--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/CSP2/CSP2_env/env-d9b9114564458d9d-741b3de822f2aaca6c6caa4325c4afce/include/openssl/ec.h	Tue Mar 18 17:55:14 2025 -0400
@@ -0,0 +1,1484 @@
+/*
+ * Copyright 2002-2021 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
+ *
+ * Licensed under the OpenSSL license (the "License").  You may not use
+ * this file except in compliance with the License.  You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
+ */
+
+#ifndef HEADER_EC_H
+# define HEADER_EC_H
+
+# include <openssl/opensslconf.h>
+
+# ifndef OPENSSL_NO_EC
+# include <openssl/asn1.h>
+# include <openssl/symhacks.h>
+# if OPENSSL_API_COMPAT < 0x10100000L
+#  include <openssl/bn.h>
+# endif
+# include <openssl/ecerr.h>
+# ifdef  __cplusplus
+extern "C" {
+# endif
+
+# ifndef OPENSSL_ECC_MAX_FIELD_BITS
+#  define OPENSSL_ECC_MAX_FIELD_BITS 661
+# endif
+
+/** Enum for the point conversion form as defined in X9.62 (ECDSA)
+ *  for the encoding of a elliptic curve point (x,y) */
+typedef enum {
+        /** the point is encoded as z||x, where the octet z specifies
+         *  which solution of the quadratic equation y is  */
+    POINT_CONVERSION_COMPRESSED = 2,
+        /** the point is encoded as z||x||y, where z is the octet 0x04  */
+    POINT_CONVERSION_UNCOMPRESSED = 4,
+        /** the point is encoded as z||x||y, where the octet z specifies
+         *  which solution of the quadratic equation y is  */
+    POINT_CONVERSION_HYBRID = 6
+} point_conversion_form_t;
+
+typedef struct ec_method_st EC_METHOD;
+typedef struct ec_group_st EC_GROUP;
+typedef struct ec_point_st EC_POINT;
+typedef struct ecpk_parameters_st ECPKPARAMETERS;
+typedef struct ec_parameters_st ECPARAMETERS;
+
+/********************************************************************/
+/*               EC_METHODs for curves over GF(p)                   */
+/********************************************************************/
+
+/** Returns the basic GFp ec methods which provides the basis for the
+ *  optimized methods.
+ *  \return  EC_METHOD object
+ */
+const EC_METHOD *EC_GFp_simple_method(void);
+
+/** Returns GFp methods using montgomery multiplication.
+ *  \return  EC_METHOD object
+ */
+const EC_METHOD *EC_GFp_mont_method(void);
+
+/** Returns GFp methods using optimized methods for NIST recommended curves
+ *  \return  EC_METHOD object
+ */
+const EC_METHOD *EC_GFp_nist_method(void);
+
+# ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
+/** Returns 64-bit optimized methods for nistp224
+ *  \return  EC_METHOD object
+ */
+const EC_METHOD *EC_GFp_nistp224_method(void);
+
+/** Returns 64-bit optimized methods for nistp256
+ *  \return  EC_METHOD object
+ */
+const EC_METHOD *EC_GFp_nistp256_method(void);
+
+/** Returns 64-bit optimized methods for nistp521
+ *  \return  EC_METHOD object
+ */
+const EC_METHOD *EC_GFp_nistp521_method(void);
+# endif
+
+# ifndef OPENSSL_NO_EC2M
+/********************************************************************/
+/*           EC_METHOD for curves over GF(2^m)                      */
+/********************************************************************/
+
+/** Returns the basic GF2m ec method
+ *  \return  EC_METHOD object
+ */
+const EC_METHOD *EC_GF2m_simple_method(void);
+
+# endif
+
+/********************************************************************/
+/*                   EC_GROUP functions                             */
+/********************************************************************/
+
+/** Creates a new EC_GROUP object
+ *  \param   meth  EC_METHOD to use
+ *  \return  newly created EC_GROUP object or NULL in case of an error.
+ */
+EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
+
+/** Frees a EC_GROUP object
+ *  \param  group  EC_GROUP object to be freed.
+ */
+void EC_GROUP_free(EC_GROUP *group);
+
+/** Clears and frees a EC_GROUP object
+ *  \param  group  EC_GROUP object to be cleared and freed.
+ */
+void EC_GROUP_clear_free(EC_GROUP *group);
+
+/** Copies EC_GROUP objects. Note: both EC_GROUPs must use the same EC_METHOD.
+ *  \param  dst  destination EC_GROUP object
+ *  \param  src  source EC_GROUP object
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
+
+/** Creates a new EC_GROUP object and copies the copies the content
+ *  form src to the newly created EC_KEY object
+ *  \param  src  source EC_GROUP object
+ *  \return newly created EC_GROUP object or NULL in case of an error.
+ */
+EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
+
+/** Returns the EC_METHOD of the EC_GROUP object.
+ *  \param  group  EC_GROUP object
+ *  \return EC_METHOD used in this EC_GROUP object.
+ */
+const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
+
+/** Returns the field type of the EC_METHOD.
+ *  \param  meth  EC_METHOD object
+ *  \return NID of the underlying field type OID.
+ */
+int EC_METHOD_get_field_type(const EC_METHOD *meth);
+
+/** Sets the generator and its order/cofactor of a EC_GROUP object.
+ *  \param  group      EC_GROUP object
+ *  \param  generator  EC_POINT object with the generator.
+ *  \param  order      the order of the group generated by the generator.
+ *  \param  cofactor   the index of the sub-group generated by the generator
+ *                     in the group of all points on the elliptic curve.
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
+                           const BIGNUM *order, const BIGNUM *cofactor);
+
+/** Returns the generator of a EC_GROUP object.
+ *  \param  group  EC_GROUP object
+ *  \return the currently used generator (possibly NULL).
+ */
+const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
+
+/** Returns the montgomery data for order(Generator)
+ *  \param  group  EC_GROUP object
+ *  \return the currently used montgomery data (possibly NULL).
+*/
+BN_MONT_CTX *EC_GROUP_get_mont_data(const EC_GROUP *group);
+
+/** Gets the order of a EC_GROUP
+ *  \param  group  EC_GROUP object
+ *  \param  order  BIGNUM to which the order is copied
+ *  \param  ctx    unused
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
+
+/** Gets the order of an EC_GROUP
+ *  \param  group  EC_GROUP object
+ *  \return the group order
+ */
+const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);
+
+/** Gets the number of bits of the order of an EC_GROUP
+ *  \param  group  EC_GROUP object
+ *  \return number of bits of group order.
+ */
+int EC_GROUP_order_bits(const EC_GROUP *group);
+
+/** Gets the cofactor of a EC_GROUP
+ *  \param  group     EC_GROUP object
+ *  \param  cofactor  BIGNUM to which the cofactor is copied
+ *  \param  ctx       unused
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor,
+                          BN_CTX *ctx);
+
+/** Gets the cofactor of an EC_GROUP
+ *  \param  group  EC_GROUP object
+ *  \return the group cofactor
+ */
+const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group);
+
+/** Sets the name of a EC_GROUP object
+ *  \param  group  EC_GROUP object
+ *  \param  nid    NID of the curve name OID
+ */
+void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
+
+/** Returns the curve name of a EC_GROUP object
+ *  \param  group  EC_GROUP object
+ *  \return NID of the curve name OID or 0 if not set.
