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ec.h (21240B)


      1 // Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved.
      2 // Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved.
      3 //
      4 // Licensed under the Apache License, Version 2.0 (the "License");
      5 // you may not use this file except in compliance with the License.
      6 // You may obtain a copy of the License at
      7 //
      8 //     https://www.apache.org/licenses/LICENSE-2.0
      9 //
     10 // Unless required by applicable law or agreed to in writing, software
     11 // distributed under the License is distributed on an "AS IS" BASIS,
     12 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     13 // See the License for the specific language governing permissions and
     14 // limitations under the License.
     15 
     16 #ifndef OPENSSL_HEADER_EC_H
     17 #define OPENSSL_HEADER_EC_H
     18 
     19 #include <openssl/base.h>   // IWYU pragma: export
     20 
     21 #if defined(__cplusplus)
     22 extern "C" {
     23 #endif
     24 
     25 
     26 // Low-level operations on elliptic curves.
     27 
     28 
     29 // point_conversion_form_t enumerates forms, as defined in X9.62 (ECDSA), for
     30 // the encoding of a elliptic curve point (x,y)
     31 typedef enum {
     32   // POINT_CONVERSION_COMPRESSED indicates that the point is encoded as z||x,
     33   // where the octet z specifies which solution of the quadratic equation y
     34   // is.
     35   POINT_CONVERSION_COMPRESSED = 2,
     36 
     37   // POINT_CONVERSION_UNCOMPRESSED indicates that the point is encoded as
     38   // z||x||y, where z is the octet 0x04.
     39   POINT_CONVERSION_UNCOMPRESSED = 4,
     40 
     41   // POINT_CONVERSION_HYBRID indicates that the point is encoded as z||x||y,
     42   // where z specifies which solution of the quadratic equation y is. This is
     43   // not supported by the code and has never been observed in use.
     44   //
     45   // TODO(agl): remove once node.js no longer references this.
     46   POINT_CONVERSION_HYBRID = 6,
     47 } point_conversion_form_t;
     48 
     49 
     50 // Elliptic curve groups.
     51 //
     52 // Elliptic curve groups are represented by |EC_GROUP| objects. Unlike OpenSSL,
     53 // if limited to the APIs in this section, callers may treat |EC_GROUP|s as
     54 // static, immutable objects which do not need to be copied or released. In
     55 // BoringSSL, only custom |EC_GROUP|s created by |EC_GROUP_new_curve_GFp|
     56 // (deprecated) are dynamic.
     57 //
     58 // Callers may cast away |const| and use |EC_GROUP_dup| and |EC_GROUP_free| with
     59 // static groups, for compatibility with OpenSSL or dynamic groups, but it is
     60 // otherwise unnecessary.
     61 
     62 // EC_group_p224 returns an |EC_GROUP| for P-224, also known as secp224r1.
     63 OPENSSL_EXPORT const EC_GROUP *EC_group_p224(void);
     64 
     65 // EC_group_p256 returns an |EC_GROUP| for P-256, also known as secp256r1 or
     66 // prime256v1.
     67 OPENSSL_EXPORT const EC_GROUP *EC_group_p256(void);
     68 
     69 // EC_group_p384 returns an |EC_GROUP| for P-384, also known as secp384r1.
     70 OPENSSL_EXPORT const EC_GROUP *EC_group_p384(void);
     71 
     72 // EC_group_p521 returns an |EC_GROUP| for P-521, also known as secp521r1.
     73 OPENSSL_EXPORT const EC_GROUP *EC_group_p521(void);
     74 
     75 // EC_GROUP_new_by_curve_name returns the |EC_GROUP| object for the elliptic
     76 // curve specified by |nid|, or NULL on unsupported NID.  For OpenSSL
     77 // compatibility, this function returns a non-const pointer which may be passed
     78 // to |EC_GROUP_free|. However, the resulting object is actually static and
     79 // calling |EC_GROUP_free| is optional.
     80 //
     81 // The supported NIDs are:
     82 // - |NID_secp224r1| (P-224)
     83 // - |NID_X9_62_prime256v1| (P-256)
     84 // - |NID_secp384r1| (P-384)
     85 // - |NID_secp521r1| (P-521)
     86 //
     87 // Calling this function causes all four curves to be linked into the binary.
