include/openssl/ec.h - boringssl - Git at Google

 /* Originally written by Bodo Moeller for the OpenSSL project.
  * ====================================================================
  * Copyright (c) 1998-2005 The OpenSSL Project.  All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
  * are met:
  *
  * 1. Redistributions of source code must retain the above copyright
  *    notice, this list of conditions and the following disclaimer.
  *
  * 2. Redistributions in binary form must reproduce the above copyright
  *    notice, this list of conditions and the following disclaimer in
  *    the documentation and/or other materials provided with the
  *    distribution.
  *
  * 3. All advertising materials mentioning features or use of this
  *    software must display the following acknowledgment:
  *    "This product includes software developed by the OpenSSL Project
  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  *
  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  *    endorse or promote products derived from this software without
  *    prior written permission. For written permission, please contact
  *    openssl-core@openssl.org.
  *
  * 5. Products derived from this software may not be called "OpenSSL"
  *    nor may "OpenSSL" appear in their names without prior written
  *    permission of the OpenSSL Project.
  *
  * 6. Redistributions of any form whatsoever must retain the following
  *    acknowledgment:
  *    "This product includes software developed by the OpenSSL Project
  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  *
  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  * OF THE POSSIBILITY OF SUCH DAMAGE.
  * ====================================================================
  *
  * This product includes cryptographic software written by Eric Young
  * (eay@cryptsoft.com).  This product includes software written by Tim
  * Hudson (tjh@cryptsoft.com).
  *
  */
 /* ====================================================================
  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  *
  * Portions of the attached software ("Contribution") are developed by
  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
  *
  * The Contribution is licensed pursuant to the OpenSSL open source
  * license provided above.
  *
  * The elliptic curve binary polynomial software is originally written by
  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
  * Laboratories. */

 #ifndef OPENSSL_HEADER_EC_H
 #define OPENSSL_HEADER_EC_H

 #include <openssl/base.h>

 #if defined(__cplusplus)
 extern "C" {
 #endif


 // Low-level operations on elliptic curves.


 // point_conversion_form_t enumerates forms, as defined in X9.62 (ECDSA), for
 // the encoding of a elliptic curve point (x,y)
 typedef enum {
   // POINT_CONVERSION_COMPRESSED indicates that the point is encoded as z||x,
   // where the octet z specifies which solution of the quadratic equation y
   // is.
   POINT_CONVERSION_COMPRESSED = 2,

   // POINT_CONVERSION_UNCOMPRESSED indicates that the point is encoded as
   // z||x||y, where z is the octet 0x04.
   POINT_CONVERSION_UNCOMPRESSED = 4,

   // POINT_CONVERSION_HYBRID indicates that the point is encoded as z||x||y,
   // where z specifies which solution of the quadratic equation y is. This is
   // not supported by the code and has never been observed in use.
   //
   // TODO(agl): remove once node.js no longer references this.
   POINT_CONVERSION_HYBRID = 6,
 } point_conversion_form_t;


 // Elliptic curve groups.

 // EC_GROUP_new_by_curve_name returns a fresh EC_GROUP object for the elliptic
 // curve specified by |nid|, or NULL on unsupported NID or allocation failure.
 //
 // The supported NIDs are:
 //   NID_secp224r1 (P-224),
 //   NID_X9_62_prime256v1 (P-256),
 //   NID_secp384r1 (P-384),
 //   NID_secp521r1 (P-521)
 //
 // If in doubt, use |NID_X9_62_prime256v1|, or see the curve25519.h header for
 // more modern primitives.
 OPENSSL_EXPORT EC_GROUP *EC_GROUP_new_by_curve_name(int nid);

 // EC_GROUP_free releases a reference to |group|.
 OPENSSL_EXPORT void EC_GROUP_free(EC_GROUP *group);

 // EC_GROUP_dup takes a reference to |a| and returns it.
 OPENSSL_EXPORT EC_GROUP *EC_GROUP_dup(const EC_GROUP *a);

 // EC_GROUP_cmp returns zero if |a| and |b| are the same group and non-zero
 // otherwise.
 OPENSSL_EXPORT int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b,
                                 BN_CTX *ignored);

 // EC_GROUP_get0_generator returns a pointer to the internal |EC_POINT| object
 // in |group| that specifies the generator for the group.
 OPENSSL_EXPORT const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);

 // EC_GROUP_get0_order returns a pointer to the internal |BIGNUM| object in
 // |group| that specifies the order of the group.
 OPENSSL_EXPORT const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);

 // EC_GROUP_order_bits returns the number of bits of the order of |group|.
 OPENSSL_EXPORT int EC_GROUP_order_bits(const EC_GROUP *group);

 // EC_GROUP_get_cofactor sets |*cofactor| to the cofactor of |group| using
 // |ctx|, if it's not NULL. It returns one on success and zero otherwise.
 OPENSSL_EXPORT int EC_GROUP_get_cofactor(const EC_GROUP *group,
                                          BIGNUM *cofactor, BN_CTX *ctx);

