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 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */ 84 int (*group_init)(EC_GROUP *); 85 void (*group_finish)(EC_GROUP *); 86 void (*group_clear_finish)(EC_GROUP *); 87 int (*group_copy)(EC_GROUP *, const EC_GROUP *); 88 89 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */ 90 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */ 91 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 92 const BIGNUM *b, BN_CTX *); 93 94 /* used by EC_POINT_get_affine_coordinates_GFp: */ 95 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *, 96 BIGNUM *x, BIGNUM *y, BN_CTX *); 97 98 /* Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar| 99 * are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null. 100 * Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar| 101 * and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is 102 * non-null. */ 103 int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, 104 const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx); 105 106 /* |check_pub_key_order| checks that the public key is in the proper subgroup 107 * by checking that |pub_key*group->order| is the point at infinity. This may 108 * be NULL for |EC_METHOD|s specialized for prime-order curves (i.e. with 109 * cofactor one), as this check is not necessary for such curves (See section 110 * A.3 of the NSA's "Suite B Implementer's Guide to FIPS 186-3 111 * (ECDSA)"). */ 112 int (*check_pub_key_order)(const EC_GROUP *group, const EC_POINT *pub_key, 113 BN_CTX *ctx); 114 115 /* internal functions */ 116 117 /* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that the 118 * same implementations of point operations can be used with different 119 * optimized implementations of expensive field operations: */ 120 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 121 const BIGNUM *b, BN_CTX *); 122 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 123 124 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 125 BN_CTX *); /* e.g. to Montgomery */ 126 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 127 BN_CTX *); /* e.g. from Montgomery */ 128 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *); 129 } /* EC_METHOD */; 130 131 const EC_METHOD* EC_GFp_mont_method(void); 132 133 struct ec_group_st { 134 const EC_METHOD *meth; 135 136 EC_POINT *generator; /* optional */ 137 BIGNUM order, cofactor; 138 139 int curve_name; /* optional NID for named curve */ 140 141 const BN_MONT_CTX *mont_data; /* data for ECDSA inverse */ 142 143 /* The following members are handled by the method functions, 144 * even if they appear generic */ 145 146 BIGNUM field; /* For curves over GF(p), this is the modulus. */ 147 148 BIGNUM a, b; /* Curve coefficients. */ 149 150 int a_is_minus3; /* enable optimized point arithmetics for special case */ 151 152 BN_MONT_CTX *mont; /* Montgomery structure. */ 153 BIGNUM *one; /* The value one */ 154 } /* EC_GROUP */; 155 156 struct ec_point_st { 157 const EC_METHOD *meth; 158 159 /* All members except 'meth' are handled by the method functions, 160 * even if they appear generic */ 161 162 BIGNUM X; 163 BIGNUM Y; 164 BIGNUM Z; /* Jacobian projective coordinates: 165 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ 166 int Z_is_one; /* enable optimized point arithmetics for special case */ 167 } /* EC_POINT */; 168 169 EC_GROUP *ec_group_new(const EC_METHOD *meth); 170 int ec_group_copy(EC_GROUP *dest, const EC_GROUP *src); 171 172 /* ec_group_get_mont_data returns a Montgomery context for operations in the 173 * scalar field of |group|. It may return NULL in the case that |group| is not 174 * a built-in group. */ 175 const BN_MONT_CTX *ec_group_get_mont_data(const EC_GROUP *group); 176 177 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, 178 const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx); 179 180 /* method functions in simple.c */ 181 int ec_GFp_simple_group_init(EC_GROUP *); 182 void ec_GFp_simple_group_finish(EC_GROUP *); 183 void ec_GFp_simple_group_clear_finish(EC_GROUP *); 184 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); 185 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 186 const BIGNUM *b, BN_CTX *); 187 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 188 BIGNUM *b, BN_CTX *); 189 unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *); 190 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 191 int ec_GFp_simple_point_init(EC_POINT *); 192 void ec_GFp_simple_point_finish(EC_POINT *); 193 void ec_GFp_simple_point_clear_finish(EC_POINT *); 194 