- NAME
- SYNOPSIS
- DESCRIPTION
- RETURN VALUES
- SEE ALSO
- COPYRIGHT

# NAME

EC_POINT_set_Jprojective_coordinates_GFp, EC_POINT_point2buf, EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy, EC_POINT_dup, EC_POINT_method_of, EC_POINT_set_to_infinity, EC_POINT_get_Jprojective_coordinates_GFp, EC_POINT_set_affine_coordinates, EC_POINT_get_affine_coordinates, EC_POINT_set_compressed_coordinates, EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp, EC_POINT_set_compressed_coordinates_GFp, EC_POINT_set_affine_coordinates_GF2m, EC_POINT_get_affine_coordinates_GF2m, EC_POINT_set_compressed_coordinates_GF2m, EC_POINT_point2oct, EC_POINT_oct2point, EC_POINT_point2bn, EC_POINT_bn2point, EC_POINT_point2hex, EC_POINT_hex2point - Functions for creating, destroying and manipulating EC_POINT objects

# SYNOPSIS

     #include <openssl/ec.h>

     EC_POINT *EC_POINT_new(const EC_GROUP *group);
     void EC_POINT_free(EC_POINT *point);
     void EC_POINT_clear_free(EC_POINT *point);
     int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
     EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
     const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
     int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
     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);
     int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
                                                  const EC_POINT *p,
                                                  BIGNUM *x, BIGNUM *y, BIGNUM *z,
                                                  BN_CTX *ctx);
     int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *p,
                                         const BIGNUM *x, const BIGNUM *y,
                                         BN_CTX *ctx);
     int EC_POINT_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *p,
                                         BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
     int EC_POINT_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p,
                                             const BIGNUM *x, int y_bit,
                                             BN_CTX *ctx);
     int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
                                             const BIGNUM *x, const BIGNUM *y,
                                             BN_CTX *ctx);
     int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
                                             const EC_POINT *p,
                                             BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
     int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
                                                 EC_POINT *p,
                                                 const BIGNUM *x, int y_bit,
                                                 BN_CTX *ctx);
     int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
                                              const BIGNUM *x, const BIGNUM *y,
                                              BN_CTX *ctx);
     int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
                                              const EC_POINT *p,
                                              BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
     int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group,
                                                  EC_POINT *p,
                                                  const BIGNUM *x, int y_bit,
                                                  BN_CTX *ctx);
     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);
     size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point,
                               point_conversion_form_t form,
                               unsigned char **pbuf, BN_CTX *ctx);
     int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
                            const unsigned char *buf, size_t len, BN_CTX *ctx);
     BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, const EC_POINT *p,
                               point_conversion_form_t form, BIGNUM *bn,
                               BN_CTX *ctx);
     EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, const BIGNUM *bn,
                                 EC_POINT *p, BN_CTX *ctx);
     char *EC_POINT_point2hex(const EC_GROUP *group, const EC_POINT *p,
                              point_conversion_form_t form, BN_CTX *ctx);
     EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, const char *hex,
                                  EC_POINT *p, BN_CTX *ctx);

# DESCRIPTION

An EC_POINT structure represents a point on a curve. A new point is constructed by calling the function EC_POINT_new() and providing the group object that the point relates to.

EC_POINT_free() frees the memory associated with the EC_POINT. if point is NULL nothing is done.

EC_POINT_clear_free() destroys any sensitive data held within the EC_POINT and then frees its memory. If point is NULL nothing is done.

EC_POINT_copy() copies the point src into dst. Both src and dst must use the same EC_METHOD.

EC_POINT_dup() creates a new EC_POINT object and copies the content from src to the newly created EC_POINT object.

EC_POINT_method_of() obtains the EC_METHOD associated with point.

A valid point on a curve is the special point at infinity. A point is set to be at infinity by calling EC_POINT_set_to_infinity().

The affine co-ordinates for a point describe a point in terms of its x and y position. The function EC_POINT_set_affine_coordinates() sets the x and y co-ordinates for the point p defined over the curve given in group. The function EC_POINT_get_affine_coordinates() sets x and y, either of which may be NULL, to the corresponding coordinates of p.

The functions EC_POINT_set_affine_coordinates_GFp() and EC_POINT_set_affine_coordinates_GF2m() are synonyms for EC_POINT_set_affine_coordinates(). They are defined for backwards compatibility only and should not be used.

The functions EC_POINT_get_affine_coordinates_GFp() and EC_POINT_get_affine_coordinates_GF2m() are synonyms for EC_POINT_get_affine_coordinates(). They are defined for backwards compatibility only and should not be used.