     88 // Prefer calling |EC_group_*| to allow the static linker to drop unused curves.
     89 //
     90 // If in doubt, use |NID_X9_62_prime256v1|, or see the curve25519.h header for
     91 // more modern primitives.
     92 OPENSSL_EXPORT EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
     93 
     94 // EC_GROUP_cmp returns zero if |a| and |b| are the same group and non-zero
     95 // otherwise.
     96 OPENSSL_EXPORT int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b,
     97                                 BN_CTX *ignored);
     98 
     99 // EC_GROUP_get0_generator returns a pointer to the internal |EC_POINT| object
    100 // in |group| that specifies the generator for the group.
    101 OPENSSL_EXPORT const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
    102 
    103 // EC_GROUP_get0_order returns a pointer to the internal |BIGNUM| object in
    104 // |group| that specifies the order of the group.
    105 OPENSSL_EXPORT const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);
    106 
    107 // EC_GROUP_order_bits returns the number of bits of the order of |group|.
    108 OPENSSL_EXPORT int EC_GROUP_order_bits(const EC_GROUP *group);
    109 
    110 // EC_GROUP_get_cofactor sets |*cofactor| to the cofactor of |group| using
    111 // |ctx|, if it's not NULL. It returns one on success and zero otherwise.
    112 OPENSSL_EXPORT int EC_GROUP_get_cofactor(const EC_GROUP *group,
    113                                          BIGNUM *cofactor, BN_CTX *ctx);
    114 
    115 // EC_GROUP_get_curve_GFp gets various parameters about a group. It sets
    116 // |*out_p| to the order of the coordinate field and |*out_a| and |*out_b| to
    117 // the parameters of the curve when expressed as y² = x³ + ax + b. Any of the
    118 // output parameters can be NULL. It returns one on success and zero on
    119 // error.
    120 OPENSSL_EXPORT int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *out_p,
    121                                           BIGNUM *out_a, BIGNUM *out_b,
    122                                           BN_CTX *ctx);
    123 
    124 // EC_GROUP_get_curve_name returns a NID that identifies |group|.
    125 OPENSSL_EXPORT int EC_GROUP_get_curve_name(const EC_GROUP *group);
    126 
    127 // EC_GROUP_get_degree returns the number of bits needed to represent an
    128 // element of the field underlying |group|.
    129 OPENSSL_EXPORT unsigned EC_GROUP_get_degree(const EC_GROUP *group);
    130 
    131 // EC_curve_nid2nist returns the NIST name of the elliptic curve specified by
    132 // |nid|, or NULL if |nid| is not a NIST curve. For example, it returns "P-256"
    133 // for |NID_X9_62_prime256v1|.
    134 OPENSSL_EXPORT const char *EC_curve_nid2nist(int nid);
    135 
    136 // EC_curve_nist2nid returns the NID of the elliptic curve specified by the NIST
    137 // name |name|, or |NID_undef| if |name| is not a recognized name. For example,
    138 // it returns |NID_X9_62_prime256v1| for "P-256".
    139 OPENSSL_EXPORT int EC_curve_nist2nid(const char *name);
    140 
    141 
    142 // Points on elliptic curves.
    143 
    144 // EC_POINT_new returns a fresh |EC_POINT| object in the given group, or NULL
    145 // on error.
    146 OPENSSL_EXPORT EC_POINT *EC_POINT_new(const EC_GROUP *group);
    147 
    148 // EC_POINT_free frees |point| and the data that it points to.
    149 OPENSSL_EXPORT void EC_POINT_free(EC_POINT *point);
    150 
    151 // EC_POINT_copy sets |*dest| equal to |*src|. It returns one on success and
    152 // zero otherwise.
    153 OPENSSL_EXPORT int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src);
    154 
    155 // EC_POINT_dup returns a fresh |EC_POINT| that contains the same values as
    156 // |src|, or NULL on error.
    157 OPENSSL_EXPORT EC_POINT *EC_POINT_dup(const EC_POINT *src,
    158                                       const EC_GROUP *group);
    159 
    160 // EC_POINT_set_to_infinity sets |point| to be the "point at infinity" for the
    161 // given group.
    162 OPENSSL_EXPORT int EC_POINT_set_to_infinity(const EC_GROUP *group,
    163                                             EC_POINT *point);
    164 
    165 // EC_POINT_is_at_infinity returns one iff |point| is the point at infinity and
    166 // zero otherwise.
