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 #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 #include <openssl/type_check.h> 77 78 #include "../bn/internal.h" 79 80 #if defined(__cplusplus) 81 extern "C" { 82 #endif 83 84 85 // Cap the size of all field elements and scalars, including custom curves, to 86 // 66 bytes, large enough to fit secp521r1 and brainpoolP512r1, which appear to 87 // be the largest fields anyone plausibly uses. 88 #define EC_MAX_SCALAR_BYTES 66 89 #define EC_MAX_SCALAR_WORDS ((66 + BN_BYTES - 1) / BN_BYTES) 90 91 OPENSSL_COMPILE_ASSERT(EC_MAX_SCALAR_WORDS <= BN_SMALL_MAX_WORDS, 92 bn_small_functions_applicable); 93 94 // An EC_SCALAR is an integer fully reduced modulo the order. Only the first 95 // |order->top| words are used. An |EC_SCALAR| is specific to an |EC_GROUP| and 96 // must not be mixed between groups. 97 typedef union { 98 // bytes is the representation of the scalar in little-endian order. 99 uint8_t bytes[EC_MAX_SCALAR_BYTES]; 100 BN_ULONG words[EC_MAX_SCALAR_WORDS]; 101 } EC_SCALAR; 102 103 struct ec_method_st { 104 int (*group_init)(EC_GROUP *); 105 void (*group_finish)(EC_GROUP *); 106 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 107 const BIGNUM *b, BN_CTX *); 108 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *, 109 BIGNUM *x, BIGNUM *y, BN_CTX *); 110 111 // Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar| 112 // are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null. 113 // Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar| 114 // and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is 115 // non-null. 116 int (*mul)(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar, 117 const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx); 118 // mul_public performs the same computation as mul. It further assumes that 119 // the inputs are public so there is no concern about leaking their values 120 // through timing. 121 int (*mul_public)(const EC_GROUP *group, EC_POINT *r, 122 const EC_SCALAR *g_scalar, const EC_POINT *p, 123 const EC_SCALAR *p_scalar, BN_CTX *ctx); 124 125 // 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that the 126 // same implementations of point operations can be used with different 127 // optimized implementations of expensive field operations: 128 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 129 const BIGNUM *b, BN_CTX *); 130 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 131 132 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 133 BN_CTX *); // e.g. to Montgomery 134 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 135 BN_CTX *); // e.g. from Montgomery 136 } /* EC_METHOD */; 137 138 const EC_METHOD *EC_GFp_mont_method(void); 139 140 struct ec_group_st { 141 const EC_METHOD *meth; 142 143 // Unlike all other |EC_POINT|s, |generator| does not own |generator->group| 144 // to avoid a reference cycle. 145 EC_POINT *generator; 146 BIGNUM order; 147 148 int curve_name; // optional NID for named curve 149 150 BN_MONT_CTX *order_mont; // data for ECDSA inverse 151 152 // The following members are handled by the method functions, 153 // even if they appear generic 154 155 BIGNUM field; // For curves over GF(p), this is the modulus. 156 157 BIGNUM a, b; // Curve coefficients. 158 159 int a_is_minus3; // enable optimized point arithmetics for special case 160 161 CRYPTO_refcount_t references; 162 163 BN_MONT_CTX *mont; // Montgomery structure. 164 165 BIGNUM one; // The value one. 166 } /* EC_GROUP */; 167 168 struct ec_point_st { 169 // group is an owning reference to |group|, unless this is 170 // |group->generator|. 171 EC_GROUP *group; 172 173 BIGNUM X; 174 BIGNUM Y; 175 BIGNUM Z; // Jacobian projective coordinates: 176 // (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 177 } /* EC_POINT */; 178 179 EC_GROUP *ec_group_new(const EC_METHOD *meth); 180 181 // ec_bignum_to_scalar converts |in| to an |EC_SCALAR| and writes it to 182 // |*out|. It returns one on success and zero if |in| is out of range. 183 int ec_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out, 184 const BIGNUM *in); 185 186 // ec_bignum_to_scalar_unchecked behaves like |ec_bignum_to_scalar| but does not 187 // check |in| is fully reduced. 188 int ec_bignum_to_scalar_unchecked(const EC_GROUP *group, EC_SCALAR *out, 189 const BIGNUM *in); 190 191 // ec_random_nonzero_scalar sets |out| to a uniformly selected random value from 192 // 1 to |group->order| - 1. It returns one on success and zero on error. 