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         /* used by EC_POINT_set_to_infinity,
 121          * EC_POINT_set_Jprojective_coordinates_GFp,
 122          * EC_POINT_get_Jprojective_coordinates_GFp,
 123          * EC_POINT_set_affine_coordinates_GFp,     ..._GF2m,
 124          * EC_POINT_get_affine_coordinates_GFp,     ..._GF2m,
 125          * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
 126          */
 127         int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
 128         int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
 129                 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
 130         int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
 131                 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
 132         int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
 133                 const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 134         int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
 135                 BIGNUM *x, BIGNUM *y, BN_CTX *);
 136         int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
 137                 const BIGNUM *x, int y_bit, BN_CTX *);
 138
 139         /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
 140         size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 141                 unsigned char *buf, size_t len, BN_CTX *);
 142         int (*oct2point)(const EC_GROUP *, EC_POINT *,
 143                 const unsigned char *buf, size_t len, BN_CTX *);
 144
 145         /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
 146         int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 147         int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 148         int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
 149
 150         /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
 151         int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
 152         int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 153         int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 154
 155         /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
 156         int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
 157         int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 158
 159         /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
 160          * (default implementations are used if the 'mul' pointer is 0): */
 161         int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 162                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 163         int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
 164         int (*have_precompute_mult)(const EC_GROUP *group);
 165
 166
 167         /* internal functions */
 168
 169         /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
 170          * the same implementations of point operations can be used with different
 171          * optimized implementations of expensive field operations: */
 172         int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 173         int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 174         int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 175
 176         int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
 177         int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
 178         int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
 179 } /* EC_METHOD */;
 180
 181 typedef struct ec_extra_data_st {
 182         struct ec_extra_data_st *next;
 183         void *data;
 184         void *(*dup_func)(void *);
 185         void (*free_func)(void *);
 186         void (*clear_free_func)(void *);
 187 } EC_EXTRA_DATA; /* used in EC_GROUP */
 188
 189 struct ec_group_st {
 190         const EC_METHOD *meth;
 191
 192         EC_POINT *generator; /* optional */
 193         BIGNUM *order, *cofactor;
 194
 195         int curve_name;/* optional NID for named curve */
 196         int asn1_flag; /* flag to control the asn1 encoding */
 197         point_conversion_form_t asn1_form;
 198
 199         unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
 200         size_t seed_len;
 201
 202         EC_EXTRA_DATA *extra_data; /* linked list */
 203
 204         /* The following members are handled by the method functions,
 205          * even if they appear generic */
 206
 207         BIGNUM *field; /* Field specification.
 208                        * For curves over GF(p), this is the modulus;
 209                        * for curves over GF(2^m), this is the
 210                        * irreducible polynomial defining the field.
 211                        */
 212
 213         int poly[6]; /* Field specification for curves over GF(2^m).
 214                       * The irreducible f(t) is then of the form:
 215                       *     t^poly[0] + t^poly[1] + ... + t^poly[k]
 216                       * where m = poly[0] > poly[1] > ... > poly[k] = 0.
 217                       * The array is terminated with poly[k+1]=-1.
 218                       * All elliptic curve irreducibles have at most 5
 219                       * non-zero terms.
 220                       */
 221
 222         BIGNUM *a, *b; /* Curve coefficients.
 223                       * (Here the assumption is that BIGNUMs can be used
 224                       * or abused for all kinds of fields, not just GF(p).)
 225                       * For characteristic  > 3,  the curve is defined
 226                       * by a Weierstrass equation of the form
 227                       *     y^2 = x^3 + a*x + b.
 228                       * For characteristic  2,  the curve is defined by
 229                       * an equation of the form
 230                       *     y^2 + x*y = x^3 + a*x^2 + b.
 231                       */
 232
 233         int a_is_minus3; /* enable optimized point arithmetics for special case */
 234
 235         void *field_data1; /* method-specific (e.g., Montgomery structure) */
 236         void *field_data2; /* method-specific */
 237         int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
 238
 239         BN_MONT_CTX *mont_data;    /* data for ECDSA inverse */
 240 } /* EC_GROUP */;
 241
 242 struct ec_key_st {
 243         int version;
 244
 245         EC_GROUP *group;
 246
 247         EC_POINT *pub_key;
 248         BIGNUM   *priv_key;
 249
 250         unsigned int enc_flag;
 251         point_conversion_form_t conv_form;
 252
 253         int     references;
 254         int     flags;
 255
 256         EC_EXTRA_DATA *method_data;
 257 } /* EC_KEY */;
 258
 259 /* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
 260  * (with visibility limited to 'package' level for now).
 261  * We use the function pointers as index for retrieval; this obviates
 262  * global ex_data-style index tables.