    167 OPENSSL_EXPORT int EC_POINT_is_at_infinity(const EC_GROUP *group,
    168                                            const EC_POINT *point);
    169 
    170 // EC_POINT_is_on_curve returns one if |point| is an element of |group| and
    171 // and zero otherwise or when an error occurs. This is different from OpenSSL,
    172 // which returns -1 on error. If |ctx| is non-NULL, it may be used.
    173 OPENSSL_EXPORT int EC_POINT_is_on_curve(const EC_GROUP *group,
    174                                         const EC_POINT *point, BN_CTX *ctx);
    175 
    176 // EC_POINT_cmp returns zero if |a| is equal to |b|, greater than zero if
    177 // not equal and -1 on error. If |ctx| is not NULL, it may be used.
    178 OPENSSL_EXPORT int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a,
    179                                 const EC_POINT *b, BN_CTX *ctx);
    180 
    181 
    182 // Point conversion.
    183 
    184 // EC_POINT_get_affine_coordinates_GFp sets |x| and |y| to the affine value of
    185 // |point| using |ctx|, if it's not NULL. It returns one on success and zero
    186 // otherwise.
    187 //
    188 // Either |x| or |y| may be NULL to skip computing that coordinate. This is
    189 // slightly faster in the common case where only the x-coordinate is needed.
    190 OPENSSL_EXPORT int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
    191                                                        const EC_POINT *point,
    192                                                        BIGNUM *x, BIGNUM *y,
    193                                                        BN_CTX *ctx);
    194 
    195 // EC_POINT_get_affine_coordinates is an alias of
    196 // |EC_POINT_get_affine_coordinates_GFp|.
    197 OPENSSL_EXPORT int EC_POINT_get_affine_coordinates(const EC_GROUP *group,
    198                                                    const EC_POINT *point,
    199                                                    BIGNUM *x, BIGNUM *y,
    200                                                    BN_CTX *ctx);
    201 
    202 // EC_POINT_set_affine_coordinates_GFp sets the value of |point| to be
    203 // (|x|, |y|). The |ctx| argument may be used if not NULL. It returns one
    204 // on success or zero on error. It's considered an error if the point is not on
    205 // the curve.
    206 //
    207 // Note that the corresponding function in OpenSSL versions prior to 1.0.2s does
    208 // not check if the point is on the curve. This is a security-critical check, so
    209 // code additionally supporting OpenSSL should repeat the check with
    210 // |EC_POINT_is_on_curve| or check for older OpenSSL versions with
    211 // |OPENSSL_VERSION_NUMBER|.
    212 OPENSSL_EXPORT int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group,
    213                                                        EC_POINT *point,
    214                                                        const BIGNUM *x,
    215                                                        const BIGNUM *y,
    216                                                        BN_CTX *ctx);
    217 
    218 // EC_POINT_set_affine_coordinates is an alias of
    219 // |EC_POINT_set_affine_coordinates_GFp|.
    220 OPENSSL_EXPORT int EC_POINT_set_affine_coordinates(const EC_GROUP *group,
    221                                                    EC_POINT *point,
    222                                                    const BIGNUM *x,
    223                                                    const BIGNUM *y,
    224                                                    BN_CTX *ctx);
    225 
    226 // EC_POINT_point2oct serialises |point| into the X9.62 form given by |form|
    227 // into, at most, |max_out| bytes at |buf|. It returns the number of bytes
    228 // written or zero on error if |buf| is non-NULL, else the number of bytes
    229 // needed. The |ctx| argument may be used if not NULL.
    230 OPENSSL_EXPORT size_t EC_POINT_point2oct(const EC_GROUP *group,
    231                                          const EC_POINT *point,
    232                                          point_conversion_form_t form,
    233                                          uint8_t *buf, size_t max_out,
    234                                          BN_CTX *ctx);
    235 
    236 // EC_POINT_point2buf serialises |point| into the X9.62 form given by |form| to
    237 // a newly-allocated buffer and sets |*out_buf| to point to it. It returns the
    238 // length of the result on success or zero on error. The caller must release
    239 // |*out_buf| with |OPENSSL_free| when done.