+ */
+int EC_GROUP_get_curve_name(const EC_GROUP *group);
+
+void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
+int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
+
+void EC_GROUP_set_point_conversion_form(EC_GROUP *group,
+                                        point_conversion_form_t form);
+point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
+
+unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
+size_t EC_GROUP_get_seed_len(const EC_GROUP *);
+size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
+
+/** Sets the parameters of a ec curve defined by y^2 = x^3 + a*x + b (for GFp)
+ *  or y^2 + x*y = x^3 + a*x^2 + b (for GF2m)
+ *  \param  group  EC_GROUP object
+ *  \param  p      BIGNUM with the prime number (GFp) or the polynomial
+ *                 defining the underlying field (GF2m)
+ *  \param  a      BIGNUM with parameter a of the equation
+ *  \param  b      BIGNUM with parameter b of the equation
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_GROUP_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
+                       const BIGNUM *b, BN_CTX *ctx);
+
+/** Gets the parameters of the ec curve defined by y^2 = x^3 + a*x + b (for GFp)
+ *  or y^2 + x*y = x^3 + a*x^2 + b (for GF2m)
+ *  \param  group  EC_GROUP object
+ *  \param  p      BIGNUM with the prime number (GFp) or the polynomial
+ *                 defining the underlying field (GF2m)
+ *  \param  a      BIGNUM for parameter a of the equation
+ *  \param  b      BIGNUM for parameter b of the equation
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b,
+                       BN_CTX *ctx);
+
+/** Sets the parameters of an ec curve. Synonym for EC_GROUP_set_curve
+ *  \param  group  EC_GROUP object
+ *  \param  p      BIGNUM with the prime number (GFp) or the polynomial
+ *                 defining the underlying field (GF2m)
+ *  \param  a      BIGNUM with parameter a of the equation
+ *  \param  b      BIGNUM with parameter b of the equation
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p,
+                                              const BIGNUM *a, const BIGNUM *b,
+                                              BN_CTX *ctx))
+
+/** Gets the parameters of an ec curve. Synonym for EC_GROUP_get_curve
+ *  \param  group  EC_GROUP object
+ *  \param  p      BIGNUM with the prime number (GFp) or the polynomial
+ *                 defining the underlying field (GF2m)
+ *  \param  a      BIGNUM for parameter a of the equation
+ *  \param  b      BIGNUM for parameter b of the equation
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p,
+                                              BIGNUM *a, BIGNUM *b,
+                                              BN_CTX *ctx))
+
+# ifndef OPENSSL_NO_EC2M
+/** Sets the parameter of an ec curve. Synonym for EC_GROUP_set_curve
+ *  \param  group  EC_GROUP object
+ *  \param  p      BIGNUM with the prime number (GFp) or the polynomial
+ *                 defining the underlying field (GF2m)
+ *  \param  a      BIGNUM with parameter a of the equation
+ *  \param  b      BIGNUM with parameter b of the equation
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p,
+                                               const BIGNUM *a, const BIGNUM *b,
+                                               BN_CTX *ctx))
+
+/** Gets the parameters of an ec curve. Synonym for EC_GROUP_get_curve
+ *  \param  group  EC_GROUP object
+ *  \param  p      BIGNUM with the prime number (GFp) or the polynomial
+ *                 defining the underlying field (GF2m)
+ *  \param  a      BIGNUM for parameter a of the equation
+ *  \param  b      BIGNUM for parameter b of the equation
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p,
+                                               BIGNUM *a, BIGNUM *b,
+                                               BN_CTX *ctx))
+# endif
+/** Returns the number of bits needed to represent a field element
+ *  \param  group  EC_GROUP object
+ *  \return number of bits needed to represent a field element
+ */
+int EC_GROUP_get_degree(const EC_GROUP *group);
+
+/** Checks whether the parameter in the EC_GROUP define a valid ec group
+ *  \param  group  EC_GROUP object
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 if group is a valid ec group and 0 otherwise
+ */
+int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
+
+/** Checks whether the discriminant of the elliptic curve is zero or not
+ *  \param  group  EC_GROUP object
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 if the discriminant is not zero and 0 otherwise
+ */
+int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
+
+/** Compares two EC_GROUP objects
+ *  \param  a    first EC_GROUP object
+ *  \param  b    second EC_GROUP object
+ *  \param  ctx  BN_CTX object (optional)
+ *  \return 0 if the groups are equal, 1 if not, or -1 on error
+ */
+int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
+
+/*
+ * EC_GROUP_new_GF*() calls EC_GROUP_new() and EC_GROUP_set_GF*() after
+ * choosing an appropriate EC_METHOD
+ */
+
+/** Creates a new EC_GROUP object with the specified parameters defined
+ *  over GFp (defined by the equation y^2 = x^3 + a*x + b)
+ *  \param  p    BIGNUM with the prime number
+ *  \param  a    BIGNUM with the parameter a of the equation
+ *  \param  b    BIGNUM with the parameter b of the equation
+ *  \param  ctx  BN_CTX object (optional)
+ *  \return newly created EC_GROUP object with the specified parameters
+ */
+EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a,
+                                 const BIGNUM *b, BN_CTX *ctx);
+# ifndef OPENSSL_NO_EC2M
+/** Creates a new EC_GROUP object with the specified parameters defined
+ *  over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b)
+ *  \param  p    BIGNUM with the polynomial defining the underlying field
+ *  \param  a    BIGNUM with the parameter a of the equation
+ *  \param  b    BIGNUM with the parameter b of the equation
+ *  \param  ctx  BN_CTX object (optional)
+ *  \return newly created EC_GROUP object with the specified parameters
+ */
+EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a,
+                                  const BIGNUM *b, BN_CTX *ctx);
+# endif
+
+/** Creates a EC_GROUP object with a curve specified by a NID
+ *  \param  nid  NID of the OID of the curve name
+ *  \return newly created EC_GROUP object with specified curve or NULL
+ *          if an error occurred
+ */
+EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
+
+/** Creates a new EC_GROUP object from an ECPARAMETERS object
+ *  \param  params  pointer to the ECPARAMETERS object
+ *  \return newly created EC_GROUP object with specified curve or NULL
+ *          if an error occurred
+ */
+EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params);
+
+/** Creates an ECPARAMETERS object for the given EC_GROUP object.
+ *  \param  group   pointer to the EC_GROUP object
+ *  \param  params  pointer to an existing ECPARAMETERS object or NULL
+ *  \return pointer to the new ECPARAMETERS object or NULL
+ *          if an error occurred.
+ */
+ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group,
+                                        ECPARAMETERS *params);
+
+/** Creates a new EC_GROUP object from an ECPKPARAMETERS object
+ *  \param  params  pointer to an existing ECPKPARAMETERS object, or NULL
+ *  \return newly created EC_GROUP object with specified curve, or NULL
+ *          if an error occurred
+ */
+EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params);
+
+/** Creates an ECPKPARAMETERS object for the given EC_GROUP object.
