crypto/openssl/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) 1998-2003 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 /* Structure details are not part of the exported interface,
  86  * so all this may change in future versions. */
  87
  88 struct ec_method_st {
  89         /* used by EC_METHOD_get_field_type: */
  90         int field_type; /* a NID */
  91
  92         /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
  93         int (*group_init)(EC_GROUP *);
  94         void (*group_finish)(EC_GROUP *);
  95         void (*group_clear_finish)(EC_GROUP *);
  96         int (*group_copy)(EC_GROUP *, const EC_GROUP *);
  97
  98         /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
  99         /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
 100         int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 101         int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 102
 103         /* used by EC_GROUP_get_degree: */
 104         int (*group_get_degree)(const EC_GROUP *);
 105
 106         /* used by EC_GROUP_check: */
 107         int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
 108
 109         /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
 110         int (*point_init)(EC_POINT *);
 111         void (*point_finish)(EC_POINT *);
 112         void (*point_clear_finish)(EC_POINT *);
 113         int (*point_copy)(EC_POINT *, const EC_POINT *);
 114
 115         /* used by EC_POINT_set_to_infinity,
 116          * EC_POINT_set_Jprojective_coordinates_GFp,
 117          * EC_POINT_get_Jprojective_coordinates_GFp,
 118          * EC_POINT_set_affine_coordinates_GFp,     ..._GF2m,
 119          * EC_POINT_get_affine_coordinates_GFp,     ..._GF2m,
 120          * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
 121          */
 122         int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
 123         int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
 124                 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
 125         int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
 126                 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
 127         int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
 128                 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 129         int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
 130                 BIGNUM *x, BIGNUM *y, BN_CTX *);
 131         int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
 132                 const BIGNUM *x, int y_bit, BN_CTX *);
 133
 134         /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
 135         size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 136                 unsigned char *buf, size_t len, BN_CTX *);
 137         int (*oct2point)(const EC_GROUP *, EC_POINT *,
 138                 const unsigned char *buf, size_t len, BN_CTX *);
 139
 140         /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
 141         int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 142         int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 143         int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
 144
 145         /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
 146         int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
 147         int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 148         int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 149
 150         /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
 151         int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
 152         int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 153
 154         /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
 155          * (default implementations are used if the 'mul' pointer is 0): */
 156         int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 157                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 158         int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
 159         int (*have_precompute_mult)(const EC_GROUP *group);
 160
 161
 162         /* internal functions */
 163
 164         /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
 165          * the same implementations of point operations can be used with different
 166          * optimized implementations of expensive field operations: */
 167         int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 168         int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 169         int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 170
 171         int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
 172         int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
 173         int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
 174 } /* EC_METHOD */;
 175
 176 typedef struct ec_extra_data_st {
 177         struct ec_extra_data_st *next;
 178         void *data;
 179         void *(*dup_func)(void *);
 180         void (*free_func)(void *);
 181         void (*clear_free_func)(void *);
 182 } EC_EXTRA_DATA; /* used in EC_GROUP */
 183
 184 struct ec_group_st {
 185         const EC_METHOD *meth;
 186
 187         EC_POINT *generator; /* optional */
 188         BIGNUM order, cofactor;
 189
 190         int curve_name;/* optional NID for named curve */
 191         int asn1_flag; /* flag to control the asn1 encoding */
 192         point_conversion_form_t asn1_form;
 193
 194         unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
 195         size_t seed_len;
 196
 197         EC_EXTRA_DATA *extra_data; /* linked list */
 198
 199         /* The following members are handled by the method functions,
 200          * even if they appear generic */
 201
 202         BIGNUM field; /* Field specification.
 203                        * For curves over GF(p), this is the modulus;
 204                        * for curves over GF(2^m), this is the
 205                        * irreducible polynomial defining the field.
 206                        */
 207
 208         unsigned int poly[5]; /* Field specification for curves over GF(2^m).
 209                                * The irreducible f(t) is then of the form:
 210                                *     t^poly[0] + t^poly[1] + ... + t^poly[k]
 211                                * where m = poly[0] > poly[1] > ... > poly[k] = 0.
 212                                */
 213
 214         BIGNUM a, b; /* Curve coefficients.
 215                       * (Here the assumption is that BIGNUMs can be used
 216                       * or abused for all kinds of fields, not just GF(p).)
 217                       * For characteristic  > 3,  the curve is defined
 218                       * by a Weierstrass equation of the form
 219                       *     y^2 = x^3 + a*x + b.