 // EC_GROUP_get_curve_GFp gets various parameters about a group. It sets
 // |*out_p| to the order of the coordinate field and |*out_a| and |*out_b| to
 // the parameters of the curve when expressed as y² = x³ + ax + b. Any of the
 // output parameters can be NULL. It returns one on success and zero on
 // error.
 OPENSSL_EXPORT int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *out_p,
                                           BIGNUM *out_a, BIGNUM *out_b,
                                           BN_CTX *ctx);

 // EC_GROUP_get_curve_name returns a NID that identifies |group|.
 OPENSSL_EXPORT int EC_GROUP_get_curve_name(const EC_GROUP *group);

 // EC_GROUP_get_degree returns the number of bits needed to represent an
 // element of the field underlying |group|.
 OPENSSL_EXPORT unsigned EC_GROUP_get_degree(const EC_GROUP *group);

 // EC_curve_nid2nist returns the NIST name of the elliptic curve specified by
 // |nid|, or NULL if |nid| is not a NIST curve. For example, it returns "P-256"
 // for |NID_X9_62_prime256v1|.
 OPENSSL_EXPORT const char *EC_curve_nid2nist(int nid);

 // EC_curve_nist2nid returns the NID of the elliptic curve specified by the NIST
 // name |name|, or |NID_undef| if |name| is not a recognized name. For example,
 // it returns |NID_X9_62_prime256v1| for "P-256".
 OPENSSL_EXPORT int EC_curve_nist2nid(const char *name);


 // Points on elliptic curves.

 // EC_POINT_new returns a fresh |EC_POINT| object in the given group, or NULL
 // on error.
 OPENSSL_EXPORT EC_POINT *EC_POINT_new(const EC_GROUP *group);

 // EC_POINT_free frees |point| and the data that it points to.
 OPENSSL_EXPORT void EC_POINT_free(EC_POINT *point);

 // EC_POINT_copy sets |*dest| equal to |*src|. It returns one on success and
 // zero otherwise.
 OPENSSL_EXPORT int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src);

 // EC_POINT_dup returns a fresh |EC_POINT| that contains the same values as
 // |src|, or NULL on error.
 OPENSSL_EXPORT EC_POINT *EC_POINT_dup(const EC_POINT *src,
                                       const EC_GROUP *group);

 // EC_POINT_set_to_infinity sets |point| to be the "point at infinity" for the
 // given group.
 OPENSSL_EXPORT int EC_POINT_set_to_infinity(const EC_GROUP *group,
                                             EC_POINT *point);

 // EC_POINT_is_at_infinity returns one iff |point| is the point at infinity and
 // zero otherwise.
 OPENSSL_EXPORT int EC_POINT_is_at_infinity(const EC_GROUP *group,
                                            const EC_POINT *point);

 // EC_POINT_is_on_curve returns one if |point| is an element of |group| and
 // and zero otherwise or when an error occurs. This is different from OpenSSL,
 // which returns -1 on error. If |ctx| is non-NULL, it may be used.
 OPENSSL_EXPORT int EC_POINT_is_on_curve(const EC_GROUP *group,
                                         const EC_POINT *point, BN_CTX *ctx);

 // EC_POINT_cmp returns zero if |a| is equal to |b|, greater than zero if
 // not equal and -1 on error. If |ctx| is not NULL, it may be used.
 OPENSSL_EXPORT int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a,
                                 const EC_POINT *b, BN_CTX *ctx);


 // Point conversion.

 // EC_POINT_get_affine_coordinates_GFp sets |x| and |y| to the affine value of
 // |point| using |ctx|, if it's not NULL. It returns one on success and zero
 // otherwise.
 //
 // Either |x| or |y| may be NULL to skip computing that coordinate. This is
 // slightly faster in the common case where only the x-coordinate is needed.
 OPENSSL_EXPORT int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
                                                        const EC_POINT *point,
                                                        BIGNUM *x, BIGNUM *y,
                                                        BN_CTX *ctx);

 // EC_POINT_get_affine_coordinates is an alias of
 // |EC_POINT_get_affine_coordinates_GFp|.
 OPENSSL_EXPORT int EC_POINT_get_affine_coordinates(const EC_GROUP *group,
                                                    const EC_POINT *point,
                                                    BIGNUM *x, BIGNUM *y,
                                                    BN_CTX *ctx);

 // EC_POINT_set_affine_coordinates_GFp sets the value of |point| to be
 // (|x|, |y|). The |ctx| argument may be used if not NULL. It returns one
 // on success or zero on error. It's considered an error if the point is not on
 // the curve.
 //
 // Note that the corresponding function in OpenSSL versions prior to 1.0.2s does
 // not check if the point is on the curve. This is a security-critical check, so
 // code additionally supporting OpenSSL should repeat the check with
 // |EC_POINT_is_on_curve| or check for older OpenSSL versions with
 // |OPENSSL_VERSION_NUMBER|.
 OPENSSL_EXPORT int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group,
                                                        EC_POINT *point,
                                                        const BIGNUM *x,
                                                        const BIGNUM *y,
                                                        BN_CTX *ctx);