+ *  \param  group   pointer to the EC_GROUP object
+ *  \param  params  pointer to an existing ECPKPARAMETERS object or NULL
+ *  \return pointer to the new ECPKPARAMETERS object or NULL
+ *          if an error occurred.
+ */
+ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group,
+                                            ECPKPARAMETERS *params);
+
+/********************************************************************/
+/*               handling of internal curves                        */
+/********************************************************************/
+
+typedef struct {
+    int nid;
+    const char *comment;
+} EC_builtin_curve;
+
+/*
+ * EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number of all
+ * available curves or zero if a error occurred. In case r is not zero,
+ * nitems EC_builtin_curve structures are filled with the data of the first
+ * nitems internal groups
+ */
+size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
+
+const char *EC_curve_nid2nist(int nid);
+int EC_curve_nist2nid(const char *name);
+
+/********************************************************************/
+/*                    EC_POINT functions                            */
+/********************************************************************/
+
+/** Creates a new EC_POINT object for the specified EC_GROUP
+ *  \param  group  EC_GROUP the underlying EC_GROUP object
+ *  \return newly created EC_POINT object or NULL if an error occurred
+ */
+EC_POINT *EC_POINT_new(const EC_GROUP *group);
+
+/** Frees a EC_POINT object
+ *  \param  point  EC_POINT object to be freed
+ */
+void EC_POINT_free(EC_POINT *point);
+
+/** Clears and frees a EC_POINT object
+ *  \param  point  EC_POINT object to be cleared and freed
+ */
+void EC_POINT_clear_free(EC_POINT *point);
+
+/** Copies EC_POINT object
+ *  \param  dst  destination EC_POINT object
+ *  \param  src  source EC_POINT object
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
+
+/** Creates a new EC_POINT object and copies the content of the supplied
+ *  EC_POINT
+ *  \param  src    source EC_POINT object
+ *  \param  group  underlying the EC_GROUP object
+ *  \return newly created EC_POINT object or NULL if an error occurred
+ */
+EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
+
+/** Returns the EC_METHOD used in EC_POINT object
+ *  \param  point  EC_POINT object
+ *  \return the EC_METHOD used
+ */
+const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
+
+/** Sets a point to infinity (neutral element)
+ *  \param  group  underlying EC_GROUP object
+ *  \param  point  EC_POINT to set to infinity
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
+
+/** Sets the jacobian projective coordinates of a EC_POINT over GFp
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM with the x-coordinate
+ *  \param  y      BIGNUM with the y-coordinate
+ *  \param  z      BIGNUM with the z-coordinate
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
+                                             EC_POINT *p, const BIGNUM *x,
+                                             const BIGNUM *y, const BIGNUM *z,
+                                             BN_CTX *ctx);
+
+/** Gets the jacobian projective coordinates of a EC_POINT over GFp
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM for the x-coordinate
+ *  \param  y      BIGNUM for the y-coordinate
+ *  \param  z      BIGNUM for the z-coordinate
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
+                                             const EC_POINT *p, BIGNUM *x,
+                                             BIGNUM *y, BIGNUM *z,
+                                             BN_CTX *ctx);
+
+/** Sets the affine coordinates of an EC_POINT
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM with the x-coordinate
+ *  \param  y      BIGNUM with the y-coordinate
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *p,
+                                    const BIGNUM *x, const BIGNUM *y,
+                                    BN_CTX *ctx);
+
+/** Gets the affine coordinates of an EC_POINT.
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM for the x-coordinate
+ *  \param  y      BIGNUM for the y-coordinate
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *p,
+                                    BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
+
+/** Sets the affine coordinates of an EC_POINT. A synonym of
+ *  EC_POINT_set_affine_coordinates
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM with the x-coordinate
+ *  \param  y      BIGNUM with the y-coordinate
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group,
+                                                           EC_POINT *p,
+                                                           const BIGNUM *x,
+                                                           const BIGNUM *y,
+                                                           BN_CTX *ctx))
+
+/** Gets the affine coordinates of an EC_POINT. A synonym of
+ *  EC_POINT_get_affine_coordinates
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM for the x-coordinate
+ *  \param  y      BIGNUM for the y-coordinate
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
+                                                           const EC_POINT *p,
+                                                           BIGNUM *x,
+                                                           BIGNUM *y,
+                                                           BN_CTX *ctx))
+
+/** Sets the x9.62 compressed coordinates of a EC_POINT
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM with x-coordinate
+ *  \param  y_bit  integer with the y-Bit (either 0 or 1)
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p,
+                                        const BIGNUM *x, int y_bit,
+                                        BN_CTX *ctx);
+
+/** Sets the x9.62 compressed coordinates of a EC_POINT. A synonym of
+ *  EC_POINT_set_compressed_coordinates
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM with x-coordinate
+ *  \param  y_bit  integer with the y-Bit (either 0 or 1)
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
+                                                               EC_POINT *p,
+                                                               const BIGNUM *x,
+                                                               int y_bit,
+                                                               BN_CTX *ctx))
+# ifndef OPENSSL_NO_EC2M
+/** Sets the affine coordinates of an EC_POINT. A synonym of
+ *  EC_POINT_set_affine_coordinates
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM with the x-coordinate
+ *  \param  y      BIGNUM with the y-coordinate
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group,
+                                                            EC_POINT *p,
+                                                            const BIGNUM *x,
+                                                            const BIGNUM *y,
+                                                            BN_CTX *ctx))
+
+/** Gets the affine coordinates of an EC_POINT. A synonym of
+ *  EC_POINT_get_affine_coordinates
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM for the x-coordinate
+ *  \param  y      BIGNUM for the y-coordinate
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
+                                                            const EC_POINT *p,
+                                                            BIGNUM *x,
+                                                            BIGNUM *y,
+                                                            BN_CTX *ctx))
+
+/** Sets the x9.62 compressed coordinates of a EC_POINT. A synonym of
+ *  EC_POINT_set_compressed_coordinates
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  x      BIGNUM with x-coordinate
+ *  \param  y_bit  integer with the y-Bit (either 0 or 1)
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+DEPRECATEDIN_1_2_0(int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group,
+                                                                EC_POINT *p,
+                                                                const BIGNUM *x,
+                                                                int y_bit,
+                                                                BN_CTX *ctx))
+# endif
+/** Encodes a EC_POINT object to a octet string
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  form   point conversion form
+ *  \param  buf    memory buffer for the result. If NULL the function returns
+ *                 required buffer size.
