* EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with 229 * x86-64 optimized P256. See http://eprint.iacr.org/2013/816. */ 230 extern const EC_METHOD EC_GFp_nistz256_method; 231 232 struct ec_key_st { 233 EC_GROUP *group; 234 235 EC_POINT *pub_key; 236 BIGNUM *priv_key; 237 238 unsigned int enc_flag; 239 point_conversion_form_t conv_form; 240 241 CRYPTO_refcount_t references; 242 243 ECDSA_METHOD *ecdsa_meth; 244 245 CRYPTO_EX_DATA ex_data; 246 } /* EC_KEY */; 247 248 /* curve_data contains data about a built-in elliptic curve. */ 249 struct curve_data { 250 /* comment is a human-readable string describing the curve. */ 251 const char *comment; 252 /* param_len is the number of bytes needed to store a field element. */ 253 uint8_t param_len; 254 /* data points to an array of 6*|param_len| bytes which hold the field 255 * elements of the following (in big-endian order): prime, a, b, generator x, 256 * generator y, order. */ 257 const uint8_t data[]; 258 }; 259 260 struct built_in_curve { 261 int nid; 262 uint8_t oid[8]; 263 uint8_t oid_len; 264 const struct curve_data *data; 265 const EC_METHOD *method; 266 }; 267 268 /* OPENSSL_built_in_curves is terminated with an entry where |nid| is 269 * |NID_undef|. */ 270 extern const struct built_in_curve OPENSSL_built_in_curves[]; 271 272 #if defined(__cplusplus) 273 } /* extern C */ 274 #endif 275 276 #endif /* OPENSSL_HEADER_EC_INTERNAL_H */ 277
