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 #include <stdlib.h>
  73
  74 #include <openssl/obj_mac.h>
  75 #include <openssl/ec.h>
  76 #include <openssl/bn.h>
  77
  78 #if defined(__SUNPRO_C)
  79 # if __SUNPRO_C >= 0x520
  80 #  pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
  81 # endif
  82 #endif
  83
  84 /* Use default functions for poin2oct, oct2point and compressed coordinates */
  85 #define EC_FLAGS_DEFAULT_OCT    0x1
  86
  87 /*
  88  * Structure details are not part of the exported interface, so all this may
  89  * change in future versions.
  90  */
  91
  92 struct ec_method_st {
  93     /* Various method flags */
  94     int flags;
  95     /* used by EC_METHOD_get_field_type: */
  96     int field_type;             /* a NID */
  97     /*
  98      * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free,
  99      * EC_GROUP_copy:
 100      */
 101     int (*group_init) (EC_GROUP *);
 102     void (*group_finish) (EC_GROUP *);
 103     void (*group_clear_finish) (EC_GROUP *);
 104     int (*group_copy) (EC_GROUP *, const EC_GROUP *);
 105     /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
 106     /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
 107     int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
 108                             const BIGNUM *b, BN_CTX *);
 109     int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b,
 110                             BN_CTX *);
 111     /* used by EC_GROUP_get_degree: */
 112     int (*group_get_degree) (const EC_GROUP *);
 113     /* used by EC_GROUP_check: */
 114     int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *);
 115     /*
 116      * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
 117      * EC_POINT_copy:
 118      */
 119     int (*point_init) (EC_POINT *);
 120     void (*point_finish) (EC_POINT *);
 121     void (*point_clear_finish) (EC_POINT *);
 122     int (*point_copy) (EC_POINT *, const EC_POINT *);
 123     /*-
 124      * used by EC_POINT_set_to_infinity,
 125      * EC_POINT_set_Jprojective_coordinates_GFp,
 126      * EC_POINT_get_Jprojective_coordinates_GFp,
 127      * EC_POINT_set_affine_coordinates_GFp,     ..._GF2m,
 128      * EC_POINT_get_affine_coordinates_GFp,     ..._GF2m,
 129      * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
 130      */
 131     int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *);
 132     int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *,
 133                                                   EC_POINT *, const BIGNUM *x,
 134                                                   const BIGNUM *y,
 135                                                   const BIGNUM *z, BN_CTX *);
 136     int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *,
 137                                                   const EC_POINT *, BIGNUM *x,
 138                                                   BIGNUM *y, BIGNUM *z,
 139                                                   BN_CTX *);
 140     int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *,
 141                                          const BIGNUM *x, const BIGNUM *y,
 142                                          BN_CTX *);
 143     int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *,
 144                                          BIGNUM *x, BIGNUM *y, BN_CTX *);
 145     int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *,
 146                                              const BIGNUM *x, int y_bit,
 147                                              BN_CTX *);
 148     /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
 149     size_t (*point2oct) (const EC_GROUP *, const EC_POINT *,
 150                          point_conversion_form_t form, unsigned char *buf,
 151                          size_t len, BN_CTX *);
 152     int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf,
 153                       size_t len, BN_CTX *);
 154     /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
 155     int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
 156                 const EC_POINT *b, BN_CTX *);
 157     int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
 158     int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *);
 159     /*
 160      * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp:
 161      */
 162     int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *);
 163     int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *);
 164     int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
 165                       BN_CTX *);
 166     /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
 167     int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *);
 168     int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[],
 169                                BN_CTX *);
 170     /*
 171      * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult,
 172      * EC_POINT_have_precompute_mult (default implementations are used if the
 173      * 'mul' pointer is 0):
 174      */
 175     int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 176                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
 177                 BN_CTX *);
 178     int (*precompute_mult) (EC_GROUP *group, BN_CTX *);
 179     int (*have_precompute_mult) (const EC_GROUP *group);
 180     /* internal functions */
 181     /*
 182      * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and
 183      * 'dbl' so that the same implementations of point operations can be used
 184      * with different optimized implementations of expensive field
 185      * operations:
 186      */
 187     int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 188                       const BIGNUM *b, BN_CTX *);
 189     int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 190     int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 191                       const BIGNUM *b, BN_CTX *);
 192     /* e.g. to Montgomery */
 193     int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 194                          BN_CTX *);
 195     /* e.g. from Montgomery */
 196     int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 197                          BN_CTX *);
 198     int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *);
 199 } /* EC_METHOD */ ;
 200
 201 typedef struct ec_extra_data_st {
 202     struct ec_extra_data_st *next;
 203     void *data;
 204     void *(*dup_func) (void *);
 205     void (*free_func) (void *);
 206     void (*clear_free_func) (void *);
 207 } EC_EXTRA_DATA;                /* used in EC_GROUP */
 208
 209 struct ec_group_st {
 210     const EC_METHOD *meth;
 211     EC_POINT *generator;        /* optional */
 212     BIGNUM *order, *cofactor;
 213     int curve_name;             /* optional NID for named curve */
 214     int asn1_flag;              /* flag to control the asn1 encoding */
 215     point_conversion_form_t asn1_form;
 216     unsigned char *seed;        /* optional seed for parameters (appears in
 217                                  * ASN1) */
 218     size_t seed_len;
 219     EC_EXTRA_DATA *extra_data;  /* linked list */
 220     /*
 221      * The following members are handled by the method functions, even if
 222      * they appear generic
 223      */
 224     /*
 225      * Field specification. For curves over GF(p), this is the modulus; for
 226      * curves over GF(2^m), this is the irreducible polynomial defining the
 227      * field.