+ *  \param  len    length of the memory buffer
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return the length of the encoded octet string or 0 if an error occurred
+ */
+size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
+                          point_conversion_form_t form,
+                          unsigned char *buf, size_t len, BN_CTX *ctx);
+
+/** Decodes a EC_POINT from a octet string
+ *  \param  group  underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \param  buf    memory buffer with the encoded ec point
+ *  \param  len    length of the encoded ec point
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
+                       const unsigned char *buf, size_t len, BN_CTX *ctx);
+
+/** Encodes an EC_POINT object to an allocated octet string
+ *  \param  group  underlying EC_GROUP object
+ *  \param  point  EC_POINT object
+ *  \param  form   point conversion form
+ *  \param  pbuf   returns pointer to allocated buffer
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return the length of the encoded octet string or 0 if an error occurred
+ */
+size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point,
+                          point_conversion_form_t form,
+                          unsigned char **pbuf, BN_CTX *ctx);
+
+/* other interfaces to point2oct/oct2point: */
+BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *,
+                          point_conversion_form_t form, BIGNUM *, BN_CTX *);
+EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
+                            EC_POINT *, BN_CTX *);
+char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
+                         point_conversion_form_t form, BN_CTX *);
+EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
+                             EC_POINT *, BN_CTX *);
+
+/********************************************************************/
+/*         functions for doing EC_POINT arithmetic                  */
+/********************************************************************/
+
+/** Computes the sum of two EC_POINT
+ *  \param  group  underlying EC_GROUP object
+ *  \param  r      EC_POINT object for the result (r = a + b)
+ *  \param  a      EC_POINT object with the first summand
+ *  \param  b      EC_POINT object with the second summand
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
+                 const EC_POINT *b, BN_CTX *ctx);
+
+/** Computes the double of a EC_POINT
+ *  \param  group  underlying EC_GROUP object
+ *  \param  r      EC_POINT object for the result (r = 2 * a)
+ *  \param  a      EC_POINT object
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
+                 BN_CTX *ctx);
+
+/** Computes the inverse of a EC_POINT
+ *  \param  group  underlying EC_GROUP object
+ *  \param  a      EC_POINT object to be inverted (it's used for the result as well)
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
+
+/** Checks whether the point is the neutral element of the group
+ *  \param  group  the underlying EC_GROUP object
+ *  \param  p      EC_POINT object
+ *  \return 1 if the point is the neutral element and 0 otherwise
+ */
+int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
+
+/** Checks whether the point is on the curve
+ *  \param  group  underlying EC_GROUP object
+ *  \param  point  EC_POINT object to check
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 if the point is on the curve, 0 if not, or -1 on error
+ */
+int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
+                         BN_CTX *ctx);
+
+/** Compares two EC_POINTs
+ *  \param  group  underlying EC_GROUP object
+ *  \param  a      first EC_POINT object
+ *  \param  b      second EC_POINT object
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 if the points are not equal, 0 if they are, or -1 on error
+ */
+int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b,
+                 BN_CTX *ctx);
+
+int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
+int EC_POINTs_make_affine(const EC_GROUP *group, size_t num,
+                          EC_POINT *points[], BN_CTX *ctx);
+
+/** Computes r = generator * n + sum_{i=0}^{num-1} p[i] * m[i]
+ *  \param  group  underlying EC_GROUP object
+ *  \param  r      EC_POINT object for the result
+ *  \param  n      BIGNUM with the multiplier for the group generator (optional)
+ *  \param  num    number further summands
+ *  \param  p      array of size num of EC_POINT objects
+ *  \param  m      array of size num of BIGNUM objects
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n,
+                  size_t num, const EC_POINT *p[], const BIGNUM *m[],
+                  BN_CTX *ctx);
+
+/** Computes r = generator * n + q * m
+ *  \param  group  underlying EC_GROUP object
+ *  \param  r      EC_POINT object for the result
+ *  \param  n      BIGNUM with the multiplier for the group generator (optional)
+ *  \param  q      EC_POINT object with the first factor of the second summand
+ *  \param  m      BIGNUM with the second factor of the second summand
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n,
+                 const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
+
+/** Stores multiples of generator for faster point multiplication
+ *  \param  group  EC_GROUP object
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
+
+/** Reports whether a precomputation has been done
+ *  \param  group  EC_GROUP object
+ *  \return 1 if a pre-computation has been done and 0 otherwise
+ */
+int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
+
+/********************************************************************/
+/*                       ASN1 stuff                                 */
+/********************************************************************/
+
+DECLARE_ASN1_ITEM(ECPKPARAMETERS)
+DECLARE_ASN1_ALLOC_FUNCTIONS(ECPKPARAMETERS)
+DECLARE_ASN1_ITEM(ECPARAMETERS)
+DECLARE_ASN1_ALLOC_FUNCTIONS(ECPARAMETERS)
+
+/*
+ * EC_GROUP_get_basis_type() returns the NID of the basis type used to
+ * represent the field elements
+ */
+int EC_GROUP_get_basis_type(const EC_GROUP *);
+# ifndef OPENSSL_NO_EC2M
+int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
+int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
+                                   unsigned int *k2, unsigned int *k3);
+# endif
+
+# define OPENSSL_EC_EXPLICIT_CURVE  0x000
+# define OPENSSL_EC_NAMED_CURVE     0x001
+
+EC_GROUP *d2i_ECPKParameters(EC_GROUP **, const unsigned char **in, long len);
+int i2d_ECPKParameters(const EC_GROUP *, unsigned char **out);
+
+# define d2i_ECPKParameters_bio(bp,x) \
+    ASN1_d2i_bio_of(EC_GROUP, NULL, d2i_ECPKParameters, bp, x)
+# define i2d_ECPKParameters_bio(bp,x) \
+    ASN1_i2d_bio_of_const(EC_GROUP, i2d_ECPKParameters, bp, x)
+# define d2i_ECPKParameters_fp(fp,x) \
+    (EC_GROUP *)ASN1_d2i_fp(NULL, (d2i_of_void *)d2i_ECPKParameters, (fp), \
+                            (void **)(x))
+# define i2d_ECPKParameters_fp(fp,x) \
+    ASN1_i2d_fp((i2d_of_void *)i2d_ECPKParameters, (fp), (void *)(x))
+
+int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off);
+# ifndef OPENSSL_NO_STDIO
+int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off);
+# endif
+
+/********************************************************************/
+/*                      EC_KEY functions                            */
+/********************************************************************/
+
+/* some values for the encoding_flag */
+# define EC_PKEY_NO_PARAMETERS   0x001
+# define EC_PKEY_NO_PUBKEY       0x002
+
+/* some values for the flags field */
+# define EC_FLAG_NON_FIPS_ALLOW  0x1
+# define EC_FLAG_FIPS_CHECKED    0x2
+# define EC_FLAG_COFACTOR_ECDH   0x1000
+
+/** Creates a new EC_KEY object.
+ *  \return EC_KEY object or NULL if an error occurred.
+ */
+EC_KEY *EC_KEY_new(void);
+
+int EC_KEY_get_flags(const EC_KEY *key);
+
+void EC_KEY_set_flags(EC_KEY *key, int flags);
+
+void EC_KEY_clear_flags(EC_KEY *key, int flags);
+
+int EC_KEY_decoded_from_explicit_params(const EC_KEY *key);
+
+/** Creates a new EC_KEY object using a named curve as underlying
+ *  EC_GROUP object.
+ *  \param  nid  NID of the named curve.
+ *  \return EC_KEY object or NULL if an error occurred.
+ */
+EC_KEY *EC_KEY_new_by_curve_name(int nid);
+
+/** Frees a EC_KEY object.
+ *  \param  key  EC_KEY object to be freed.
+ */
+void EC_KEY_free(EC_KEY *key);
+
+/** Copies a EC_KEY object.
+ *  \param  dst  destination EC_KEY object
+ *  \param  src  src EC_KEY object
+ *  \return dst or NULL if an error occurred.
+ */
+EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src);
+
+/** Creates a new EC_KEY object and copies the content from src to it.
