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      1 /* Originally written by Bodo Moeller for the OpenSSL project.
      2  * ====================================================================
      3  * Copyright (c) 1998-2005 The OpenSSL Project.  All rights reserved.
      4  *
      5  * Redistribution and use in source and binary forms, with or without
      6  * modification, are permitted provided that the following conditions
      7  * are met:
      8  *
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  *
     12  * 2. Redistributions in binary form must reproduce the above copyright
     13  *    notice, this list of conditions and the following disclaimer in
     14  *    the documentation and/or other materials provided with the
     15  *    distribution.
     16  *
     17  * 3. All advertising materials mentioning features or use of this
     18  *    software must display the following acknowledgment:
     19  *    "This product includes software developed by the OpenSSL Project
     20  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
     21  *
     22  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
     23  *    endorse or promote products derived from this software without
     24  *    prior written permission. For written permission, please contact
     25  *    openssl-core (at) openssl.org.
     26  *
     27  * 5. Products derived from this software may not be called "OpenSSL"
     28  *    nor may "OpenSSL" appear in their names without prior written
     29  *    permission of the OpenSSL Project.
     30  *
     31  * 6. Redistributions of any form whatsoever must retain the following
     32  *    acknowledgment:
     33  *    "This product includes software developed by the OpenSSL Project
     34  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
     35  *
     36  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
     37  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     38  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
     39  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
     40  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
     41  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
     42  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
     43  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     44  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
     45  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
     46  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
     47  * OF THE POSSIBILITY OF SUCH DAMAGE.
     48  * ====================================================================
     49  *
     50  * This product includes cryptographic software written by Eric Young
     51  * (eay (at) cryptsoft.com).  This product includes software written by Tim
     52  * Hudson (tjh (at) cryptsoft.com).
     53  *
     54  */
     55 /* ====================================================================
     56  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
     57  *
     58  * Portions of the attached software ("Contribution") are developed by
     59  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
     60  *
     61  * The Contribution is licensed pursuant to the OpenSSL open source
     62  * license provided above.
     63  *
     64  * The elliptic curve binary polynomial software is originally written by
     65  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
     66  * Laboratories. */
     67 
     68 #ifndef OPENSSL_HEADER_EC_INTERNAL_H
     69 #define OPENSSL_HEADER_EC_INTERNAL_H
     70 
     71 #include <openssl/base.h>
     72 
     73 #include <openssl/bn.h>
     74 #include <openssl/ex_data.h>
     75 #include <openssl/thread.h>
     76 
     77 #if defined(__cplusplus)
     78 extern "C" {
     79 #endif
     80 
     81 
     82 struct ec_method_st {
     83   int (*group_init)(EC_GROUP *);
     84   void (*group_finish)(EC_GROUP *);
     85   int (*group_copy)(EC_GROUP *, const EC_GROUP *);
     86   int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
     87                          const BIGNUM *b, BN_CTX *);
     88   int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
     89                                       BIGNUM *x, BIGNUM *y, BN_CTX *);
     90 
     91   /* Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar|
     92    * are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null.
     93    * Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar|
     94    * and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is
     95    * non-null. */
     96   int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
     97              const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx);
     98 
     99   /* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that the
    100    * same implementations of point operations can be used with different
    101    * optimized implementations of expensive field operations: */
    102   int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    103                    const BIGNUM *b, BN_CTX *);
    104   int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
    105 
    106   int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    107                       BN_CTX *); /* e.g. to Montgomery */
    108   int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    109                       BN_CTX *); /* e.g. from Montgomery */
    110 } /* EC_METHOD */;
    111 
    112 extern const EC_METHOD EC_GFp_mont_method;
    113 
    114 struct ec_group_st {
    115   const EC_METHOD *meth;
    116 
    117   EC_POINT *generator;
    118   BIGNUM order;
    119 
    120   int curve_name; /* optional NID for named curve */
    121 
    122   const BN_MONT_CTX *mont_data; /* data for ECDSA inverse */
    123 
    124   /* The following members are handled by the method functions,
    125    * even if they appear generic */
    126 
    127   BIGNUM field; /* For curves over GF(p), this is the modulus. */
    128 
    129   BIGNUM a, b; /* Curve coefficients. */
    130 
    131   int a_is_minus3; /* enable optimized point arithmetics for special case */
    132 
    133   BN_MONT_CTX *mont; /* Montgomery structure. */
    134 
    135   BIGNUM one; /* The value one. */
    136 } /* EC_GROUP */;
    137 
    138 struct ec_point_st {
    139   const EC_METHOD *meth;
    140 
    141   BIGNUM X;
    142   BIGNUM Y;
    143   BIGNUM Z; /* Jacobian projective coordinates:
