crypto/ec/ec_lcl.h

   1 /* crypto/ec/ec_lcl.h */
   2 /*
   3  * Originally written by Bodo Moeller for the OpenSSL project.
   4  */
   5 /* ====================================================================
   6  * Copyright (c) 1998-2010 The OpenSSL Project.  All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  *
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  *
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in
  17  *    the documentation and/or other materials provided with the
  18  *    distribution.
  19  *
  20  * 3. All advertising materials mentioning features or use of this
  21  *    software must display the following acknowledgment:
  22  *    "This product includes software developed by the OpenSSL Project
  23  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  24  *
  25  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  26  *    endorse or promote products derived from this software without
  27  *    prior written permission. For written permission, please contact
  28  *    openssl-core@openssl.org.
  29  *
  30  * 5. Products derived from this software may not be called "OpenSSL"
  31  *    nor may "OpenSSL" appear in their names without prior written
  32  *    permission of the OpenSSL Project.
  33  *
  34  * 6. Redistributions of any form whatsoever must retain the following
  35  *    acknowledgment:
  36  *    "This product includes software developed by the OpenSSL Project
  37  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  38  *
  39  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  40  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  41  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  42  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  43  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  44  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  45  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  46  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  48  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  49  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  50  * OF THE POSSIBILITY OF SUCH DAMAGE.
  51  * ====================================================================
  52  *
  53  * This product includes cryptographic software written by Eric Young
  54  * (eay@cryptsoft.com).  This product includes software written by Tim
  55  * Hudson (tjh@cryptsoft.com).
  56  *
  57  */
  58 /* ====================================================================
  59  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  60  *
  61  * Portions of the attached software ("Contribution") are developed by
  62  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
  63  *
  64  * The Contribution is licensed pursuant to the OpenSSL open source
  65  * license provided above.
  66  *
  67  * The elliptic curve binary polynomial software is originally written by
  68  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
  69  *
  70  */
  71
  72
  73 #include <stdlib.h>
  74
  75 #include <openssl/obj_mac.h>
  76 #include <openssl/ec.h>
  77 #include <openssl/bn.h>
  78
  79 #if defined(__SUNPRO_C)
  80 # if __SUNPRO_C >= 0x520
  81 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
  82 # endif
  83 #endif
  84
  85 /* Use default functions for poin2oct, oct2point and compressed coordinates */
  86 #define EC_FLAGS_DEFAULT_OCT    0x1
  87
  88 /* Structure details are not part of the exported interface,
  89  * so all this may change in future versions. */
  90
  91 struct ec_method_st {
  92         /* Various method flags */
  93         int flags;
  94         /* used by EC_METHOD_get_field_type: */
  95         int field_type; /* a NID */
  96
  97         /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
  98         int (*group_init)(EC_GROUP *);
  99         void (*group_finish)(EC_GROUP *);
 100         void (*group_clear_finish)(EC_GROUP *);
 101         int (*group_copy)(EC_GROUP *, const EC_GROUP *);
 102
 103         /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
 104         /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
 105         int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 106         int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 107
 108         /* used by EC_GROUP_get_degree: */
 109         int (*group_get_degree)(const EC_GROUP *);
 110
 111         /* used by EC_GROUP_check: */
 112         int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
 113
 114         /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
 115         int (*point_init)(EC_POINT *);
 116         void (*point_finish)(EC_POINT *);
 117         void (*point_clear_finish)(EC_POINT *);
 118         int (*point_copy)(EC_POINT *, const EC_POINT *);
 119
 120         /*-
 121          * used by EC_POINT_set_to_infinity,
 122          * EC_POINT_set_Jprojective_coordinates_GFp,
 123          * EC_POINT_get_Jprojective_coordinates_GFp,
 124          * EC_POINT_set_affine_coordinates_GFp,     ..._GF2m,
 125          * EC_POINT_get_affine_coordinates_GFp,     ..._GF2m,
 126          * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
 127          */
 128         int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
 129         int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
 130                 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
 131         int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
 132                 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
 133         int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
 134                 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 135         int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