 // EC_POINT_set_affine_coordinates is an alias of
 // |EC_POINT_set_affine_coordinates_GFp|.
 OPENSSL_EXPORT int EC_POINT_set_affine_coordinates(const EC_GROUP *group,
                                                    EC_POINT *point,
                                                    const BIGNUM *x,
                                                    const BIGNUM *y,
                                                    BN_CTX *ctx);

 // EC_POINT_point2oct serialises |point| into the X9.62 form given by |form|
 // into, at most, |len| bytes at |buf|. It returns the number of bytes written
 // or zero on error if |buf| is non-NULL, else the number of bytes needed. The
 // |ctx| argument may be used if not NULL.
 OPENSSL_EXPORT size_t EC_POINT_point2oct(const EC_GROUP *group,
                                          const EC_POINT *point,
                                          point_conversion_form_t form,
                                          uint8_t *buf, size_t len, BN_CTX *ctx);

 // EC_POINT_point2cbb behaves like |EC_POINT_point2oct| but appends the
 // serialised point to |cbb|. It returns one on success and zero on error.
 OPENSSL_EXPORT int EC_POINT_point2cbb(CBB *out, const EC_GROUP *group,
                                       const EC_POINT *point,
                                       point_conversion_form_t form,
                                       BN_CTX *ctx);

 // EC_POINT_oct2point sets |point| from |len| bytes of X9.62 format
 // serialisation in |buf|. It returns one on success and zero on error. The
 // |ctx| argument may be used if not NULL. It's considered an error if |buf|
 // does not represent a point on the curve.
 OPENSSL_EXPORT int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point,
                                       const uint8_t *buf, size_t len,
                                       BN_CTX *ctx);

 // EC_POINT_set_compressed_coordinates_GFp sets |point| to equal the point with
 // the given |x| coordinate and the y coordinate specified by |y_bit| (see
 // X9.62). It returns one on success and zero otherwise.
 OPENSSL_EXPORT int EC_POINT_set_compressed_coordinates_GFp(
     const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, int y_bit,
     BN_CTX *ctx);


 // Group operations.

 // EC_POINT_add sets |r| equal to |a| plus |b|. It returns one on success and
 // zero otherwise. If |ctx| is not NULL, it may be used.
 OPENSSL_EXPORT int EC_POINT_add(const EC_GROUP *group, EC_POINT *r,
                                 const EC_POINT *a, const EC_POINT *b,
                                 BN_CTX *ctx);

 // EC_POINT_dbl sets |r| equal to |a| plus |a|. It returns one on success and
 // zero otherwise. If |ctx| is not NULL, it may be used.
 OPENSSL_EXPORT int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r,
                                 const EC_POINT *a, BN_CTX *ctx);

 // EC_POINT_invert sets |a| equal to minus |a|. It returns one on success and
 // zero otherwise. If |ctx| is not NULL, it may be used.
 OPENSSL_EXPORT int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a,
                                    BN_CTX *ctx);

 // EC_POINT_mul sets r = generator*n + q*m. It returns one on success and zero
 // otherwise. If |ctx| is not NULL, it may be used.
 OPENSSL_EXPORT int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r,
                                 const BIGNUM *n, const EC_POINT *q,
                                 const BIGNUM *m, BN_CTX *ctx);


 // Deprecated functions.

 // EC_GROUP_new_curve_GFp creates a new, arbitrary elliptic curve group based
 // on the equation y² = x³ + a·x + b. It returns the new group or NULL on
 // error.
 //
 // This new group has no generator. It is an error to use a generator-less group
 // with any functions except for |EC_GROUP_free|, |EC_POINT_new|,
 // |EC_POINT_set_affine_coordinates_GFp|, and |EC_GROUP_set_generator|.
 //
 // |EC_GROUP|s returned by this function will always compare as unequal via
 // |EC_GROUP_cmp| (even to themselves). |EC_GROUP_get_curve_name| will always
 // return |NID_undef|.
 //
 // This function is provided for compatibility with some legacy applications
 // only. Avoid using arbitrary curves and use |EC_GROUP_new_by_curve_name|
 // instead. This ensures the result meets preconditions necessary for
 // elliptic curve algorithms to function correctly and securely.
 //
 // Given invalid parameters, this function may fail or it may return an
 // |EC_GROUP| which breaks these preconditions. Subsequent operations may then
 // return arbitrary, incorrect values. Callers should not pass
 // attacker-controlled values to this function.
 OPENSSL_EXPORT EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p,
                                                 const BIGNUM *a,
                                                 const BIGNUM *b, BN_CTX *ctx);

 // EC_GROUP_set_generator sets the generator for |group| to |generator|, which
 // must have the given order and cofactor. It may only be used with |EC_GROUP|
 // objects returned by |EC_GROUP_new_curve_GFp| and may only be used once on
 // each group. |generator| must have been created using |group|.
 OPENSSL_EXPORT int EC_GROUP_set_generator(EC_GROUP *group,
                                           const EC_POINT *generator,
                                           const BIGNUM *order,
                                           const BIGNUM *cofactor);

 // EC_GROUP_get_order sets |*order| to the order of |group|, if it's not
 // NULL. It returns one on success and zero otherwise. |ctx| is ignored. Use
 // |EC_GROUP_get0_order| instead.
 OPENSSL_EXPORT int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order,
                                       BN_CTX *ctx);