    144              * (X, Y, Z)  represents  (X/Z^2, Y/Z^3)  if  Z != 0 */
    145 } /* EC_POINT */;
    146 
    147 EC_GROUP *ec_group_new(const EC_METHOD *meth);
    148 int ec_group_copy(EC_GROUP *dest, const EC_GROUP *src);
    149 
    150 /* ec_group_get_mont_data returns a Montgomery context for operations in the
    151  * scalar field of |group|. It may return NULL in the case that |group| is not
    152  * a built-in group. */
    153 const BN_MONT_CTX *ec_group_get_mont_data(const EC_GROUP *group);
    154 
    155 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
    156                 const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx);
    157 
    158 /* method functions in simple.c */
    159 int ec_GFp_simple_group_init(EC_GROUP *);
    160 void ec_GFp_simple_group_finish(EC_GROUP *);
    161 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
    162 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
    163                                   const BIGNUM *b, BN_CTX *);
    164 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a,
    165                                   BIGNUM *b, BN_CTX *);
    166 unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *);
    167 int ec_GFp_simple_point_init(EC_POINT *);
    168 void ec_GFp_simple_point_finish(EC_POINT *);
    169 void ec_GFp_simple_point_clear_finish(EC_POINT *);
    170 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
    171 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
    172 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
    173                                                   const BIGNUM *x,
    174                                                   const BIGNUM *y,
    175                                                   const BIGNUM *z, BN_CTX *);
    176 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *,
    177                                                   const EC_POINT *, BIGNUM *x,
    178                                                   BIGNUM *y, BIGNUM *z,
    179                                                   BN_CTX *);
    180 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
    181                                                const BIGNUM *x, const BIGNUM *y,
    182                                                BN_CTX *);
    183 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
    184                                              const BIGNUM *x, int y_bit,
    185                                              BN_CTX *);
    186 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
    187                       const EC_POINT *b, BN_CTX *);
    188 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a,
    189                       BN_CTX *);
    190 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
    191 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
    192 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
    193 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b,
    194                       BN_CTX *);
    195 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
    196 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num,
    197                                      EC_POINT * [], BN_CTX *);
    198 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    199                             const BIGNUM *b, BN_CTX *);
    200 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    201                             BN_CTX *);
    202 
    203 /* method functions in montgomery.c */
    204 int ec_GFp_mont_group_init(EC_GROUP *);
    205 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a,
    206                                 const BIGNUM *b, BN_CTX *);
    207 void ec_GFp_mont_group_finish(EC_GROUP *);
    208 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
    209 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    210                           const BIGNUM *b, BN_CTX *);
    211 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    212                           BN_CTX *);
    213 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    214                              BN_CTX *);
    215 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
    216                              BN_CTX *);
    217 
    218 int ec_point_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
    219                                              EC_POINT *point, const BIGNUM *x,
    220                                              const BIGNUM *y, const BIGNUM *z,
    221                                              BN_CTX *ctx);
    222 
    223 void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in);
    224 
    225 extern const EC_METHOD EC_GFp_nistp224_method;
    226 extern const EC_METHOD EC_GFp_nistp256_method;
    227 
    228 /* EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with
    229  * x86-64 optimized P256. See http://eprint.iacr.org/2013/816. */
    230 extern const EC_METHOD EC_GFp_nistz256_method;
    231 
    232 struct ec_key_st {
    233   EC_GROUP *group;
    234 
    235   EC_POINT *pub_key;
    236   BIGNUM *priv_key;
    237 
    238   unsigned int enc_flag;
    239   point_conversion_form_t conv_form;
    240 
    241   CRYPTO_refcount_t references;
    242 
    243   ECDSA_METHOD *ecdsa_meth;
    244 
    245   CRYPTO_EX_DATA ex_data;
    246 } /* EC_KEY */;
    247 
    248 /* curve_data contains data about a built-in elliptic curve. */
    249 struct curve_data {
    250   /* comment is a human-readable string describing the curve. */
    251   const char *comment;
    252   /* param_len is the number of bytes needed to store a field element. */
    253   uint8_t param_len;
    254   /* data points to an array of 6*|param_len| bytes which hold the field
    255    * elements of the following (in big-endian order): prime, a, b, generator x,
    256    * generator y, order. */
    257   const uint8_t data[];
    258 };
    259 
    260 struct built_in_curve {
    261   int nid;
    262   uint8_t oid[8];
    263   uint8_t oid_len;
    264   const struct curve_data *data;
    265   const EC_METHOD *method;
    266 };
    267 
    268 /* OPENSSL_built_in_curves is terminated with an entry where |nid| is
    269  * |NID_undef|. */
    270 extern const struct built_in_curve OPENSSL_built_in_curves[];
    271 
    272 #if defined(__cplusplus)
    273 }  /* extern C */
    274 #endif
    275 
    276 #endif  /* OPENSSL_HEADER_EC_INTERNAL_H */
    277