    240 OPENSSL_EXPORT size_t EC_POINT_point2buf(const EC_GROUP *group,
    241                                          const EC_POINT *point,
    242                                          point_conversion_form_t form,
    243                                          uint8_t **out_buf, BN_CTX *ctx);
    244 
    245 // EC_POINT_point2cbb behaves like |EC_POINT_point2oct| but appends the
    246 // serialised point to |cbb|. It returns one on success and zero on error.
    247 OPENSSL_EXPORT int EC_POINT_point2cbb(CBB *out, const EC_GROUP *group,
    248                                       const EC_POINT *point,
    249                                       point_conversion_form_t form,
    250                                       BN_CTX *ctx);
    251 
    252 // EC_POINT_oct2point sets |point| from |len| bytes of X9.62 format
    253 // serialisation in |buf|. It returns one on success and zero on error. The
    254 // |ctx| argument may be used if not NULL. It's considered an error if |buf|
    255 // does not represent a point on the curve.
    256 OPENSSL_EXPORT int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point,
    257                                       const uint8_t *buf, size_t len,
    258                                       BN_CTX *ctx);
    259 
    260 // EC_POINT_set_compressed_coordinates_GFp sets |point| to equal the point with
    261 // the given |x| coordinate and the y coordinate specified by |y_bit| (see
    262 // X9.62). It returns one on success and zero otherwise.
    263 OPENSSL_EXPORT int EC_POINT_set_compressed_coordinates_GFp(
    264     const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, int y_bit,
    265     BN_CTX *ctx);
    266 
    267 
    268 // Group operations.
    269 
    270 // EC_POINT_add sets |r| equal to |a| plus |b|. It returns one on success and
    271 // zero otherwise. If |ctx| is not NULL, it may be used.
    272 OPENSSL_EXPORT int EC_POINT_add(const EC_GROUP *group, EC_POINT *r,
    273                                 const EC_POINT *a, const EC_POINT *b,
    274                                 BN_CTX *ctx);
    275 
    276 // EC_POINT_dbl sets |r| equal to |a| plus |a|. It returns one on success and
    277 // zero otherwise. If |ctx| is not NULL, it may be used.
    278 OPENSSL_EXPORT int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r,
    279                                 const EC_POINT *a, BN_CTX *ctx);
    280 
    281 // EC_POINT_invert sets |a| equal to minus |a|. It returns one on success and
    282 // zero otherwise. If |ctx| is not NULL, it may be used.
    283 OPENSSL_EXPORT int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a,
    284                                    BN_CTX *ctx);
    285 
    286 // EC_POINT_mul sets r = generator*n + q*m. It returns one on success and zero
    287 // otherwise. If |ctx| is not NULL, it may be used.
    288 OPENSSL_EXPORT int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r,
    289                                 const BIGNUM *n, const EC_POINT *q,
    290                                 const BIGNUM *m, BN_CTX *ctx);
    291 
    292 
    293 // Hash-to-curve.
    294 //
    295 // The following functions implement primitives from RFC 9380. The |dst|
    296 // parameter in each function is the domain separation tag and must be unique
    297 // for each protocol and between the |hash_to_curve| and |hash_to_scalar|
    298 // variants. See section 3.1 of the spec for additional guidance on this
    299 // parameter.
    300 
    301 // EC_hash_to_curve_p256_xmd_sha256_sswu hashes |msg| to a point on |group| and
    302 // writes the result to |out|, implementing the P256_XMD:SHA-256_SSWU_RO_ suite
    303 // from RFC 9380. It returns one on success and zero on error.
    304 OPENSSL_EXPORT int EC_hash_to_curve_p256_xmd_sha256_sswu(
    305     const EC_GROUP *group, EC_POINT *out, const uint8_t *dst, size_t dst_len,
    306     const uint8_t *msg, size_t msg_len);
    307 
    308 // EC_hash_to_curve_p384_xmd_sha384_sswu hashes |msg| to a point on |group| and
    309 // writes the result to |out|, implementing the P384_XMD:SHA-384_SSWU_RO_ suite
    310 // from RFC 9380. It returns one on success and zero on error.
    311 OPENSSL_EXPORT int EC_hash_to_curve_p384_xmd_sha384_sswu(
    312     const EC_GROUP *group, EC_POINT *out, const uint8_t *dst, size_t dst_len,
    313     const uint8_t *msg, size_t msg_len);
    314 
    315 
    316 // Deprecated functions.