 #define OPENSSL_EC_EXPLICIT_CURVE 0
 #define OPENSSL_EC_NAMED_CURVE 1

 // EC_GROUP_set_asn1_flag does nothing.
 OPENSSL_EXPORT void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);

 // EC_GROUP_get_asn1_flag returns |OPENSSL_EC_NAMED_CURVE|.
 OPENSSL_EXPORT int EC_GROUP_get_asn1_flag(const EC_GROUP *group);

 typedef struct ec_method_st EC_METHOD;

 // EC_GROUP_method_of returns a dummy non-NULL pointer.
 OPENSSL_EXPORT const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);

 // EC_METHOD_get_field_type returns NID_X9_62_prime_field.
 OPENSSL_EXPORT int EC_METHOD_get_field_type(const EC_METHOD *meth);

 // EC_GROUP_set_point_conversion_form aborts the process if |form| is not
 // |POINT_CONVERSION_UNCOMPRESSED| and otherwise does nothing.
 OPENSSL_EXPORT void EC_GROUP_set_point_conversion_form(
     EC_GROUP *group, point_conversion_form_t form);

 // EC_builtin_curve describes a supported elliptic curve.
 typedef struct {
   int nid;
   const char *comment;
 } EC_builtin_curve;

 // EC_get_builtin_curves writes at most |max_num_curves| elements to
 // |out_curves| and returns the total number that it would have written, had
 // |max_num_curves| been large enough.
 //
 // The |EC_builtin_curve| items describe the supported elliptic curves.
 OPENSSL_EXPORT size_t EC_get_builtin_curves(EC_builtin_curve *out_curves,
                                             size_t max_num_curves);

 // EC_POINT_clear_free calls |EC_POINT_free|.
 OPENSSL_EXPORT void EC_POINT_clear_free(EC_POINT *point);


 #if defined(__cplusplus)
 }  // extern C
 #endif

 // Old code expects to get EC_KEY from ec.h.
 #include <openssl/ec_key.h>

 #if defined(__cplusplus)
 extern "C++" {

 BSSL_NAMESPACE_BEGIN

 BORINGSSL_MAKE_DELETER(EC_POINT, EC_POINT_free)
 BORINGSSL_MAKE_DELETER(EC_GROUP, EC_GROUP_free)

 BSSL_NAMESPACE_END

 }  // extern C++

 #endif

 #define EC_R_BUFFER_TOO_SMALL 100
 #define EC_R_COORDINATES_OUT_OF_RANGE 101
 #define EC_R_D2I_ECPKPARAMETERS_FAILURE 102
 #define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 103
 #define EC_R_GROUP2PKPARAMETERS_FAILURE 104
 #define EC_R_I2D_ECPKPARAMETERS_FAILURE 105
 #define EC_R_INCOMPATIBLE_OBJECTS 106
 #define EC_R_INVALID_COMPRESSED_POINT 107
 #define EC_R_INVALID_COMPRESSION_BIT 108
 #define EC_R_INVALID_ENCODING 109
 #define EC_R_INVALID_FIELD 110
 #define EC_R_INVALID_FORM 111
 #define EC_R_INVALID_GROUP_ORDER 112
 #define EC_R_INVALID_PRIVATE_KEY 113
 #define EC_R_MISSING_PARAMETERS 114
 #define EC_R_MISSING_PRIVATE_KEY 115
 #define EC_R_NON_NAMED_CURVE 116
 #define EC_R_NOT_INITIALIZED 117
 #define EC_R_PKPARAMETERS2GROUP_FAILURE 118
 #define EC_R_POINT_AT_INFINITY 119
 #define EC_R_POINT_IS_NOT_ON_CURVE 120
 #define EC_R_SLOT_FULL 121
 #define EC_R_UNDEFINED_GENERATOR 122
 #define EC_R_UNKNOWN_GROUP 123
 #define EC_R_UNKNOWN_ORDER 124
 #define EC_R_WRONG_ORDER 125
 #define EC_R_BIGNUM_OUT_OF_RANGE 126
 #define EC_R_WRONG_CURVE_PARAMETERS 127
 #define EC_R_DECODE_ERROR 128
 #define EC_R_ENCODE_ERROR 129
 #define EC_R_GROUP_MISMATCH 130
 #define EC_R_INVALID_COFACTOR 131
 #define EC_R_PUBLIC_KEY_VALIDATION_FAILED 132
 #define EC_R_INVALID_SCALAR 133