 228      */
 229     BIGNUM *field;
 230     /*
 231      * Field specification for curves over GF(2^m). The irreducible f(t) is
 232      * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m =
 233      * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with
 234      * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero
 235      * terms.
 236      */
 237     int poly[6];
 238     /*
 239      * Curve coefficients. (Here the assumption is that BIGNUMs can be used
 240      * or abused for all kinds of fields, not just GF(p).) For characteristic
 241      * > 3, the curve is defined by a Weierstrass equation of the form y^2 =
 242      * x^3 + a*x + b. For characteristic 2, the curve is defined by an
 243      * equation of the form y^2 + x*y = x^3 + a*x^2 + b.
 244      */
 245     BIGNUM *a, *b;
 246     /* enable optimized point arithmetics for special case */
 247     int a_is_minus3;
 248     /* method-specific (e.g., Montgomery structure) */
 249     void *field_data1;
 250     /* method-specific */
 251     void *field_data2;
 252     /* method-specific */
 253     int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *,
 254                            BN_CTX *);
 255     /* data for ECDSA inverse */
 256     BN_MONT_CTX *mont_data;
 257 } /* EC_GROUP */ ;
 258
 259 struct ec_key_st {
 260     const EC_KEY_METHOD *meth;
 261     ENGINE *engine;
 262     int version;
 263     EC_GROUP *group;
 264     EC_POINT *pub_key;
 265     BIGNUM *priv_key;
 266     unsigned int enc_flag;
 267     point_conversion_form_t conv_form;
 268     int references;
 269     int flags;
 270     EC_EXTRA_DATA *method_data;
 271 } /* EC_KEY */ ;
 272
 273 /*
 274  * Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs
 275  * only (with visibility limited to 'package' level for now). We use the
 276  * function pointers as index for retrieval; this obviates global
 277  * ex_data-style index tables.
