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<ul>
<li><a href="#name">NAME</a></li>
<li><a href="#synopsis">SYNOPSIS</a></li>
<li><a href="#description">DESCRIPTION</a></li>
<li><a href="#return_values">RETURN VALUES</a></li>
<li><a href="#see_also">SEE ALSO</a></li>
<li><a href="#copyright">COPYRIGHT</a></li>
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<p>
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<hr />
<h1><a name="name">NAME</a></h1>
<p>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</p>
<p>
</p>
<hr />
<h1><a name="synopsis">SYNOPSIS</a></h1>
<pre>
#include <openssl/ec.h></pre>
<pre>
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);</pre>
<p>
</p>
<hr />
<h1><a name="description">DESCRIPTION</a></h1>
<p>An <strong>EC_POINT</strong> structure represents a point on a curve. A new point is
constructed by calling the function <code>EC_POINT_new()</code> and providing the
<strong>group</strong> object that the point relates to.</p>
<p><code>EC_POINT_free()</code> frees the memory associated with the <strong>EC_POINT</strong>.
if <strong>point</strong> is NULL nothing is done.</p>
<p><code>EC_POINT_clear_free()</code> destroys any sensitive data held within the EC_POINT and
then frees its memory. If <strong>point</strong> is NULL nothing is done.</p>
<p><code>EC_POINT_copy()</code> copies the point <strong>src</strong> into <strong>dst</strong>. Both <strong>src</strong> and <strong>dst</strong>
must use the same <strong>EC_METHOD</strong>.</p>
<p><code>EC_POINT_dup()</code> creates a new <strong>EC_POINT</strong> object and copies the content from
<strong>src</strong> to the newly created <strong>EC_POINT</strong> object.</p>
<p><code>EC_POINT_method_of()</code> obtains the <strong>EC_METHOD</strong> associated with <strong>point</strong>.</p>
<p>A valid point on a curve is the special point at infinity. A point is set to
be at infinity by calling <code>EC_POINT_set_to_infinity()</code>.</p>
<p>The affine co-ordinates for a point describe a point in terms of its x and y
position. The function <code>EC_POINT_set_affine_coordinates()</code> sets the <strong>x</strong> and <strong>y</strong>
co-ordinates for the point <strong>p</strong> defined over the curve given in <strong>group</strong>. The
function <code>EC_POINT_get_affine_coordinates()</code> sets <strong>x</strong> and <strong>y</strong>, either of which
may be NULL, to the corresponding coordinates of <strong>p</strong>.</p>
<p>The functions <code>EC_POINT_set_affine_coordinates_GFp()</code> and
EC_POINT_set_affine_coordinates_GF2m() are synonyms for
<code>EC_POINT_set_affine_coordinates()</code>. They are defined for backwards compatibility
only and should not be used.</p>
<p>The functions <code>EC_POINT_get_affine_coordinates_GFp()</code> and
EC_POINT_get_affine_coordinates_GF2m() are synonyms for
<code>EC_POINT_get_affine_coordinates()</code>. They are defined for backwards compatibility
only and should not be used.</p>
<p>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
<code>EC_POINT_set_Jprojective_coordinates_GFp()</code> and
<code>EC_POINT_get_Jprojective_coordinates_GFp()</code> respectively.</p>
<p>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 <code>EC_POINT_set_compressed_coordinates()</code> function where <strong>x</strong> is the x
co-ordinate and <strong>y_bit</strong> is a value 0 or 1 to identify which of the two
possible values for y should be used.</p>
<p>The functions <code>EC_POINT_set_compressed_coordinates_GFp()</code> and
EC_POINT_set_compressed_coordinates_GF2m() are synonyms for
<code>EC_POINT_set_compressed_coordinates()</code>. They are defined for backwards
compatibility only and should not be used.</p>
<p>In addition <strong>EC_POINT</strong> can be converted to and from various external
representations. The octet form is the binary encoding of the <strong>ECPoint</strong>
structure (as defined in <a href="http://www.ietf.org/rfc/rfc5480.txt" class="rfc">RFC5480</a> and used in certificates and TLS records):
only the content octets are present, the <strong>OCTET STRING</strong> tag and length are
not included. <strong>BIGNUM</strong> form is the octet form interpreted as a big endian
integer converted to a <strong>BIGNUM</strong> 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).</p>
<p>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.</p>
<p>The function EC_POINT_point2oct() encodes the given curve point <strong>p</strong> as an
octet string into the buffer <strong>buf</strong> of size <strong>len</strong>, using the specified
conversion form <strong>form</strong>.
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 <strong>p</strong> from
the octet string contained in the given buffer <strong>buf</strong> of size <strong>len</strong>, conforming
to Sec. 2.3.4 of the SECG SEC 1 ("Elliptic Curve Cryptography") standard.</p>
<p>The functions EC_POINT_point2hex() and EC_POINT_point2bn() convert a point <strong>p</strong>,
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 <strong>p</strong>.</p>
<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.</p>
<p>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.</p>
<p>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
<strong>*pbuf</strong> and its length is returned. The caller must free up the allocated
buffer with a call to <code>OPENSSL_free()</code>. Since the allocated buffer value is
written to <strong>*pbuf</strong> the <strong>pbuf</strong> parameter <strong>MUST NOT</strong> be <strong>NULL</strong>.</p>
<p>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 <code>OPENSSL_free()</code>.</p>
<p>
</p>
<hr />
<h1><a name="return_values">RETURN VALUES</a></h1>
<p><code>EC_POINT_new()</code> and <code>EC_POINT_dup()</code> return the newly allocated EC_POINT or NULL
on error.</p>
<p>The following functions return 1 on success or 0 on error: <code>EC_POINT_copy()</code>,
<code>EC_POINT_set_to_infinity()</code>, <code>EC_POINT_set_Jprojective_coordinates_GFp()</code>,
<code>EC_POINT_get_Jprojective_coordinates_GFp()</code>,
<code>EC_POINT_set_affine_coordinates_GFp()</code>, <code>EC_POINT_get_affine_coordinates_GFp()</code>,
<code>EC_POINT_set_compressed_coordinates_GFp()</code>,
EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(),
EC_POINT_set_compressed_coordinates_GF2m() and EC_POINT_oct2point().</p>
<p>EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT.</p>
<p>EC_POINT_point2oct() and EC_POINT_point2buf() return the length of the required
buffer or 0 on error.</p>
<p>EC_POINT_point2bn() returns the pointer to the BIGNUM supplied, or NULL on
error.</p>
<p>EC_POINT_bn2point() returns the pointer to the EC_POINT supplied, or NULL on
error.</p>
<p>EC_POINT_point2hex() returns a pointer to the hex string, or NULL on error.</p>
<p>EC_POINT_hex2point() returns the pointer to the EC_POINT supplied, or NULL on
error.</p>
<p>
</p>
<hr />
<h1><a name="see_also">SEE ALSO</a></h1>
<p><em>crypto(7)</em>, <em>EC_GROUP_new(3)</em>, <em>EC_GROUP_copy(3)</em>,
<em>EC_POINT_add(3)</em>, <em>EC_KEY_new(3)</em>,
<em>EC_GFp_simple_method(3)</em>, <em>d2i_ECPKParameters(3)</em></p>
<p>
</p>
<hr />
<h1><a name="copyright">COPYRIGHT</a></h1>
<p>Copyright 2013-2020 The OpenSSL Project Authors. All Rights Reserved.</p>
<p>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
<a href="https://www.openssl.org/source/license.html">https://www.openssl.org/source/license.html</a>.</p>
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