+ *  \param  src  the source EC_KEY object
+ *  \return newly created EC_KEY object or NULL if an error occurred.
+ */
+EC_KEY *EC_KEY_dup(const EC_KEY *src);
+
+/** Increases the internal reference count of a EC_KEY object.
+ *  \param  key  EC_KEY object
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int EC_KEY_up_ref(EC_KEY *key);
+
+/** Returns the ENGINE object of a EC_KEY object
+ *  \param  eckey  EC_KEY object
+ *  \return the ENGINE object (possibly NULL).
+ */
+ENGINE *EC_KEY_get0_engine(const EC_KEY *eckey);
+
+/** Returns the EC_GROUP object of a EC_KEY object
+ *  \param  key  EC_KEY object
+ *  \return the EC_GROUP object (possibly NULL).
+ */
+const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key);
+
+/** Sets the EC_GROUP of a EC_KEY object.
+ *  \param  key    EC_KEY object
+ *  \param  group  EC_GROUP to use in the EC_KEY object (note: the EC_KEY
+ *                 object will use an own copy of the EC_GROUP).
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group);
+
+/** Returns the private key of a EC_KEY object.
+ *  \param  key  EC_KEY object
+ *  \return a BIGNUM with the private key (possibly NULL).
+ */
+const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key);
+
+/** Sets the private key of a EC_KEY object.
+ *  \param  key  EC_KEY object
+ *  \param  prv  BIGNUM with the private key (note: the EC_KEY object
+ *               will use an own copy of the BIGNUM).
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv);
+
+/** Returns the public key of a EC_KEY object.
+ *  \param  key  the EC_KEY object
+ *  \return a EC_POINT object with the public key (possibly NULL)
+ */
+const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key);
+
+/** Sets the public key of a EC_KEY object.
+ *  \param  key  EC_KEY object
+ *  \param  pub  EC_POINT object with the public key (note: the EC_KEY object
+ *               will use an own copy of the EC_POINT object).
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);
+
+unsigned EC_KEY_get_enc_flags(const EC_KEY *key);
+void EC_KEY_set_enc_flags(EC_KEY *eckey, unsigned int flags);
+point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key);
+void EC_KEY_set_conv_form(EC_KEY *eckey, point_conversion_form_t cform);
+
+#define EC_KEY_get_ex_new_index(l, p, newf, dupf, freef) \
+    CRYPTO_get_ex_new_index(CRYPTO_EX_INDEX_EC_KEY, l, p, newf, dupf, freef)
+int EC_KEY_set_ex_data(EC_KEY *key, int idx, void *arg);
+void *EC_KEY_get_ex_data(const EC_KEY *key, int idx);
+
+/* wrapper functions for the underlying EC_GROUP object */
+void EC_KEY_set_asn1_flag(EC_KEY *eckey, int asn1_flag);
+
+/** Creates a table of pre-computed multiples of the generator to
+ *  accelerate further EC_KEY operations.
+ *  \param  key  EC_KEY object
+ *  \param  ctx  BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx);
+
+/** Creates a new ec private (and optional a new public) key.
+ *  \param  key  EC_KEY object
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int EC_KEY_generate_key(EC_KEY *key);
+
+/** Verifies that a private and/or public key is valid.
+ *  \param  key  the EC_KEY object
+ *  \return 1 on success and 0 otherwise.
+ */
+int EC_KEY_check_key(const EC_KEY *key);
+
+/** Indicates if an EC_KEY can be used for signing.
+ *  \param  eckey  the EC_KEY object
+ *  \return 1 if can can sign and 0 otherwise.
+ */
+int EC_KEY_can_sign(const EC_KEY *eckey);
+
+/** Sets a public key from affine coordinates performing
+ *  necessary NIST PKV tests.
+ *  \param  key  the EC_KEY object
+ *  \param  x    public key x coordinate
+ *  \param  y    public key y coordinate
+ *  \return 1 on success and 0 otherwise.
+ */
+int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x,
+                                             BIGNUM *y);
+
+/** Encodes an EC_KEY public key to an allocated octet string
+ *  \param  key    key to encode
+ *  \param  form   point conversion form
+ *  \param  pbuf   returns pointer to allocated buffer
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return the length of the encoded octet string or 0 if an error occurred
+ */
+size_t EC_KEY_key2buf(const EC_KEY *key, point_conversion_form_t form,
+                      unsigned char **pbuf, BN_CTX *ctx);
+
+/** Decodes a EC_KEY public key from a octet string
+ *  \param  key    key to decode
+ *  \param  buf    memory buffer with the encoded ec point
+ *  \param  len    length of the encoded ec point
+ *  \param  ctx    BN_CTX object (optional)
+ *  \return 1 on success and 0 if an error occurred
+ */
+
+int EC_KEY_oct2key(EC_KEY *key, const unsigned char *buf, size_t len,
+                   BN_CTX *ctx);
+
+/** Decodes an EC_KEY private key from an octet string
+ *  \param  key    key to decode
+ *  \param  buf    memory buffer with the encoded private key
+ *  \param  len    length of the encoded key
+ *  \return 1 on success and 0 if an error occurred
+ */
+
+int EC_KEY_oct2priv(EC_KEY *key, const unsigned char *buf, size_t len);
+
+/** Encodes a EC_KEY private key to an octet string
+ *  \param  key    key to encode
+ *  \param  buf    memory buffer for the result. If NULL the function returns
+ *                 required buffer size.
+ *  \param  len    length of the memory buffer
+ *  \return the length of the encoded octet string or 0 if an error occurred
+ */
+
+size_t EC_KEY_priv2oct(const EC_KEY *key, unsigned char *buf, size_t len);
+
+/** Encodes an EC_KEY private key to an allocated octet string
+ *  \param  eckey  key to encode
+ *  \param  pbuf   returns pointer to allocated buffer
+ *  \return the length of the encoded octet string or 0 if an error occurred
+ */
+size_t EC_KEY_priv2buf(const EC_KEY *eckey, unsigned char **pbuf);
+
+/********************************************************************/
+/*        de- and encoding functions for SEC1 ECPrivateKey          */
+/********************************************************************/
+
+/** Decodes a private key from a memory buffer.
+ *  \param  key  a pointer to a EC_KEY object which should be used (or NULL)
+ *  \param  in   pointer to memory with the DER encoded private key
+ *  \param  len  length of the DER encoded private key
+ *  \return the decoded private key or NULL if an error occurred.
+ */
+EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);
+
+/** Encodes a private key object and stores the result in a buffer.
+ *  \param  key  the EC_KEY object to encode
+ *  \param  out  the buffer for the result (if NULL the function returns number
+ *               of bytes needed).
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);
+
+/********************************************************************/
+/*        de- and encoding functions for EC parameters              */
+/********************************************************************/
+
+/** Decodes ec parameter from a memory buffer.
+ *  \param  key  a pointer to a EC_KEY object which should be used (or NULL)
+ *  \param  in   pointer to memory with the DER encoded ec parameters
+ *  \param  len  length of the DER encoded ec parameters
+ *  \return a EC_KEY object with the decoded parameters or NULL if an error
+ *          occurred.