 278  */
 279 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
 280                         void *(*dup_func) (void *),
 281                         void (*free_func) (void *),
 282                         void (*clear_free_func) (void *));
 283 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *, void *(*dup_func) (void *),
 284                           void (*free_func) (void *),
 285                           void (*clear_free_func) (void *));
 286 void EC_EX_DATA_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *),
 287                           void (*free_func) (void *),
 288                           void (*clear_free_func) (void *));
 289 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *),
 290                                 void (*free_func) (void *),
 291                                 void (*clear_free_func) (void *));
 292 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
 293 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
 294
 295 struct ec_point_st {
 296     const EC_METHOD *meth;
 297     /*
 298      * All members except 'meth' are handled by the method functions, even if
 299      * they appear generic
 300      */
 301     BIGNUM *X;
 302     BIGNUM *Y;
 303     BIGNUM *Z;                  /* Jacobian projective coordinates: * (X, Y,
 304                                  * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
 305     int Z_is_one;               /* enable optimized point arithmetics for
 306                                  * special case */
 307 } /* EC_POINT */ ;
 308
 309 /*
 310  * method functions in ec_mult.c (ec_lib.c uses these as defaults if
 311  * group->method->mul is 0)
 312  */
 313 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
 314                 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
 315                 BN_CTX *);
 316 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
 317 int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
 318
 319 /* method functions in ecp_smpl.c */
 320 int ec_GFp_simple_group_init(EC_GROUP *);
 321 void ec_GFp_simple_group_finish(EC_GROUP *);
 322 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
 323 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
 324 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
 325                                   const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 326 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
 327                                   BIGNUM *b, BN_CTX *);
 328 int ec_GFp_simple_group_get_degree(const EC_GROUP *);
 329 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
 330 int ec_GFp_simple_point_init(EC_POINT *);
 331 void ec_GFp_simple_point_finish(EC_POINT *);
 332 void ec_GFp_simple_point_clear_finish(EC_POINT *);
 333 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
 334 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
 335 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *,
 336                                                   EC_POINT *, const BIGNUM *x,
 337                                                   const BIGNUM *y,
 338                                                   const BIGNUM *z, BN_CTX *);
 339 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
 340                                                   const EC_POINT *, BIGNUM *x,
 341                                                   BIGNUM *y, BIGNUM *z,
 342                                                   BN_CTX *);
 343 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
 344                                                const BIGNUM *x,
 345                                                const BIGNUM *y, BN_CTX *);
 346 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *,
 347                                                const EC_POINT *, BIGNUM *x,
 348                                                BIGNUM *y, BN_CTX *);
 349 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
 350                                              const BIGNUM *x, int y_bit,
 351                                              BN_CTX *);
 352 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *,
 353                                point_conversion_form_t form,
 354                                unsigned char *buf, size_t len, BN_CTX *);
 355 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
 356                             const unsigned char *buf, size_t len, BN_CTX *);
 357 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
 358                       const EC_POINT *b, BN_CTX *);
 359 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
 360                       BN_CTX *);
 361 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
 362 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 363 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 364 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
 365                       BN_CTX *);
 366 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 367 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
 368                                      EC_POINT *[], BN_CTX *);
 369 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 370                             const BIGNUM *b, BN_CTX *);
 371 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 372                             BN_CTX *);
 373
 374 /* method functions in ecp_mont.c */
 375 int ec_GFp_mont_group_init(EC_GROUP *);
 376 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
 377                                 const BIGNUM *b, BN_CTX *);
 378 void ec_GFp_mont_group_finish(EC_GROUP *);
 379 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
 380 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
 381 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 382                           const BIGNUM *b, BN_CTX *);
 383 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 384                           BN_CTX *);
 385 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 386                              BN_CTX *);
 387 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 388                              BN_CTX *);
 389 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
 390
 391 /* method functions in ecp_nist.c */
 392 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
 393 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
 394                                 const BIGNUM *b, BN_CTX *);
 395 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 396                           const BIGNUM *b, BN_CTX *);
 397 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 398                           BN_CTX *);
 399
 400 /* method functions in ec2_smpl.c */
 401 int ec_GF2m_simple_group_init(EC_GROUP *);
 402 void ec_GF2m_simple_group_finish(EC_GROUP *);
 403 void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
 404 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
 405 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p,
 406                                    const BIGNUM *a, const BIGNUM *b,
 407                                    BN_CTX *);
 408 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
 409                                    BIGNUM *b, BN_CTX *);
 410 int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
 411 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
 412 int ec_GF2m_simple_point_init(EC_POINT *);
 413 void ec_GF2m_simple_point_finish(EC_POINT *);
 414 void ec_GF2m_simple_point_clear_finish(EC_POINT *);
 415 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
 416 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
 417 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
 418                                                 const BIGNUM *x,
 419                                                 const BIGNUM *y, BN_CTX *);
 420 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *,
 421                                                 const EC_POINT *, BIGNUM *x,
 422                                                 BIGNUM *y, BN_CTX *);
 423 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
 424                                               const BIGNUM *x, int y_bit,
 425                                               BN_CTX *);