 #endif  // OPENSSL_HEADER_EC_H
	/* Originally written by Bodo Moeller for the OpenSSL project.
	* ====================================================================
	* Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
	*
	* Redistribution and use in source and binary forms, with or without
	* modification, are permitted provided that the following conditions
	* are met:
	*
	* 1. Redistributions of source code must retain the above copyright
	* notice, this list of conditions and the following disclaimer.
	*
	* 2. Redistributions in binary form must reproduce the above copyright
	* notice, this list of conditions and the following disclaimer in
	* the documentation and/or other materials provided with the
	* distribution.
	*
	* 3. All advertising materials mentioning features or use of this
	* software must display the following acknowledgment:
	* "This product includes software developed by the OpenSSL Project
	* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
	*
	* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
	* endorse or promote products derived from this software without
	* prior written permission. For written permission, please contact
	* openssl-core@openssl.org.
	*
	* 5. Products derived from this software may not be called "OpenSSL"
	* nor may "OpenSSL" appear in their names without prior written
	* permission of the OpenSSL Project.
	*
	* 6. Redistributions of any form whatsoever must retain the following
	* acknowledgment:
	* "This product includes software developed by the OpenSSL Project
	* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
	*
	* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
	* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
	* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
	* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
	* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
	* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
	* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
	* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
	* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
	* OF THE POSSIBILITY OF SUCH DAMAGE.
	* ====================================================================
	*
	* This product includes cryptographic software written by Eric Young
	* (eay@cryptsoft.com). This product includes software written by Tim
	* Hudson (tjh@cryptsoft.com).
	*
	*/
	/* ====================================================================
	* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
	*
	* Portions of the attached software ("Contribution") are developed by
	* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
	*
	* The Contribution is licensed pursuant to the OpenSSL open source
	* license provided above.
	*
	* The elliptic curve binary polynomial software is originally written by
	* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
	* Laboratories. */

	#ifndef OPENSSL_HEADER_EC_H
	#define OPENSSL_HEADER_EC_H

	#include <openssl/base.h>

	#if defined(__cplusplus)
	extern "C" {
	#endif


	// Low-level operations on elliptic curves.


	// point_conversion_form_t enumerates forms, as defined in X9.62 (ECDSA), for
	// the encoding of a elliptic curve point (x,y)
	typedef enum {
	// POINT_CONVERSION_COMPRESSED indicates that the point is encoded as z\|\|x,
	// where the octet z specifies which solution of the quadratic equation y
	// is.
	POINT_CONVERSION_COMPRESSED = 2,

	// POINT_CONVERSION_UNCOMPRESSED indicates that the point is encoded as
	// z\|\|x\|\|y, where z is the octet 0x04.
	POINT_CONVERSION_UNCOMPRESSED = 4,

	// POINT_CONVERSION_HYBRID indicates that the point is encoded as z\|\|x\|\|y,
	// where z specifies which solution of the quadratic equation y is. This is
	// not supported by the code and has never been observed in use.
	//
	// TODO(agl): remove once node.js no longer references this.
	POINT_CONVERSION_HYBRID = 6,
	} point_conversion_form_t;


	// Elliptic curve groups.

	// EC_GROUP_new_by_curve_name returns a fresh EC_GROUP object for the elliptic
	// curve specified by \|nid\|, or NULL on unsupported NID or allocation failure.
	//
	// The supported NIDs are:
	// NID_secp224r1 (P-224),
	// NID_X9_62_prime256v1 (P-256),
	// NID_secp384r1 (P-384),
	// NID_secp521r1 (P-521)
	//
	// If in doubt, use \|NID_X9_62_prime256v1\|, or see the curve25519.h header for
	// more modern primitives.
	OPENSSL_EXPORT EC_GROUP *EC_GROUP_new_by_curve_name(int nid);

	// EC_GROUP_free releases a reference to \|group\|.
	OPENSSL_EXPORT void EC_GROUP_free(EC_GROUP *group);

	// EC_GROUP_dup takes a reference to \|a\| and returns it.
	OPENSSL_EXPORT EC_GROUP EC_GROUP_dup(const EC_GROUP a);

	// EC_GROUP_cmp returns zero if \|a\| and \|b\| are the same group and non-zero
	// otherwise.
	OPENSSL_EXPORT int EC_GROUP_cmp(const EC_GROUP a, const EC_GROUP b,
	BN_CTX *ignored);

	// EC_GROUP_get0_generator returns a pointer to the internal \|EC_POINT\| object
	// in \|group\| that specifies the generator for the group.
	OPENSSL_EXPORT const EC_POINT EC_GROUP_get0_generator(const EC_GROUP group);

	// EC_GROUP_get0_order returns a pointer to the internal \|BIGNUM\| object in
	// \|group\| that specifies the order of the group.
	OPENSSL_EXPORT const BIGNUM EC_GROUP_get0_order(const EC_GROUP group);

	// EC_GROUP_order_bits returns the number of bits of the order of \|group\|.
	OPENSSL_EXPORT int EC_GROUP_order_bits(const EC_GROUP *group);

	// EC_GROUP_get_cofactor sets \|*cofactor\| to the cofactor of \|group\| using
	// \|ctx\|, if it's not NULL. It returns one on success and zero otherwise.
	OPENSSL_EXPORT int EC_GROUP_get_cofactor(const EC_GROUP *group,
	BIGNUM cofactor, BN_CTX ctx);

	// EC_GROUP_get_curve_GFp gets various parameters about a group. It sets
	// \|out_p\| to the order of the coordinate field and \|out_a\| and \|*out_b\| to
	// the parameters of the curve when expressed as y² = x³ + ax + b. Any of the
	// output parameters can be NULL. It returns one on success and zero on
	// error.
	OPENSSL_EXPORT int EC_GROUP_get_curve_GFp(const EC_GROUP group, BIGNUM out_p,
	BIGNUM out_a, BIGNUM out_b,
	BN_CTX *ctx);