As well as the affine co-ordinates, a point can alternatively be described in terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian projective co-ordinates are expressed as three values x, y and z. Working in this co-ordinate system provides more efficient point multiplication operations. A mapping exists between Jacobian projective co-ordinates and affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian projective from affine co-ordinates is simple. The co-ordinate (x, y) is mapped to (x, y, 1). To set or get the projective co-ordinates use EC_POINT_set_Jprojective_coordinates_GFp() and EC_POINT_get_Jprojective_coordinates_GFp() respectively.

Points can also be described in terms of their compressed co-ordinates. For a point (x, y), for any given value for x such that the point is on the curve there will only ever be two possible values for y. Therefore, a point can be set using the EC_POINT_set_compressed_coordinates() function where x is the x co-ordinate and y_bit is a value 0 or 1 to identify which of the two possible values for y should be used.

The functions EC_POINT_set_compressed_coordinates_GFp() and EC_POINT_set_compressed_coordinates_GF2m() are synonyms for EC_POINT_set_compressed_coordinates(). They are defined for backwards compatibility only and should not be used.

In addition EC_POINT can be converted to and from various external representations. The octet form is the binary encoding of the ECPoint structure (as defined in RFC5480 and used in certificates and TLS records): only the content octets are present, the OCTET STRING tag and length are not included. BIGNUM form is the octet form interpreted as a big endian integer converted to a BIGNUM structure. Hexadecimal form is the octet form converted to a NULL terminated character string where each character is one of the printable values 0-9 or A-F (or a-f).

The functions EC_POINT_point2oct(), EC_POINT_oct2point(), EC_POINT_point2bn(), EC_POINT_bn2point(), EC_POINT_point2hex() and EC_POINT_hex2point() convert from and to EC_POINTs for the formats: octet, BIGNUM and hexadecimal respectively.

The function EC_POINT_point2oct() encodes the given curve point p as an octet string into the buffer buf of size len, using the specified conversion form form. The encoding conforms with Sec. 2.3.3 of the SECG SEC 1 ("Elliptic Curve Cryptography") standard. Similarly the function EC_POINT_oct2point() decodes a curve point into p from the octet string contained in the given buffer buf of size len, conforming to Sec. 2.3.4 of the SECG SEC 1 ("Elliptic Curve Cryptography") standard.

The functions EC_POINT_point2hex() and EC_POINT_point2bn() convert a point p, respectively, to the hexadecimal or BIGNUM representation of the same encoding of the function EC_POINT_point2oct(). Vice versa, similarly to the function EC_POINT_oct2point(), the functions EC_POINT_hex2point() and EC_POINT_point2bn() decode the hexadecimal or BIGNUM representation into the EC_POINT p.

Notice that, according to the standard, the octet string encoding of the point at infinity for a given curve is fixed to a single octet of value zero and that, vice versa, a single octet of size zero is decoded as the point at infinity.

The function EC_POINT_point2oct() must be supplied with a buffer long enough to store the octet form. The return value provides the number of octets stored. Calling the function with a NULL buffer will not perform the conversion but will still return the required buffer length.

The function EC_POINT_point2buf() allocates a buffer of suitable length and writes an EC_POINT to it in octet format. The allocated buffer is written to *pbuf and its length is returned. The caller must free up the allocated buffer with a call to OPENSSL_free(). Since the allocated buffer value is written to *pbuf the pbuf parameter MUST NOT be NULL.

The function EC_POINT_point2hex() will allocate sufficient memory to store the hexadecimal string. It is the caller's responsibility to free this memory with a subsequent call to OPENSSL_free().

# RETURN VALUES

EC_POINT_new() and EC_POINT_dup() return the newly allocated EC_POINT or NULL on error.

The following functions return 1 on success or 0 on error: EC_POINT_copy(), EC_POINT_set_to_infinity(), EC_POINT_set_Jprojective_coordinates_GFp(), EC_POINT_get_Jprojective_coordinates_GFp(), EC_POINT_set_affine_coordinates_GFp(), EC_POINT_get_affine_coordinates_GFp(), EC_POINT_set_compressed_coordinates_GFp(), EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(), EC_POINT_set_compressed_coordinates_GF2m() and EC_POINT_oct2point().

EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT.

EC_POINT_point2oct() and EC_POINT_point2buf() return the length of the required buffer or 0 on error.

EC_POINT_point2bn() returns the pointer to the BIGNUM supplied, or NULL on error.

EC_POINT_bn2point() returns the pointer to the EC_POINT supplied, or NULL on error.

EC_POINT_point2hex() returns a pointer to the hex string, or NULL on error.

EC_POINT_hex2point() returns the pointer to the EC_POINT supplied, or NULL on error.

# SEE ALSO

crypto(7), EC_GROUP_new(3), EC_GROUP_copy(3), EC_POINT_add(3), EC_KEY_new(3), EC_GFp_simple_method(3), d2i_ECPKParameters(3)

# COPYRIGHT

Copyright 2013-2020 The OpenSSL Project Authors. 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.