+ */
+EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);
+
+/** Encodes ec parameter and stores the result in a buffer.
+ *  \param  key  the EC_KEY object with ec parameters to encode
+ *  \param  out  the buffer for the result (if NULL the function returns number
+ *               of bytes needed).
+ *  \return 1 on success and 0 if an error occurred.
+ */
+int i2d_ECParameters(EC_KEY *key, unsigned char **out);
+
+/********************************************************************/
+/*         de- and encoding functions for EC public key             */
+/*         (octet string, not DER -- hence 'o2i' and 'i2o')         */
+/********************************************************************/
+
+/** Decodes a ec public key from a octet string.
+ *  \param  key  a pointer to a EC_KEY object which should be used
+ *  \param  in   memory buffer with the encoded public key
+ *  \param  len  length of the encoded public key
+ *  \return EC_KEY object with decoded public key or NULL if an error
+ *          occurred.
+ */
+EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len);
+
+/** Encodes a ec public key in an octet string.
+ *  \param  key  the EC_KEY object with the public key
+ *  \param  out  the buffer for the result (if NULL the function returns number
+ *               of bytes needed).
+ *  \return 1 on success and 0 if an error occurred
+ */
+int i2o_ECPublicKey(const EC_KEY *key, unsigned char **out);
+
+/** Prints out the ec parameters on human readable form.
+ *  \param  bp   BIO object to which the information is printed
+ *  \param  key  EC_KEY object
+ *  \return 1 on success and 0 if an error occurred
+ */
+int ECParameters_print(BIO *bp, const EC_KEY *key);
+
+/** Prints out the contents of a EC_KEY object
+ *  \param  bp   BIO object to which the information is printed
+ *  \param  key  EC_KEY object
+ *  \param  off  line offset
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_KEY_print(BIO *bp, const EC_KEY *key, int off);
+
+# ifndef OPENSSL_NO_STDIO
+/** Prints out the ec parameters on human readable form.
+ *  \param  fp   file descriptor to which the information is printed
+ *  \param  key  EC_KEY object
+ *  \return 1 on success and 0 if an error occurred
+ */
+int ECParameters_print_fp(FILE *fp, const EC_KEY *key);
+
+/** Prints out the contents of a EC_KEY object
+ *  \param  fp   file descriptor to which the information is printed
+ *  \param  key  EC_KEY object
+ *  \param  off  line offset
+ *  \return 1 on success and 0 if an error occurred
+ */
+int EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);
+
+# endif
+
+const EC_KEY_METHOD *EC_KEY_OpenSSL(void);
+const EC_KEY_METHOD *EC_KEY_get_default_method(void);
+void EC_KEY_set_default_method(const EC_KEY_METHOD *meth);
+const EC_KEY_METHOD *EC_KEY_get_method(const EC_KEY *key);
+int EC_KEY_set_method(EC_KEY *key, const EC_KEY_METHOD *meth);
+EC_KEY *EC_KEY_new_method(ENGINE *engine);
+
+/** The old name for ecdh_KDF_X9_63
+ *  The ECDH KDF specification has been mistakingly attributed to ANSI X9.62,
+ *  it is actually specified in ANSI X9.63.
+ *  This identifier is retained for backwards compatibility
+ */
+int ECDH_KDF_X9_62(unsigned char *out, size_t outlen,
+                   const unsigned char *Z, size_t Zlen,
+                   const unsigned char *sinfo, size_t sinfolen,
+                   const EVP_MD *md);
+
+int ECDH_compute_key(void *out, size_t outlen, const EC_POINT *pub_key,
+                     const EC_KEY *ecdh,
+                     void *(*KDF) (const void *in, size_t inlen,
+                                   void *out, size_t *outlen));
+
+typedef struct ECDSA_SIG_st ECDSA_SIG;
+
+/** Allocates and initialize a ECDSA_SIG structure
+ *  \return pointer to a ECDSA_SIG structure or NULL if an error occurred
+ */
+ECDSA_SIG *ECDSA_SIG_new(void);
+
+/** frees a ECDSA_SIG structure
+ *  \param  sig  pointer to the ECDSA_SIG structure
+ */
+void ECDSA_SIG_free(ECDSA_SIG *sig);
+
+/** DER encode content of ECDSA_SIG object (note: this function modifies *pp
+ *  (*pp += length of the DER encoded signature)).
+ *  \param  sig  pointer to the ECDSA_SIG object
+ *  \param  pp   pointer to a unsigned char pointer for the output or NULL
+ *  \return the length of the DER encoded ECDSA_SIG object or a negative value
+ *          on error
+ */
+int i2d_ECDSA_SIG(const ECDSA_SIG *sig, unsigned char **pp);
+
+/** Decodes a DER encoded ECDSA signature (note: this function changes *pp
+ *  (*pp += len)).
+ *  \param  sig  pointer to ECDSA_SIG pointer (may be NULL)
+ *  \param  pp   memory buffer with the DER encoded signature
+ *  \param  len  length of the buffer
+ *  \return pointer to the decoded ECDSA_SIG structure (or NULL)
+ */
+ECDSA_SIG *d2i_ECDSA_SIG(ECDSA_SIG **sig, const unsigned char **pp, long len);
+
+/** Accessor for r and s fields of ECDSA_SIG
+ *  \param  sig  pointer to ECDSA_SIG structure
+ *  \param  pr   pointer to BIGNUM pointer for r (may be NULL)
+ *  \param  ps   pointer to BIGNUM pointer for s (may be NULL)
+ */
+void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps);
+
+/** Accessor for r field of ECDSA_SIG
+ *  \param  sig  pointer to ECDSA_SIG structure
+ */
+const BIGNUM *ECDSA_SIG_get0_r(const ECDSA_SIG *sig);
+
+/** Accessor for s field of ECDSA_SIG
+ *  \param  sig  pointer to ECDSA_SIG structure
+ */
+const BIGNUM *ECDSA_SIG_get0_s(const ECDSA_SIG *sig);
+
+/** Setter for r and s fields of ECDSA_SIG
+ *  \param  sig  pointer to ECDSA_SIG structure
+ *  \param  r    pointer to BIGNUM for r (may be NULL)
+ *  \param  s    pointer to BIGNUM for s (may be NULL)
+ */
+int ECDSA_SIG_set0(ECDSA_SIG *sig, BIGNUM *r, BIGNUM *s);
+
+/** Computes the ECDSA signature of the given hash value using
+ *  the supplied private key and returns the created signature.
+ *  \param  dgst      pointer to the hash value
+ *  \param  dgst_len  length of the hash value
+ *  \param  eckey     EC_KEY object containing a private EC key
+ *  \return pointer to a ECDSA_SIG structure or NULL if an error occurred
+ */
+ECDSA_SIG *ECDSA_do_sign(const unsigned char *dgst, int dgst_len,
+                         EC_KEY *eckey);
+
+/** Computes ECDSA signature of a given hash value using the supplied
+ *  private key (note: sig must point to ECDSA_size(eckey) bytes of memory).