	// EC_GROUP_get_curve_name returns a NID that identifies \|group\|.
	OPENSSL_EXPORT int EC_GROUP_get_curve_name(const EC_GROUP *group);

	// EC_GROUP_get_degree returns the number of bits needed to represent an
	// element of the field underlying \|group\|.
	OPENSSL_EXPORT unsigned EC_GROUP_get_degree(const EC_GROUP *group);

	// EC_curve_nid2nist returns the NIST name of the elliptic curve specified by
	// \|nid\|, or NULL if \|nid\| is not a NIST curve. For example, it returns "P-256"
	// for \|NID_X9_62_prime256v1\|.
	OPENSSL_EXPORT const char *EC_curve_nid2nist(int nid);

	// EC_curve_nist2nid returns the NID of the elliptic curve specified by the NIST
	// name \|name\|, or \|NID_undef\| if \|name\| is not a recognized name. For example,
	// it returns \|NID_X9_62_prime256v1\| for "P-256".
	OPENSSL_EXPORT int EC_curve_nist2nid(const char *name);


	// Points on elliptic curves.

	// EC_POINT_new returns a fresh \|EC_POINT\| object in the given group, or NULL
	// on error.
	OPENSSL_EXPORT EC_POINT EC_POINT_new(const EC_GROUP group);

	// EC_POINT_free frees \|point\| and the data that it points to.
	OPENSSL_EXPORT void EC_POINT_free(EC_POINT *point);

	// EC_POINT_copy sets \|dest\| equal to \|src\|. It returns one on success and
	// zero otherwise.
	OPENSSL_EXPORT int EC_POINT_copy(EC_POINT dest, const EC_POINT src);

	// EC_POINT_dup returns a fresh \|EC_POINT\| that contains the same values as
	// \|src\|, or NULL on error.
	OPENSSL_EXPORT EC_POINT EC_POINT_dup(const EC_POINT src,
	const EC_GROUP *group);

	// EC_POINT_set_to_infinity sets \|point\| to be the "point at infinity" for the
	// given group.
	OPENSSL_EXPORT int EC_POINT_set_to_infinity(const EC_GROUP *group,
	EC_POINT *point);

	// EC_POINT_is_at_infinity returns one iff \|point\| is the point at infinity and
	// zero otherwise.
	OPENSSL_EXPORT int EC_POINT_is_at_infinity(const EC_GROUP *group,
	const EC_POINT *point);

	// EC_POINT_is_on_curve returns one if \|point\| is an element of \|group\| and
	// and zero otherwise or when an error occurs. This is different from OpenSSL,
	// which returns -1 on error. If \|ctx\| is non-NULL, it may be used.
	OPENSSL_EXPORT int EC_POINT_is_on_curve(const EC_GROUP *group,
	const EC_POINT point, BN_CTX ctx);

	// EC_POINT_cmp returns zero if \|a\| is equal to \|b\|, greater than zero if
	// not equal and -1 on error. If \|ctx\| is not NULL, it may be used.
	OPENSSL_EXPORT int EC_POINT_cmp(const EC_GROUP group, const EC_POINT a,
	const EC_POINT b, BN_CTX ctx);


	// Point conversion.

	// EC_POINT_get_affine_coordinates_GFp sets \|x\| and \|y\| to the affine value of
	// \|point\| using \|ctx\|, if it's not NULL. It returns one on success and zero
	// otherwise.
	//
	// Either \|x\| or \|y\| may be NULL to skip computing that coordinate. This is
	// slightly faster in the common case where only the x-coordinate is needed.
	OPENSSL_EXPORT int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
	const EC_POINT *point,
	BIGNUM x, BIGNUM y,
	BN_CTX *ctx);

	// EC_POINT_get_affine_coordinates is an alias of
	// \|EC_POINT_get_affine_coordinates_GFp\|.
	OPENSSL_EXPORT int EC_POINT_get_affine_coordinates(const EC_GROUP *group,
	const EC_POINT *point,
	BIGNUM x, BIGNUM y,
	BN_CTX *ctx);

	// EC_POINT_set_affine_coordinates_GFp sets the value of \|point\| to be
	// (\|x\|, \|y\|). The \|ctx\| argument may be used if not NULL. It returns one
	// on success or zero on error. It's considered an error if the point is not on
	// the curve.
	//
	// Note that the corresponding function in OpenSSL versions prior to 1.0.2s does
	// not check if the point is on the curve. This is a security-critical check, so
	// code additionally supporting OpenSSL should repeat the check with
	// \|EC_POINT_is_on_curve\| or check for older OpenSSL versions with
	// \|OPENSSL_VERSION_NUMBER\|.
	OPENSSL_EXPORT int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group,
	EC_POINT *point,
	const BIGNUM *x,
	const BIGNUM *y,
	BN_CTX *ctx);

	// EC_POINT_set_affine_coordinates is an alias of
	// \|EC_POINT_set_affine_coordinates_GFp\|.
	OPENSSL_EXPORT int EC_POINT_set_affine_coordinates(const EC_GROUP *group,
	EC_POINT *point,
	const BIGNUM *x,
	const BIGNUM *y,
	BN_CTX *ctx);