 136                 BIGNUM *x, BIGNUM *y, BN_CTX *);
 137         int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
 138                 const BIGNUM *x, int y_bit, BN_CTX *);
 139
 140         /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
 141         size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 142                 unsigned char *buf, size_t len, BN_CTX *);
 143         int (*oct2point)(const EC_GROUP *, EC_POINT *,
 144                 const unsigned char *buf, size_t len, BN_CTX *);
 145
 146         /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
 147         int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 148         int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 149         int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
 150
 151         /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
 152         int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
 153         int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 154         int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 155
 156         /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
 157         int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
 158         int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 159
 160         /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
 161          * (default implementations are used if the 'mul' pointer is 0): */
 162         int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 163                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 164         int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
 165         int (*have_precompute_mult)(const EC_GROUP *group);
 166
 167
 168         /* internal functions */
 169
 170         /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
 171          * the same implementations of point operations can be used with different
 172          * optimized implementations of expensive field operations: */
 173         int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 174         int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 175         int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 176
 177         /* e.g. to Montgomery */
 178         int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 179         /* e.g. from Montgomery */
 180         int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 181         int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
 182 } /* EC_METHOD */;
 183
 184 typedef struct ec_extra_data_st {
 185         struct ec_extra_data_st *next;
 186         void *data;
 187         void *(*dup_func)(void *);
 188         void (*free_func)(void *);
 189         void (*clear_free_func)(void *);
 190 } EC_EXTRA_DATA; /* used in EC_GROUP */
 191
 192 struct ec_group_st {
 193         const EC_METHOD *meth;
 194
 195         EC_POINT *generator; /* optional */
 196         BIGNUM *order, *cofactor;
 197
 198         int curve_name;/* optional NID for named curve */
 199         int asn1_flag; /* flag to control the asn1 encoding */
 200         point_conversion_form_t asn1_form;
 201
 202         unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
 203         size_t seed_len;
 204
 205         EC_EXTRA_DATA *extra_data; /* linked list */
 206
 207         /* The following members are handled by the method functions,
 208          * even if they appear generic */
 209
 210         /* Field specification.
 211          * For curves over GF(p), this is the modulus;
 212          * for curves over GF(2^m), this is the
 213          * irreducible polynomial defining the field.
 214          */
 215         BIGNUM *field;
 216
 217         /* Field specification for curves over GF(2^m).
 218          * The irreducible f(t) is then of the form:
 219          *     t^poly[0] + t^poly[1] + ... + t^poly[k]
 220          * where m = poly[0] > poly[1] > ... > poly[k] = 0.
 221          * The array is terminated with poly[k+1]=-1.
 222          * All elliptic curve irreducibles have at most 5
 223          * non-zero terms.
 224          */
 225         int poly[6];
 226
 227         /* Curve coefficients.
 228          * (Here the assumption is that BIGNUMs can be used
 229          * or abused for all kinds of fields, not just GF(p).)
 230          * For characteristic  > 3,  the curve is defined
 231          * by a Weierstrass equation of the form
 232          *     y^2 = x^3 + a*x + b.
 233          * For characteristic  2,  the curve is defined by
 234          * an equation of the form
 235          *     y^2 + x*y = x^3 + a*x^2 + b.
 236          */
 237         BIGNUM *a, *b;
 238
 239         /* enable optimized point arithmetics for special case */
 240         int a_is_minus3;
 241
 242         /* method-specific (e.g., Montgomery structure) */
 243         void *field_data1;
 244
 245         /* method-specific */
 246         void *field_data2;
 247
 248         /* method-specific */
 249         int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
 250
 251         /* data for ECDSA inverse */
 252         BN_MONT_CTX *mont_data;
 253 } /* EC_GROUP */;
 254
 255 struct ec_key_st {
 256         int version;
 257
 258         EC_GROUP *group;
 259
 260         EC_POINT *pub_key;
 261         BIGNUM   *priv_key;
 262
 263         unsigned int enc_flag;
 264         point_conversion_form_t conv_form;
 265
 266         int     references;
 267         int     flags;
 268
 269         EC_EXTRA_DATA *method_data;
 270 } /* EC_KEY */;
 271
 272 /* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
 273  * (with visibility limited to 'package' level for now).
 274  * We use the function pointers as index for retrieval; this obviates
 275  * global ex_data-style index tables.