    317 
    318 // EC_GROUP_free releases a reference to |group|, if |group| was created by
    319 // |EC_GROUP_new_curve_GFp|. If |group| is static, it does nothing.
    320 //
    321 // This function exists for OpenSSL compatibilty, and to manage dynamic
    322 // |EC_GROUP|s constructed by |EC_GROUP_new_curve_GFp|. Callers that do not need
    323 // either may ignore this function.
    324 OPENSSL_EXPORT void EC_GROUP_free(EC_GROUP *group);
    325 
    326 // EC_GROUP_dup increments |group|'s reference count and returns it, if |group|
    327 // was created by |EC_GROUP_new_curve_GFp|. If |group| is static, it simply
    328 // returns |group|.
    329 //
    330 // This function exists for OpenSSL compatibilty, and to manage dynamic
    331 // |EC_GROUP|s constructed by |EC_GROUP_new_curve_GFp|. Callers that do not need
    332 // either may ignore this function.
    333 OPENSSL_EXPORT EC_GROUP *EC_GROUP_dup(const EC_GROUP *group);
    334 
    335 // EC_GROUP_new_curve_GFp creates a new, arbitrary elliptic curve group based
    336 // on the equation y² = x³ + a·x + b. It returns the new group or NULL on
    337 // error. The lifetime of the resulting object must be managed with
    338 // |EC_GROUP_dup| and |EC_GROUP_free|.
    339 //
    340 // This new group has no generator. It is an error to use a generator-less group
    341 // with any functions except for |EC_GROUP_free|, |EC_POINT_new|,
    342 // |EC_POINT_set_affine_coordinates_GFp|, and |EC_GROUP_set_generator|.
    343 //
    344 // |EC_GROUP|s returned by this function will always compare as unequal via
    345 // |EC_GROUP_cmp| (even to themselves). |EC_GROUP_get_curve_name| will always
    346 // return |NID_undef|.
    347 //
    348 // This function is provided for compatibility with some legacy applications
    349 // only. Avoid using arbitrary curves and use |EC_GROUP_new_by_curve_name|
    350 // instead. This ensures the result meets preconditions necessary for
    351 // elliptic curve algorithms to function correctly and securely.
    352 //
    353 // Given invalid parameters, this function may fail or it may return an
    354 // |EC_GROUP| which breaks these preconditions. Subsequent operations may then
    355 // return arbitrary, incorrect values. Callers should not pass
    356 // attacker-controlled values to this function.
    357 OPENSSL_EXPORT EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p,
    358                                                 const BIGNUM *a,
    359                                                 const BIGNUM *b, BN_CTX *ctx);
    360 
    361 // EC_GROUP_set_generator sets the generator for |group| to |generator|, which
    362 // must have the given order and cofactor. It may only be used with |EC_GROUP|
    363 // objects returned by |EC_GROUP_new_curve_GFp| and may only be used once on
    364 // each group. |generator| must have been created using |group|.
    365 OPENSSL_EXPORT int EC_GROUP_set_generator(EC_GROUP *group,
    366                                           const EC_POINT *generator,
    367                                           const BIGNUM *order,
    368                                           const BIGNUM *cofactor);
    369 
    370 // EC_GROUP_get_order sets |*order| to the order of |group|, if it's not
    371 // NULL. It returns one on success and zero otherwise. |ctx| is ignored. Use
    372 // |EC_GROUP_get0_order| instead.
    373 OPENSSL_EXPORT int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order,
    374                                       BN_CTX *ctx);
    375 
    376 #define OPENSSL_EC_EXPLICIT_CURVE 0
    377 #define OPENSSL_EC_NAMED_CURVE 1
    378 
    379 // EC_GROUP_set_asn1_flag does nothing.
    380 OPENSSL_EXPORT void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
    381 
    382 // EC_GROUP_get_asn1_flag returns |OPENSSL_EC_NAMED_CURVE|.
    383 OPENSSL_EXPORT int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
    384 
    385 typedef struct ec_method_st EC_METHOD;
    386 
    387 // EC_GROUP_method_of returns a dummy non-NULL pointer.
    388 OPENSSL_EXPORT const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
    389 
    390 // EC_METHOD_get_field_type returns NID_X9_62_prime_field.