+ *  \param  dgst     pointer to the hash value to sign
+ *  \param  dgstlen  length of the hash value
+ *  \param  kinv     BIGNUM with a pre-computed inverse k (optional)
+ *  \param  rp       BIGNUM with a pre-computed rp value (optional),
+ *                   see ECDSA_sign_setup
+ *  \param  eckey    EC_KEY object containing a private EC key
+ *  \return pointer to a ECDSA_SIG structure or NULL if an error occurred
+ */
+ECDSA_SIG *ECDSA_do_sign_ex(const unsigned char *dgst, int dgstlen,
+                            const BIGNUM *kinv, const BIGNUM *rp,
+                            EC_KEY *eckey);
+
+/** Verifies that the supplied signature is a valid ECDSA
+ *  signature of the supplied hash value using the supplied public key.
+ *  \param  dgst      pointer to the hash value
+ *  \param  dgst_len  length of the hash value
+ *  \param  sig       ECDSA_SIG structure
+ *  \param  eckey     EC_KEY object containing a public EC key
+ *  \return 1 if the signature is valid, 0 if the signature is invalid
+ *          and -1 on error
+ */
+int ECDSA_do_verify(const unsigned char *dgst, int dgst_len,
+                    const ECDSA_SIG *sig, EC_KEY *eckey);
+
+/** Precompute parts of the signing operation
+ *  \param  eckey  EC_KEY object containing a private EC key
+ *  \param  ctx    BN_CTX object (optional)
+ *  \param  kinv   BIGNUM pointer for the inverse of k
+ *  \param  rp     BIGNUM pointer for x coordinate of k * generator
+ *  \return 1 on success and 0 otherwise
+ */
+int ECDSA_sign_setup(EC_KEY *eckey, BN_CTX *ctx, BIGNUM **kinv, BIGNUM **rp);
+
+/** Computes ECDSA signature of a given hash value using the supplied
+ *  private key (note: sig must point to ECDSA_size(eckey) bytes of memory).
+ *  \param  type     this parameter is ignored
+ *  \param  dgst     pointer to the hash value to sign
+ *  \param  dgstlen  length of the hash value
+ *  \param  sig      memory for the DER encoded created signature
+ *  \param  siglen   pointer to the length of the returned signature
+ *  \param  eckey    EC_KEY object containing a private EC key
+ *  \return 1 on success and 0 otherwise
+ */
+int ECDSA_sign(int type, const unsigned char *dgst, int dgstlen,
+               unsigned char *sig, unsigned int *siglen, EC_KEY *eckey);
+
+/** Computes ECDSA signature of a given hash value using the supplied
+ *  private key (note: sig must point to ECDSA_size(eckey) bytes of memory).
+ *  \param  type     this parameter is ignored
+ *  \param  dgst     pointer to the hash value to sign
+ *  \param  dgstlen  length of the hash value
+ *  \param  sig      buffer to hold the DER encoded signature
+ *  \param  siglen   pointer to the length of the returned signature
+ *  \param  kinv     BIGNUM with a pre-computed inverse k (optional)
+ *  \param  rp       BIGNUM with a pre-computed rp value (optional),
+ *                   see ECDSA_sign_setup
+ *  \param  eckey    EC_KEY object containing a private EC key
+ *  \return 1 on success and 0 otherwise
+ */
+int ECDSA_sign_ex(int type, const unsigned char *dgst, int dgstlen,
+                  unsigned char *sig, unsigned int *siglen,
+                  const BIGNUM *kinv, const BIGNUM *rp, EC_KEY *eckey);
+
+/** Verifies that the given signature is valid ECDSA signature
+ *  of the supplied hash value using the specified public key.
+ *  \param  type     this parameter is ignored
+ *  \param  dgst     pointer to the hash value
+ *  \param  dgstlen  length of the hash value
+ *  \param  sig      pointer to the DER encoded signature
+ *  \param  siglen   length of the DER encoded signature
+ *  \param  eckey    EC_KEY object containing a public EC key
+ *  \return 1 if the signature is valid, 0 if the signature is invalid
+ *          and -1 on error
+ */
+int ECDSA_verify(int type, const unsigned char *dgst, int dgstlen,
+                 const unsigned char *sig, int siglen, EC_KEY *eckey);
+
+/** Returns the maximum length of the DER encoded signature
+ *  \param  eckey  EC_KEY object
+ *  \return numbers of bytes required for the DER encoded signature
+ */
+int ECDSA_size(const EC_KEY *eckey);
+
+/********************************************************************/
+/*  EC_KEY_METHOD constructors, destructors, writers and accessors  */
+/********************************************************************/
+
+EC_KEY_METHOD *EC_KEY_METHOD_new(const EC_KEY_METHOD *meth);
+void EC_KEY_METHOD_free(EC_KEY_METHOD *meth);
+void EC_KEY_METHOD_set_init(EC_KEY_METHOD *meth,
+                            int (*init)(EC_KEY *key),
+                            void (*finish)(EC_KEY *key),
+                            int (*copy)(EC_KEY *dest, const EC_KEY *src),
+                            int (*set_group)(EC_KEY *key, const EC_GROUP *grp),
+                            int (*set_private)(EC_KEY *key,
+                                               const BIGNUM *priv_key),
+                            int (*set_public)(EC_KEY *key,
+                                              const EC_POINT *pub_key));
+
+void EC_KEY_METHOD_set_keygen(EC_KEY_METHOD *meth,
+                              int (*keygen)(EC_KEY *key));
+
+void EC_KEY_METHOD_set_compute_key(EC_KEY_METHOD *meth,
+                                   int (*ckey)(unsigned char **psec,
+                                               size_t *pseclen,
+                                               const EC_POINT *pub_key,
+                                               const EC_KEY *ecdh));
+
+void EC_KEY_METHOD_set_sign(EC_KEY_METHOD *meth,
+                            int (*sign)(int type, const unsigned char *dgst,
+                                        int dlen, unsigned char *sig,
+                                        unsigned int *siglen,
+                                        const BIGNUM *kinv, const BIGNUM *r,
+                                        EC_KEY *eckey),
+                            int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in,
+                                              BIGNUM **kinvp, BIGNUM **rp),
+                            ECDSA_SIG *(*sign_sig)(const unsigned char *dgst,
+                                                   int dgst_len,
+                                                   const BIGNUM *in_kinv,
+                                                   const BIGNUM *in_r,
+                                                   EC_KEY *eckey));
+
+void EC_KEY_METHOD_set_verify(EC_KEY_METHOD *meth,
+                              int (*verify)(int type, const unsigned
+                                            char *dgst, int dgst_len,
+                                            const unsigned char *sigbuf,
+                                            int sig_len, EC_KEY *eckey),
+                              int (*verify_sig)(const unsigned char *dgst,
+                                                int dgst_len,
+                                                const ECDSA_SIG *sig,
+                                                EC_KEY *eckey));
+