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 195 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 196 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *, 197 const BIGNUM *x, 198 const BIGNUM *y, 199 const BIGNUM *z, BN_CTX *); 200 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, 201 const EC_POINT *, BIGNUM *x, 202 BIGNUM *y, BIGNUM *z, 203 BN_CTX *); 204 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 205 const BIGNUM *x, const BIGNUM *y, 206 BN_CTX *); 207 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, 208 const EC_POINT *, BIGNUM *x, 209 BIGNUM *y, BN_CTX *); 210 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 211 const BIGNUM *x, int y_bit, 212 BN_CTX *); 213 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 214 const EC_POINT *b, BN_CTX *); 215 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 216 BN_CTX *); 217 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 218 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 219 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 220 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 221 BN_CTX *); 222 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 223 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, 224 EC_POINT * [], BN_CTX *); 225 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 226 const BIGNUM *b, BN_CTX *); 227 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 228 BN_CTX *); 229 230 /* method functions in montgomery.c */ 231 int ec_GFp_mont_group_init(EC_GROUP *); 232 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 233 const BIGNUM *b, BN_CTX *); 234 void ec_GFp_mont_group_finish(EC_GROUP *); 235 void ec_GFp_mont_group_clear_finish(EC_GROUP *); 236 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); 237 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 238 const BIGNUM *b, BN_CTX *); 239 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 240 BN_CTX *); 241 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 242 BN_CTX *); 243 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 244 BN_CTX *); 245 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); 246 247 int ec_point_set_Jprojective_coordinates_GFp(const EC_GROUP *group, 248 EC_POINT *point, const BIGNUM *x, 249 const BIGNUM *y, const BIGNUM *z, 250 BN_CTX *ctx); 251 252 void ec_GFp_nistp_points_make_affine_internal( 253 size_t num, void *point_array, size_t felem_size, void *tmp_felems, 254 void (*felem_one)(void *out), int (*felem_is_zero)(const void *in), 255 void (*felem_assign)(void *out, const void *in), 256 void (*felem_square)(void *out, const void *in), 257 void (*felem_mul)(void *out, const void *in1, const void *in2), 258 void (*felem_inv)(void *out, const void *in), 259 void (*felem_contract)(void *out, const void *in)); 260 261 void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in); 262 263 const EC_METHOD *EC_GFp_nistp224_method(void); 264 const EC_METHOD *EC_GFp_nistp256_method(void); 265 266 /* Returns GFp methods using montgomery multiplication, with x86-64 267 * optimized P256. See http://eprint.iacr.org/2013/816. */ 268 const EC_METHOD *EC_GFp_nistz256_method(void); 269 270 struct ec_key_st { 271 int version; 272 273 EC_GROUP *group; 274 275 EC_POINT *pub_key; 276 BIGNUM *priv_key; 277 278 unsigned int enc_flag; 279 point_conversion_form_t conv_form; 280 281 CRYPTO_refcount_t references; 282 int flags; 283 284 ECDSA_METHOD *ecdsa_meth; 285 286 CRYPTO_EX_DATA ex_data; 287 } /* EC_KEY */; 288 289 /* curve_data contains data about a built-in elliptic curve. */ 290 struct curve_data { 291 /* comment is a human-readable string describing the curve. */ 292 const char *comment; 293 /* param_len is the number of bytes needed to store a field element. */ 294 uint8_t param_len; 295 /* cofactor is the cofactor of the group (i.e. the number of elements in the 296 * group divided by the size of the main subgroup. */ 297 uint8_t cofactor; /* promoted to BN_ULONG */ 298 /* data points to an array of 6*|param_len| bytes which hold the field 299 * elements of the following (in big-endian order): prime, a, b, generator x, 300 * generator y, order. */ 301 const uint8_t data[]; 302 }; 303 304 struct built_in_curve { 305 int nid; 306 const struct curve_data *data; 307 const EC_METHOD *(*method)(void); 308 }; 309 310 /* OPENSSL_built_in_curves is terminated with an entry where |nid| is 311 * |NID_undef|. */ 312 extern const struct built_in_curve OPENSSL_built_in_curves[]; 313 314 #if defined(__cplusplus) 315 } /* extern C */ 316 #endif 317 318 #endif /* OPENSSL_HEADER_EC_INTERNAL_H */ 319