193 int ec_random_nonzero_scalar(const EC_GROUP *group, EC_SCALAR *out, 194 const uint8_t additional_data[32]); 195 196 // ec_point_mul_scalar sets |r| to generator * |g_scalar| + |p| * 197 // |p_scalar|. Unlike other functions which take |EC_SCALAR|, |g_scalar| and 198 // |p_scalar| need not be fully reduced. They need only contain as many bits as 199 // the order. 200 int ec_point_mul_scalar(const EC_GROUP *group, EC_POINT *r, 201 const EC_SCALAR *g_scalar, const EC_POINT *p, 202 const EC_SCALAR *p_scalar, BN_CTX *ctx); 203 204 // ec_point_mul_scalar_public performs the same computation as 205 // ec_point_mul_scalar. It further assumes that the inputs are public so 206 // there is no concern about leaking their values through timing. 207 int ec_point_mul_scalar_public(const EC_GROUP *group, EC_POINT *r, 208 const EC_SCALAR *g_scalar, const EC_POINT *p, 209 const EC_SCALAR *p_scalar, BN_CTX *ctx); 210 211 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar, 212 const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx); 213 214 // method functions in simple.c 215 int ec_GFp_simple_group_init(EC_GROUP *); 216 void ec_GFp_simple_group_finish(EC_GROUP *); 217 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 218 const BIGNUM *b, BN_CTX *); 219 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 220 BIGNUM *b, BN_CTX *); 221 unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *); 222 int ec_GFp_simple_point_init(EC_POINT *); 223 void ec_GFp_simple_point_finish(EC_POINT *); 224 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 225 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 226 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 227 const BIGNUM *x, const BIGNUM *y, 228 BN_CTX *); 229 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 230 const EC_POINT *b, BN_CTX *); 231 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 232 BN_CTX *); 233 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 234 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 235 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 236 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 237 BN_CTX *); 238 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 239 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, 240 EC_POINT * [], BN_CTX *); 241 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 242 const BIGNUM *b, BN_CTX *); 243 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 244 BN_CTX *); 245 246 // method functions in montgomery.c 247 int ec_GFp_mont_group_init(EC_GROUP *); 248 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 249 const BIGNUM *b, BN_CTX *); 250 void ec_GFp_mont_group_finish(EC_GROUP *); 251 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 252 const BIGNUM *b, BN_CTX *); 253 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 254 BN_CTX *); 255 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 256 BN_CTX *); 257 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 258 BN_CTX *); 259 260 void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in); 261 262 const EC_METHOD *EC_GFp_nistp224_method(void); 263 const EC_METHOD *EC_GFp_nistp256_method(void); 264 265 // EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with 266 // x86-64 optimized P256. See http://eprint.iacr.org/2013/816. 267 const EC_METHOD *EC_GFp_nistz256_method(void); 268 269 struct ec_key_st { 270 EC_GROUP *group; 271 272 EC_POINT *pub_key; 273 BIGNUM *priv_key; 274 275 // fixed_k may contain a specific value of 'k', to be used in ECDSA signing. 276 // This is only for the FIPS power-on tests. 277 BIGNUM *fixed_k; 278 279 unsigned int enc_flag; 280 point_conversion_form_t conv_form; 281 282 CRYPTO_refcount_t references; 283 284 ECDSA_METHOD *ecdsa_meth; 285 286 CRYPTO_EX_DATA ex_data; 287 } /* EC_KEY */; 288 289 struct built_in_curve { 290 int nid; 291 const uint8_t *oid; 292 uint8_t oid_len; 293 // comment is a human-readable string describing the curve. 294 const char *comment; 295 // param_len is the number of bytes needed to store a field element. 296 uint8_t param_len; 297 // params points to an array of 6*|param_len| bytes which hold the field 298 // elements of the following (in big-endian order): prime, a, b, generator x, 299 // generator y, order. 300 const uint8_t *params; 301 const EC_METHOD *method; 302 }; 303 304 #define OPENSSL_NUM_BUILT_IN_CURVES 4 305 306 struct built_in_curves { 307 struct built_in_curve curves[OPENSSL_NUM_BUILT_IN_CURVES]; 308 }; 309 310 // OPENSSL_built_in_curves returns a pointer to static information about 311 // standard curves. The array is terminated with an entry where |nid| is 312 // |NID_undef|. 313 const struct built_in_curves *OPENSSL_built_in_curves(void); 314 315 #if defined(__cplusplus) 316 } // extern C 317 #endif 318 319 #endif // OPENSSL_HEADER_EC_INTERNAL_H 320