 276  */
 277 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
 278         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 279 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
 280         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 281 void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
 282         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 283 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
 284         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 285 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
 286 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
 287
 288
 289
 290 struct ec_point_st {
 291         const EC_METHOD *meth;
 292
 293         /* All members except 'meth' are handled by the method functions,
 294          * even if they appear generic */
 295
 296         BIGNUM *X;
 297         BIGNUM *Y;
 298         BIGNUM *Z; /* Jacobian projective coordinates:
 299                    * (X, Y, Z)  represents  (X/Z^2, Y/Z^3)  if  Z != 0 */
 300         int Z_is_one; /* enable optimized point arithmetics for special case */
 301 } /* EC_POINT */;
 302
 303
 304
 305 /* method functions in ec_mult.c
 306  * (ec_lib.c uses these as defaults if group->method->mul is 0) */
 307 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 308         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 309 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
 310 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
 311
 312
 313 /* method functions in ecp_smpl.c */
 314 int ec_GFp_simple_group_init(EC_GROUP *);
 315 void ec_GFp_simple_group_finish(EC_GROUP *);
 316 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
 317 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
 318 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 319 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 320 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
 321 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
 322 int ec_GFp_simple_point_init(EC_POINT *);
 323 void ec_GFp_simple_point_finish(EC_POINT *);
 324 void ec_GFp_simple_point_clear_finish(EC_POINT *);
 325 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
 326 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
 327 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
 328         const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
 329 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
 330         BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
 331 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
 332         const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 333 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
 334         BIGNUM *x, BIGNUM *y, BN_CTX *);
 335 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
 336         const BIGNUM *x, int y_bit, BN_CTX *);
 337 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 338         unsigned char *buf, size_t len, BN_CTX *);
 339 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
 340         const unsigned char *buf, size_t len, BN_CTX *);
 341 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 342 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 343 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
 344 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 345 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 346 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 347 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 348 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 349 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 350 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 351
 352
 353 /* method functions in ecp_mont.c */
 354 int ec_GFp_mont_group_init(EC_GROUP *);
 355 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 356 void ec_GFp_mont_group_finish(EC_GROUP *);
 357 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
 358 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
 359 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 360 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 361 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 362 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 363 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
 364
 365
 366 /* method functions in ecp_nist.c */
 367 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
 368 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 369 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 370 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 371
 372
 373 /* method functions in ec2_smpl.c */
 374 int ec_GF2m_simple_group_init(EC_GROUP *);
 375 void ec_GF2m_simple_group_finish(EC_GROUP *);
 376 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
 377 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
 378 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 379 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 380 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
 381 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
 382 int ec_GF2m_simple_point_init(EC_POINT *);
 383 void ec_GF2m_simple_point_finish(EC_POINT *);
 384 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
 385 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
 386 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
 387 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
 388         const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 389 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
 390         BIGNUM *x, BIGNUM *y, BN_CTX *);
 391 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
 392         const BIGNUM *x, int y_bit, BN_CTX *);
 393 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 394         unsigned char *buf, size_t len, BN_CTX *);
 395 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
 396         const unsigned char *buf, size_t len, BN_CTX *);
 397 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 398 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 399 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
 400 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 401 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 402 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 403 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 404 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 405 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 406 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 407 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 408
 409
 410 /* method functions in ec2_mult.c */
 411 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 412         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 413 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 414 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
 415
 416 /* method functions in ec2_mult.c */
 417 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 418         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 419 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 420 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
 421
 422 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
 423 /* method functions in ecp_nistp224.c */
 424 int ec_GFp_nistp224_group_init(EC_GROUP *group);
 425 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
 426 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
 427 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 428 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
 429 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 430 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
 431
 432 /* method functions in ecp_nistp256.c */
 433 int ec_GFp_nistp256_group_init(EC_GROUP *group);
 434 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
 435 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
 436 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 437 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
 438 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 439 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
 440
 441 /* method functions in ecp_nistp521.c */
 442 int ec_GFp_nistp521_group_init(EC_GROUP *group);
 443 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
 444 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
 445 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 446 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx);
 447 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 448 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
 449
 450 /* utility functions in ecp_nistputil.c */
 451 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
 452         size_t felem_size, void *tmp_felems,
 453         void (*felem_one)(void *out),
 454         int (*felem_is_zero)(const void *in),
 455         void (*felem_assign)(void *out, const void *in),
 456         void (*felem_square)(void *out, const void *in),
 457         void (*felem_mul)(void *out, const void *in1, const void *in2),
 458         void (*felem_inv)(void *out, const void *in),
 459         void (*felem_contract)(void *out, const void *in));
 460 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in);
 461 #endif
 462 int ec_precompute_mont_data(EC_GROUP *);
 463
 464 #ifdef ECP_NISTZ256_ASM
 465 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
 466  * P256. See http://eprint.iacr.org/2013/816.
 467  *  \return  EC_METHOD object
 468  */
 469 const EC_METHOD *EC_GFp_nistz256_method(void);
 470 #endif