+void EC_KEY_METHOD_get_init(const EC_KEY_METHOD *meth,
+                            int (**pinit)(EC_KEY *key),
+                            void (**pfinish)(EC_KEY *key),
+                            int (**pcopy)(EC_KEY *dest, const EC_KEY *src),
+                            int (**pset_group)(EC_KEY *key,
+                                               const EC_GROUP *grp),
+                            int (**pset_private)(EC_KEY *key,
+                                                 const BIGNUM *priv_key),
+                            int (**pset_public)(EC_KEY *key,
+                                                const EC_POINT *pub_key));
+
+void EC_KEY_METHOD_get_keygen(const EC_KEY_METHOD *meth,
+                              int (**pkeygen)(EC_KEY *key));
+
+void EC_KEY_METHOD_get_compute_key(const EC_KEY_METHOD *meth,
+                                   int (**pck)(unsigned char **psec,
+                                               size_t *pseclen,
+                                               const EC_POINT *pub_key,
+                                               const EC_KEY *ecdh));
+
+void EC_KEY_METHOD_get_sign(const EC_KEY_METHOD *meth,
+                            int (**psign)(int type, const unsigned char *dgst,
+                                          int dlen, unsigned char *sig,
+                                          unsigned int *siglen,
+                                          const BIGNUM *kinv, const BIGNUM *r,
+                                          EC_KEY *eckey),
+                            int (**psign_setup)(EC_KEY *eckey, BN_CTX *ctx_in,
+                                                BIGNUM **kinvp, BIGNUM **rp),
+                            ECDSA_SIG *(**psign_sig)(const unsigned char *dgst,
+                                                     int dgst_len,
+                                                     const BIGNUM *in_kinv,
+                                                     const BIGNUM *in_r,
+                                                     EC_KEY *eckey));
+
+void EC_KEY_METHOD_get_verify(const EC_KEY_METHOD *meth,
+                              int (**pverify)(int type, const unsigned
+                                              char *dgst, int dgst_len,
+                                              const unsigned char *sigbuf,
+                                              int sig_len, EC_KEY *eckey),
+                              int (**pverify_sig)(const unsigned char *dgst,
+                                                  int dgst_len,
+                                                  const ECDSA_SIG *sig,
+                                                  EC_KEY *eckey));
+
+# define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x)
+
+# ifndef __cplusplus
+#  if defined(__SUNPRO_C)
+#   if __SUNPRO_C >= 0x520
+#    pragma error_messages (default,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
+#   endif
+#  endif
+# endif
+
+# define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_PARAMGEN|EVP_PKEY_OP_KEYGEN, \
+                                EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)
+
+# define EVP_PKEY_CTX_set_ec_param_enc(ctx, flag) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_PARAMGEN|EVP_PKEY_OP_KEYGEN, \
+                                EVP_PKEY_CTRL_EC_PARAM_ENC, flag, NULL)
+
+# define EVP_PKEY_CTX_set_ecdh_cofactor_mode(ctx, flag) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_EC_ECDH_COFACTOR, flag, NULL)
+
+# define EVP_PKEY_CTX_get_ecdh_cofactor_mode(ctx) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_EC_ECDH_COFACTOR, -2, NULL)
+
+# define EVP_PKEY_CTX_set_ecdh_kdf_type(ctx, kdf) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_EC_KDF_TYPE, kdf, NULL)
+
+# define EVP_PKEY_CTX_get_ecdh_kdf_type(ctx) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_EC_KDF_TYPE, -2, NULL)
+
+# define EVP_PKEY_CTX_set_ecdh_kdf_md(ctx, md) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_EC_KDF_MD, 0, (void *)(md))
+
+# define EVP_PKEY_CTX_get_ecdh_kdf_md(ctx, pmd) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_GET_EC_KDF_MD, 0, (void *)(pmd))
+
+# define EVP_PKEY_CTX_set_ecdh_kdf_outlen(ctx, len) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_EC_KDF_OUTLEN, len, NULL)
+
+# define EVP_PKEY_CTX_get_ecdh_kdf_outlen(ctx, plen) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_GET_EC_KDF_OUTLEN, 0, \
+                                (void *)(plen))
+
+# define EVP_PKEY_CTX_set0_ecdh_kdf_ukm(ctx, p, plen) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_EC_KDF_UKM, plen, (void *)(p))
+
+# define EVP_PKEY_CTX_get0_ecdh_kdf_ukm(ctx, p) \
+        EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, \
+                                EVP_PKEY_OP_DERIVE, \
+                                EVP_PKEY_CTRL_GET_EC_KDF_UKM, 0, (void *)(p))
+
+/* SM2 will skip the operation check so no need to pass operation here */
+# define EVP_PKEY_CTX_set1_id(ctx, id, id_len) \
+        EVP_PKEY_CTX_ctrl(ctx, -1, -1, \
+                                EVP_PKEY_CTRL_SET1_ID, (int)id_len, (void*)(id))
+
+# define EVP_PKEY_CTX_get1_id(ctx, id) \
+        EVP_PKEY_CTX_ctrl(ctx, -1, -1, \
+                                EVP_PKEY_CTRL_GET1_ID, 0, (void*)(id))
+
+# define EVP_PKEY_CTX_get1_id_len(ctx, id_len) \
+        EVP_PKEY_CTX_ctrl(ctx, -1, -1, \
+                                EVP_PKEY_CTRL_GET1_ID_LEN, 0, (void*)(id_len))
+
+# define EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID             (EVP_PKEY_ALG_CTRL + 1)
+# define EVP_PKEY_CTRL_EC_PARAM_ENC                      (EVP_PKEY_ALG_CTRL + 2)
+# define EVP_PKEY_CTRL_EC_ECDH_COFACTOR                  (EVP_PKEY_ALG_CTRL + 3)
+# define EVP_PKEY_CTRL_EC_KDF_TYPE                       (EVP_PKEY_ALG_CTRL + 4)
+# define EVP_PKEY_CTRL_EC_KDF_MD                         (EVP_PKEY_ALG_CTRL + 5)
+# define EVP_PKEY_CTRL_GET_EC_KDF_MD                     (EVP_PKEY_ALG_CTRL + 6)
+# define EVP_PKEY_CTRL_EC_KDF_OUTLEN                     (EVP_PKEY_ALG_CTRL + 7)
+# define EVP_PKEY_CTRL_GET_EC_KDF_OUTLEN                 (EVP_PKEY_ALG_CTRL + 8)
+# define EVP_PKEY_CTRL_EC_KDF_UKM                        (EVP_PKEY_ALG_CTRL + 9)
+# define EVP_PKEY_CTRL_GET_EC_KDF_UKM                    (EVP_PKEY_ALG_CTRL + 10)
+# define EVP_PKEY_CTRL_SET1_ID                           (EVP_PKEY_ALG_CTRL + 11)
+# define EVP_PKEY_CTRL_GET1_ID                           (EVP_PKEY_ALG_CTRL + 12)
+# define EVP_PKEY_CTRL_GET1_ID_LEN                       (EVP_PKEY_ALG_CTRL + 13)
+/* KDF types */
+# define EVP_PKEY_ECDH_KDF_NONE                          1
+# define EVP_PKEY_ECDH_KDF_X9_63                         2
+/** The old name for EVP_PKEY_ECDH_KDF_X9_63
+ *  The ECDH KDF specification has been mistakingly attributed to ANSI X9.62,
+ *  it is actually specified in ANSI X9.63.
+ *  This identifier is retained for backwards compatibility
+ */
+# define EVP_PKEY_ECDH_KDF_X9_62   EVP_PKEY_ECDH_KDF_X9_63
+
+
+#  ifdef  __cplusplus
+}
+#  endif
+# endif
+#endif