 263  */
 264 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
 265         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 266 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
 267         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 268 void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
 269         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 270 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
 271         void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
 272 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
 273 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
 274
 275
 276
 277 struct ec_point_st {
 278         const EC_METHOD *meth;
 279
 280         /* All members except 'meth' are handled by the method functions,
 281          * even if they appear generic */
 282
 283         BIGNUM *X;
 284         BIGNUM *Y;
 285         BIGNUM *Z; /* Jacobian projective coordinates:
 286                    * (X, Y, Z)  represents  (X/Z^2, Y/Z^3)  if  Z != 0 */
 287         int Z_is_one; /* enable optimized point arithmetics for special case */
 288 } /* EC_POINT */;
 289
 290
 291
 292 /* method functions in ec_mult.c
 293  * (ec_lib.c uses these as defaults if group->method->mul is 0) */
 294 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 295         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 296 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
 297 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
 298
 299
 300 /* method functions in ecp_smpl.c */
 301 int ec_GFp_simple_group_init(EC_GROUP *);
 302 void ec_GFp_simple_group_finish(EC_GROUP *);
 303 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
 304 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
 305 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 306 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 307 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
 308 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
 309 int ec_GFp_simple_point_init(EC_POINT *);
 310 void ec_GFp_simple_point_finish(EC_POINT *);
 311 void ec_GFp_simple_point_clear_finish(EC_POINT *);
 312 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
 313 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
 314 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
 315         const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
 316 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
 317         BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
 318 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
 319         const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 320 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
 321         BIGNUM *x, BIGNUM *y, BN_CTX *);
 322 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
 323         const BIGNUM *x, int y_bit, BN_CTX *);
 324 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 325         unsigned char *buf, size_t len, BN_CTX *);
 326 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
 327         const unsigned char *buf, size_t len, BN_CTX *);
 328 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 329 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 330 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
 331 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 332 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 333 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 334 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 335 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 336 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 337 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 338
 339
 340 /* method functions in ecp_mont.c */
 341 int ec_GFp_mont_group_init(EC_GROUP *);
 342 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 343 void ec_GFp_mont_group_finish(EC_GROUP *);
 344 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
 345 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
 346 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 347 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 348 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 349 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 350 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
 351
 352
 353 /* method functions in ecp_nist.c */
 354 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
 355 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 356 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 357 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 358
 359
 360 /* method functions in ec2_smpl.c */
 361 int ec_GF2m_simple_group_init(EC_GROUP *);
 362 void ec_GF2m_simple_group_finish(EC_GROUP *);
 363 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
 364 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
 365 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 366 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 367 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
 368 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
 369 int ec_GF2m_simple_point_init(EC_POINT *);
 370 void ec_GF2m_simple_point_finish(EC_POINT *);
 371 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
 372 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
 373 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
 374 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
 375         const BIGNUM *x, const BIGNUM *y, BN_CTX *);
 376 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
 377         BIGNUM *x, BIGNUM *y, BN_CTX *);
 378 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
 379         const BIGNUM *x, int y_bit, BN_CTX *);
 380 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
 381         unsigned char *buf, size_t len, BN_CTX *);
 382 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
 383         const unsigned char *buf, size_t len, BN_CTX *);
 384 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 385 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 386 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
 387 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 388 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 389 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
 390 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 391 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 392 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 393 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 394 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 395
 396
 397 /* method functions in ec2_mult.c */
 398 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 399         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 400 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 401 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
 402
 403 /* method functions in ec2_mult.c */
 404 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 405         size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 406 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 407 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
 408
 409 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
 410 /* method functions in ecp_nistp224.c */
 411 int ec_GFp_nistp224_group_init(EC_GROUP *group);
 412 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
 413 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
 414 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 *);
 415 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);
 416 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 417 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
 418
 419 /* method functions in ecp_nistp256.c */
 420 int ec_GFp_nistp256_group_init(EC_GROUP *group);
 421 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
 422 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
 423 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 *);
 424 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);
 425 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 426 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
 427
 428 /* method functions in ecp_nistp521.c */
 429 int ec_GFp_nistp521_group_init(EC_GROUP *group);
 430 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
 431 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
 432 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 *);
 433 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);
 434 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 435 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
 436
 437 /* utility functions in ecp_nistputil.c */
 438 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
 439         size_t felem_size, void *tmp_felems,
 440         void (*felem_one)(void *out),
 441         int (*felem_is_zero)(const void *in),
 442         void (*felem_assign)(void *out, const void *in),
 443         void (*felem_square)(void *out, const void *in),
 444         void (*felem_mul)(void *out, const void *in1, const void *in2),
 445         void (*felem_inv)(void *out, const void *in),
 446         void (*felem_contract)(void *out, const void *in));
 447 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in);
 448 #endif
 449 int ec_precompute_mont_data(EC_GROUP *);
 450
 451 #ifdef ECP_NISTZ256_ASM
 452 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
 453  * P256. See http://eprint.iacr.org/2013/816.
 454  *  \return  EC_METHOD object
 455  */
 456 const EC_METHOD *EC_GFp_nistz256_method(void);
 457 #endif