	// EC_POINT_point2oct serialises \|point\| into the X9.62 form given by \|form\|
	// into, at most, \|len\| bytes at \|buf\|. It returns the number of bytes written
	// or zero on error if \|buf\| is non-NULL, else the number of bytes needed. The
	// \|ctx\| argument may be used if not NULL.
	OPENSSL_EXPORT size_t EC_POINT_point2oct(const EC_GROUP *group,
	const EC_POINT *point,
	point_conversion_form_t form,
	uint8_t buf, size_t len, BN_CTX ctx);

	// EC_POINT_point2cbb behaves like \|EC_POINT_point2oct\| but appends the
	// serialised point to \|cbb\|. It returns one on success and zero on error.
	OPENSSL_EXPORT int EC_POINT_point2cbb(CBB out, const EC_GROUP group,
	const EC_POINT *point,
	point_conversion_form_t form,
	BN_CTX *ctx);

	// EC_POINT_oct2point sets \|point\| from \|len\| bytes of X9.62 format
	// serialisation in \|buf\|. It returns one on success and zero on error. The
	// \|ctx\| argument may be used if not NULL. It's considered an error if \|buf\|
	// does not represent a point on the curve.
	OPENSSL_EXPORT int EC_POINT_oct2point(const EC_GROUP group, EC_POINT point,
	const uint8_t *buf, size_t len,
	BN_CTX *ctx);

	// EC_POINT_set_compressed_coordinates_GFp sets \|point\| to equal the point with
	// the given \|x\| coordinate and the y coordinate specified by \|y_bit\| (see
	// X9.62). It returns one on success and zero otherwise.
	OPENSSL_EXPORT int EC_POINT_set_compressed_coordinates_GFp(
	const EC_GROUP group, EC_POINT point, const BIGNUM *x, int y_bit,
	BN_CTX *ctx);


	// Group operations.

	// EC_POINT_add sets \|r\| equal to \|a\| plus \|b\|. It returns one on success and
	// zero otherwise. If \|ctx\| is not NULL, it may be used.
	OPENSSL_EXPORT int EC_POINT_add(const EC_GROUP group, EC_POINT r,
	const EC_POINT a, const EC_POINT b,
	BN_CTX *ctx);

	// EC_POINT_dbl sets \|r\| equal to \|a\| plus \|a\|. It returns one on success and
	// zero otherwise. If \|ctx\| is not NULL, it may be used.
	OPENSSL_EXPORT int EC_POINT_dbl(const EC_GROUP group, EC_POINT r,
	const EC_POINT a, BN_CTX ctx);

	// EC_POINT_invert sets \|a\| equal to minus \|a\|. It returns one on success and
	// zero otherwise. If \|ctx\| is not NULL, it may be used.
	OPENSSL_EXPORT int EC_POINT_invert(const EC_GROUP group, EC_POINT a,
	BN_CTX *ctx);

	// EC_POINT_mul sets r = generatorn + qm. It returns one on success and zero
	// otherwise. If \|ctx\| is not NULL, it may be used.
	OPENSSL_EXPORT int EC_POINT_mul(const EC_GROUP group, EC_POINT r,
	const BIGNUM n, const EC_POINT q,
	const BIGNUM m, BN_CTX ctx);


	// Deprecated functions.

	// EC_GROUP_new_curve_GFp creates a new, arbitrary elliptic curve group based
	// on the equation y² = x³ + a·x + b. It returns the new group or NULL on
	// error.
	//
	// This new group has no generator. It is an error to use a generator-less group
	// with any functions except for \|EC_GROUP_free\|, \|EC_POINT_new\|,
	// \|EC_POINT_set_affine_coordinates_GFp\|, and \|EC_GROUP_set_generator\|.
	//
	// \|EC_GROUP\|s returned by this function will always compare as unequal via
	// \|EC_GROUP_cmp\| (even to themselves). \|EC_GROUP_get_curve_name\| will always
	// return \|NID_undef\|.
	//
	// This function is provided for compatibility with some legacy applications
	// only. Avoid using arbitrary curves and use \|EC_GROUP_new_by_curve_name\|
	// instead. This ensures the result meets preconditions necessary for
	// elliptic curve algorithms to function correctly and securely.
	//
	// Given invalid parameters, this function may fail or it may return an
	// \|EC_GROUP\| which breaks these preconditions. Subsequent operations may then
	// return arbitrary, incorrect values. Callers should not pass
	// attacker-controlled values to this function.
	OPENSSL_EXPORT EC_GROUP EC_GROUP_new_curve_GFp(const BIGNUM p,
	const BIGNUM *a,
	const BIGNUM b, BN_CTX ctx);

	// EC_GROUP_set_generator sets the generator for \|group\| to \|generator\|, which
	// must have the given order and cofactor. It may only be used with \|EC_GROUP\|
	// objects returned by \|EC_GROUP_new_curve_GFp\| and may only be used once on
	// each group. \|generator\| must have been created using \|group\|.
	OPENSSL_EXPORT int EC_GROUP_set_generator(EC_GROUP *group,
	const EC_POINT *generator,
	const BIGNUM *order,
	const BIGNUM *cofactor);