 220                       * For characteristic  2,  the curve is defined by
 221                       * an equation of the form
 222                       *     y^2 + x*y = x^3 + a*x^2 + b.
 223                       */
 224
 225         int a_is_minus3; /* enable optimized point arithmetics for special case */
 226
 227         void *field_data1; /* method-specific (e.g., Montgomery structure) */
 228         void *field_data2; /* method-specific */
 229         int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
 230 } /* EC_GROUP */;
 231
 232 struct ec_key_st {
 233         int version;
 234
 235         EC_GROUP *group;
 236
 237         EC_POINT *pub_key;
 238         BIGNUM   *priv_key;
 239
 240         unsigned int enc_flag;
 241         point_conversion_form_t conv_form;
 242
 243         int     references;
 244
 245         EC_EXTRA_DATA *method_data;
 246 } /* EC_KEY */;
 247
 248 /* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
 249  * (with visibility limited to 'package' level for now).
 250  * We use the function pointers as index for retrieval; this obviates
 251  * global ex_data-style index tables.
 252  */
 253 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
 254         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 255 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
 256         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 257 void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
 258         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 259 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
 260         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 261 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
 262 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
 263
 264
 265
 266 struct ec_point_st {
 267         const EC_METHOD *meth;
 268
 269         /* All members except 'meth' are handled by the method functions,
 270          * even if they appear generic */
 271
 272         BIGNUM X;
 273         BIGNUM Y;
 274         BIGNUM Z; /* Jacobian projective coordinates:
 275                    * (X, Y, Z)  represents  (X/Z^2, Y/Z^3)  if  Z != 0 */
 276         int Z_is_one; /* enable optimized point arithmetics for special case */
 277 } /* EC_POINT */;
 278
 279
 280
 281 /* method functions in ec_mult.c
 282  * (ec_lib.c uses these as defaults if group->method->mul is 0) */
 283 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 284         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 285 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
 286 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
 287
 288
 289 /* method functions in ecp_smpl.c */
 290 int ec_GFp_simple_group_init(EC_GROUP *);
 291 void ec_GFp_simple_group_finish(EC_GROUP *);
 292 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
 293 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
 294 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 295 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 296 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
 297 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
 298 int ec_GFp_simple_point_init(EC_POINT *);
 299 void ec_GFp_simple_point_finish(EC_POINT *);
 300 void ec_GFp_simple_point_clear_finish(EC_POINT *);
 301 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
 302 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
 303 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
 304         const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
 305 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
 306         BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
 307 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
 308         const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 309 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
 310         BIGNUM *x, BIGNUM *y, BN_CTX *);
 311 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
 312         const BIGNUM *x, int y_bit, BN_CTX *);
 313 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 314         unsigned char *buf, size_t len, BN_CTX *);
 315 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
 316         const unsigned char *buf, size_t len, BN_CTX *);
 317 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 318 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 319 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
 320 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 321 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 322 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 323 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 324 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 325 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 326 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 327
 328
 329 /* method functions in ecp_mont.c */
 330 int ec_GFp_mont_group_init(EC_GROUP *);
 331 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 332 void ec_GFp_mont_group_finish(EC_GROUP *);
 333 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
 334 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
 335 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 336 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 337 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 338 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 339 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
 340
 341
 342 /* method functions in ecp_nist.c */
 343 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
 344 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 345 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 346 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 347
 348
 349 /* method functions in ec2_smpl.c */
 350 int ec_GF2m_simple_group_init(EC_GROUP *);
 351 void ec_GF2m_simple_group_finish(EC_GROUP *);
 352 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
 353 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
 354 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 355 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 356 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
 357 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
 358 int ec_GF2m_simple_point_init(EC_POINT *);
 359 void ec_GF2m_simple_point_finish(EC_POINT *);
 360 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
 361 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
 362 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
 363 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
 364         const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 365 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
 366         BIGNUM *x, BIGNUM *y, BN_CTX *);
 367 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
 368         const BIGNUM *x, int y_bit, BN_CTX *);
 369 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 370         unsigned char *buf, size_t len, BN_CTX *);
 371 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
 372         const unsigned char *buf, size_t len, BN_CTX *);
 373 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 374 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 375 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
 376 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 377 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 378 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 379 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 380 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 381 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 382 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 383 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 384
 385
 386 /* method functions in ec2_mult.c */
 387 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 388         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 389 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 390 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);