 426 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *,
 427                                 point_conversion_form_t form,
 428                                 unsigned char *buf, size_t len, BN_CTX *);
 429 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
 430                              const unsigned char *buf, size_t len, BN_CTX *);
 431 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
 432                        const EC_POINT *b, BN_CTX *);
 433 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
 434                        BN_CTX *);
 435 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
 436 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 437 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 438 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
 439                        BN_CTX *);
 440 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 441 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num,
 442                                       EC_POINT *[], BN_CTX *);
 443 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 444                              const BIGNUM *b, BN_CTX *);
 445 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 446                              BN_CTX *);
 447 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
 448                              const BIGNUM *b, BN_CTX *);
 449
 450 /* method functions in ec2_mult.c */
 451 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
 452                        const BIGNUM *scalar, size_t num,
 453                        const EC_POINT *points[], const BIGNUM *scalars[],
 454                        BN_CTX *);
 455 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 456 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
 457
 458 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
 459 /* method functions in ecp_nistp224.c */
 460 int ec_GFp_nistp224_group_init(EC_GROUP *group);
 461 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
 462                                     const BIGNUM *a, const BIGNUM *n,
 463                                     BN_CTX *);
 464 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
 465                                                  const EC_POINT *point,
 466                                                  BIGNUM *x, BIGNUM *y,
 467                                                  BN_CTX *ctx);
 468 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r,
 469                         const BIGNUM *scalar, size_t num,
 470                         const EC_POINT *points[], const BIGNUM *scalars[],
 471                         BN_CTX *);
 472 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
 473                                const BIGNUM *scalar, size_t num,
 474                                const EC_POINT *points[],
 475                                const BIGNUM *scalars[], BN_CTX *ctx);
 476 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 477 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
 478
 479 /* method functions in ecp_nistp256.c */
 480 int ec_GFp_nistp256_group_init(EC_GROUP *group);
 481 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p,
 482                                     const BIGNUM *a, const BIGNUM *n,
 483                                     BN_CTX *);
 484 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group,
 485                                                  const EC_POINT *point,
 486                                                  BIGNUM *x, BIGNUM *y,
 487                                                  BN_CTX *ctx);
 488 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r,
 489                         const BIGNUM *scalar, size_t num,
 490                         const EC_POINT *points[], const BIGNUM *scalars[],
 491                         BN_CTX *);
 492 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r,
 493                                const BIGNUM *scalar, size_t num,
 494                                const EC_POINT *points[],
 495                                const BIGNUM *scalars[], BN_CTX *ctx);
 496 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 497 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
 498
 499 /* method functions in ecp_nistp521.c */
 500 int ec_GFp_nistp521_group_init(EC_GROUP *group);
 501 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
 502                                     const BIGNUM *a, const BIGNUM *n,
 503                                     BN_CTX *);
 504 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
 505                                                  const EC_POINT *point,
 506                                                  BIGNUM *x, BIGNUM *y,
 507                                                  BN_CTX *ctx);
 508 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r,
 509                         const BIGNUM *scalar, size_t num,
 510                         const EC_POINT *points[], const BIGNUM *scalars[],
 511                         BN_CTX *);
 512 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
 513                                const BIGNUM *scalar, size_t num,
 514                                const EC_POINT *points[],
 515                                const BIGNUM *scalars[], BN_CTX *ctx);
 516 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 517 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
 518
 519 /* utility functions in ecp_nistputil.c */
 520 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
 521                                               size_t felem_size,
 522                                               void *tmp_felems,
 523                                               void (*felem_one) (void *out),
 524                                               int (*felem_is_zero) (const void
 525                                                                     *in),
 526                                               void (*felem_assign) (void *out,
 527                                                                     const void
 528                                                                     *in),
 529                                               void (*felem_square) (void *out,
 530                                                                     const void
 531                                                                     *in),
 532                                               void (*felem_mul) (void *out,
 533                                                                  const void
 534                                                                  *in1,
 535                                                                  const void
 536                                                                  *in2),
 537                                               void (*felem_inv) (void *out,
 538                                                                  const void
 539                                                                  *in),
 540                                               void (*felem_contract) (void
 541                                                                       *out,
 542                                                                       const
 543                                                                       void
 544                                                                       *in));
 545 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
 546                                      unsigned char *digit, unsigned char in);
 547 #endif
 548 int ec_precompute_mont_data(EC_GROUP *);
 549
 550 #ifdef ECP_NISTZ256_ASM
 551 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized
 552  * P256. See http://eprint.iacr.org/2013/816.
 553  *  \return  EC_METHOD object
 554  */
 555 const EC_METHOD *EC_GFp_nistz256_method(void);
 556 #endif
 557
 558 /* EC_METHOD definitions */
 559
 560 struct ec_key_method_st {
 561     const char *name;
 562     int32_t flags;
 563     int (*keygen)(EC_KEY *key);
 564 } /* EC_KEY_METHOD */ ;
 565
 566 #define EC_KEY_METHOD_DYNAMIC   1
 567
 568 int ossl_ec_key_gen(EC_KEY *eckey);