	// EC_GROUP_get_order sets \|*order\| to the order of \|group\|, if it's not
	// NULL. It returns one on success and zero otherwise. \|ctx\| is ignored. Use
	// \|EC_GROUP_get0_order\| instead.
	OPENSSL_EXPORT int EC_GROUP_get_order(const EC_GROUP group, BIGNUM order,
	BN_CTX *ctx);

	#define OPENSSL_EC_EXPLICIT_CURVE 0
	#define OPENSSL_EC_NAMED_CURVE 1

	// EC_GROUP_set_asn1_flag does nothing.
	OPENSSL_EXPORT void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);

	// EC_GROUP_get_asn1_flag returns \|OPENSSL_EC_NAMED_CURVE\|.
	OPENSSL_EXPORT int EC_GROUP_get_asn1_flag(const EC_GROUP *group);

	typedef struct ec_method_st EC_METHOD;

	// EC_GROUP_method_of returns a dummy non-NULL pointer.
	OPENSSL_EXPORT const EC_METHOD EC_GROUP_method_of(const EC_GROUP group);

	// EC_METHOD_get_field_type returns NID_X9_62_prime_field.
	OPENSSL_EXPORT int EC_METHOD_get_field_type(const EC_METHOD *meth);

	// EC_GROUP_set_point_conversion_form aborts the process if \|form\| is not
	// \|POINT_CONVERSION_UNCOMPRESSED\| and otherwise does nothing.
	OPENSSL_EXPORT void EC_GROUP_set_point_conversion_form(
	EC_GROUP *group, point_conversion_form_t form);

	// EC_builtin_curve describes a supported elliptic curve.
	typedef struct {
	int nid;
	const char *comment;
	} EC_builtin_curve;

	// EC_get_builtin_curves writes at most \|max_num_curves\| elements to
	// \|out_curves\| and returns the total number that it would have written, had
	// \|max_num_curves\| been large enough.
	//
	// The \|EC_builtin_curve\| items describe the supported elliptic curves.
	OPENSSL_EXPORT size_t EC_get_builtin_curves(EC_builtin_curve *out_curves,
	size_t max_num_curves);

	// EC_POINT_clear_free calls \|EC_POINT_free\|.
	OPENSSL_EXPORT void EC_POINT_clear_free(EC_POINT *point);


	#if defined(__cplusplus)
	} // extern C
	#endif

	// Old code expects to get EC_KEY from ec.h.
	#include <openssl/ec_key.h>

	#if defined(__cplusplus)
	extern "C++" {

	BSSL_NAMESPACE_BEGIN

	BORINGSSL_MAKE_DELETER(EC_POINT, EC_POINT_free)
	BORINGSSL_MAKE_DELETER(EC_GROUP, EC_GROUP_free)

	BSSL_NAMESPACE_END

	} // extern C++

	#endif

	#define EC_R_BUFFER_TOO_SMALL 100
	#define EC_R_COORDINATES_OUT_OF_RANGE 101
	#define EC_R_D2I_ECPKPARAMETERS_FAILURE 102
	#define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 103
	#define EC_R_GROUP2PKPARAMETERS_FAILURE 104
	#define EC_R_I2D_ECPKPARAMETERS_FAILURE 105
	#define EC_R_INCOMPATIBLE_OBJECTS 106
	#define EC_R_INVALID_COMPRESSED_POINT 107
	#define EC_R_INVALID_COMPRESSION_BIT 108
	#define EC_R_INVALID_ENCODING 109
	#define EC_R_INVALID_FIELD 110
	#define EC_R_INVALID_FORM 111
	#define EC_R_INVALID_GROUP_ORDER 112
	#define EC_R_INVALID_PRIVATE_KEY 113
	#define EC_R_MISSING_PARAMETERS 114
	#define EC_R_MISSING_PRIVATE_KEY 115
	#define EC_R_NON_NAMED_CURVE 116
	#define EC_R_NOT_INITIALIZED 117
	#define EC_R_PKPARAMETERS2GROUP_FAILURE 118
	#define EC_R_POINT_AT_INFINITY 119
	#define EC_R_POINT_IS_NOT_ON_CURVE 120
	#define EC_R_SLOT_FULL 121
	#define EC_R_UNDEFINED_GENERATOR 122
	#define EC_R_UNKNOWN_GROUP 123
	#define EC_R_UNKNOWN_ORDER 124
	#define EC_R_WRONG_ORDER 125
	#define EC_R_BIGNUM_OUT_OF_RANGE 126
	#define EC_R_WRONG_CURVE_PARAMETERS 127
	#define EC_R_DECODE_ERROR 128
	#define EC_R_ENCODE_ERROR 129
	#define EC_R_GROUP_MISMATCH 130
	#define EC_R_INVALID_COFACTOR 131
	#define EC_R_PUBLIC_KEY_VALIDATION_FAILED 132
	#define EC_R_INVALID_SCALAR 133

	#endif // OPENSSL_HEADER_EC_H