=pod

=head1 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

=head1 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);
 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
 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);
 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);
 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);

The following functions have been deprecated since OpenSSL 3.0, and can be
hidden entirely by defining B<OPENSSL_API_COMPAT> with a suitable version value,
see L<openssl_user_macros(7)>:

 const EC_METHOD *EC_POINT_method_of(const 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_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);
 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);

=head1 DESCRIPTION

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

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

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

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

EC_POINT_method_of() obtains the B<EC_METHOD> associated with B<point>.
This function was deprecated in OpenSSL 3.0, since EC_METHOD is no longer a
public concept.

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 B<x> and B<y>
co-ordinates for the point B<p> defined over the curve given in B<group>. The
function EC_POINT_get_affine_coordinates() sets B<x> and B<y>, either of which
may be NULL, to the corresponding coordinates of B<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). Although deprecated in OpenSSL 3.0 and should no longer be used,
to set or get the projective co-ordinates in older versions use
EC_POINT_set_Jprojective_coordinates_GFp() and
EC_POINT_get_Jprojective_coordinates_GFp() respectively.
Modern versions should instead use EC_POINT_set_affine_coordinates() and
EC_POINT_get_affine_coordinates(), performing the conversion manually using the
above maps in such rare circumstances.

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 B<x> is the x
co-ordinate and B<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 B<EC_POINT> can be converted to and from various external
representations. The octet form is the binary encoding of the B<ECPoint>
structure (as defined in RFC5480 and used in certificates and TLS records):
only the content octets are present, the B<OCTET STRING> tag and length are
not included. B<BIGNUM> form is the octet form interpreted as a big endian
integer converted to a B<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 B<p> as an
octet string into the buffer B<buf> of size B<len>, using the specified
conversion form B<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 B<p> from
the octet string contained in the given buffer B<buf> of size B<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 B<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 B<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
B<*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 B<*pbuf> the B<pbuf> parameter B<MUST NOT> be B<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().

=head1 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.

=head1 SEE ALSO

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

=head1 HISTORY

EC_POINT_method_of(),
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(),
EC_POINT_point2bn(), and EC_POINT_bn2point() were deprecated in OpenSSL 3.0.


B<EC_POINT_set_affine_coordinates>, B<EC_POINT_get_affine_coordinates>,
and B<EC_POINT_set_compressed_coordinates> were
added in OpenSSL 1.1.1.

=head1 COPYRIGHT

Copyright 2013-2021 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the Apache License 2.0 (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
L<https://www.openssl.org/source/license.html>.

=cut