    391 OPENSSL_EXPORT int EC_METHOD_get_field_type(const EC_METHOD *meth);
    392 
    393 // EC_GROUP_set_point_conversion_form aborts the process if |form| is not
    394 // |POINT_CONVERSION_UNCOMPRESSED| and otherwise does nothing.
    395 OPENSSL_EXPORT void EC_GROUP_set_point_conversion_form(
    396     EC_GROUP *group, point_conversion_form_t form);
    397 
    398 // EC_builtin_curve describes a supported elliptic curve.
    399 typedef struct {
    400   int nid;
    401   const char *comment;
    402 } EC_builtin_curve;
    403 
    404 // EC_get_builtin_curves writes at most |max_num_curves| elements to
    405 // |out_curves| and returns the total number that it would have written, had
    406 // |max_num_curves| been large enough.
    407 //
    408 // The |EC_builtin_curve| items describe the supported elliptic curves.
    409 OPENSSL_EXPORT size_t EC_get_builtin_curves(EC_builtin_curve *out_curves,
    410                                             size_t max_num_curves);
    411 
    412 // EC_POINT_clear_free calls |EC_POINT_free|.
    413 OPENSSL_EXPORT void EC_POINT_clear_free(EC_POINT *point);
    414 
    415 
    416 #if defined(__cplusplus)
    417 }  // extern C
    418 #endif
    419 
    420 // Old code expects to get EC_KEY from ec.h.
    421 #include <openssl/ec_key.h>
    422 
    423 #if defined(__cplusplus)
    424 extern "C++" {
    425 
    426 BSSL_NAMESPACE_BEGIN
    427 
    428 BORINGSSL_MAKE_DELETER(EC_POINT, EC_POINT_free)
    429 BORINGSSL_MAKE_DELETER(EC_GROUP, EC_GROUP_free)
    430 
    431 BSSL_NAMESPACE_END
    432 
    433 }  // extern C++
    434 
    435 #endif
    436 
    437 #define EC_R_BUFFER_TOO_SMALL 100
    438 #define EC_R_COORDINATES_OUT_OF_RANGE 101
    439 #define EC_R_D2I_ECPKPARAMETERS_FAILURE 102
    440 #define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 103
    441 #define EC_R_GROUP2PKPARAMETERS_FAILURE 104
    442 #define EC_R_I2D_ECPKPARAMETERS_FAILURE 105
    443 #define EC_R_INCOMPATIBLE_OBJECTS 106
    444 #define EC_R_INVALID_COMPRESSED_POINT 107
    445 #define EC_R_INVALID_COMPRESSION_BIT 108
    446 #define EC_R_INVALID_ENCODING 109
    447 #define EC_R_INVALID_FIELD 110
    448 #define EC_R_INVALID_FORM 111
    449 #define EC_R_INVALID_GROUP_ORDER 112
    450 #define EC_R_INVALID_PRIVATE_KEY 113
    451 #define EC_R_MISSING_PARAMETERS 114
    452 #define EC_R_MISSING_PRIVATE_KEY 115
    453 #define EC_R_NON_NAMED_CURVE 116
    454 #define EC_R_NOT_INITIALIZED 117
    455 #define EC_R_PKPARAMETERS2GROUP_FAILURE 118
    456 #define EC_R_POINT_AT_INFINITY 119
    457 #define EC_R_POINT_IS_NOT_ON_CURVE 120
    458 #define EC_R_SLOT_FULL 121
    459 #define EC_R_UNDEFINED_GENERATOR 122
    460 #define EC_R_UNKNOWN_GROUP 123
    461 #define EC_R_UNKNOWN_ORDER 124
    462 #define EC_R_WRONG_ORDER 125
    463 #define EC_R_BIGNUM_OUT_OF_RANGE 126
    464 #define EC_R_WRONG_CURVE_PARAMETERS 127
    465 #define EC_R_DECODE_ERROR 128
    466 #define EC_R_ENCODE_ERROR 129
    467 #define EC_R_GROUP_MISMATCH 130
    468 #define EC_R_INVALID_COFACTOR 131
    469 #define EC_R_PUBLIC_KEY_VALIDATION_FAILED 132
    470 #define EC_R_INVALID_SCALAR 133
    471 
    472 #endif  // OPENSSL_HEADER_EC_H