1=pod
2
3=head1 NAME
4
5EC_POINT_set_Jprojective_coordinates_GFp,
6EC_POINT_point2buf,
7EC_POINT_new,
8EC_POINT_free,
9EC_POINT_clear_free,
10EC_POINT_copy,
11EC_POINT_dup,
12EC_POINT_method_of,
13EC_POINT_set_to_infinity,
14EC_POINT_get_Jprojective_coordinates_GFp,
15EC_POINT_set_affine_coordinates,
16EC_POINT_get_affine_coordinates,
17EC_POINT_set_compressed_coordinates,
18EC_POINT_set_affine_coordinates_GFp,
19EC_POINT_get_affine_coordinates_GFp,
20EC_POINT_set_compressed_coordinates_GFp,
21EC_POINT_set_affine_coordinates_GF2m,
22EC_POINT_get_affine_coordinates_GF2m,
23EC_POINT_set_compressed_coordinates_GF2m,
24EC_POINT_point2oct,
25EC_POINT_oct2point,
26EC_POINT_point2bn,
27EC_POINT_bn2point,
28EC_POINT_point2hex,
29EC_POINT_hex2point
30- Functions for creating, destroying and manipulating EC_POINT objects
31
32=head1 SYNOPSIS
33
34 #include <openssl/ec.h>
35
36 EC_POINT *EC_POINT_new(const EC_GROUP *group);
37 void EC_POINT_free(EC_POINT *point);
38 void EC_POINT_clear_free(EC_POINT *point);
39 int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
40 EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
41 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
42 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
43 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
44                                              EC_POINT *p,
45                                              const BIGNUM *x, const BIGNUM *y,
46                                              const BIGNUM *z, BN_CTX *ctx);
47 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
48                                              const EC_POINT *p,
49                                              BIGNUM *x, BIGNUM *y, BIGNUM *z,
50                                              BN_CTX *ctx);
51 int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *p,
52                                     const BIGNUM *x, const BIGNUM *y,
53                                     BN_CTX *ctx);
54 int EC_POINT_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *p,
55                                     BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
56 int EC_POINT_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p,
57                                         const BIGNUM *x, int y_bit,
58                                         BN_CTX *ctx);
59 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
60                                         const BIGNUM *x, const BIGNUM *y,
61                                         BN_CTX *ctx);
62 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
63                                         const EC_POINT *p,
64                                         BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
65 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
66                                             EC_POINT *p,
67                                             const BIGNUM *x, int y_bit,
68                                             BN_CTX *ctx);
69 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
70                                          const BIGNUM *x, const BIGNUM *y,
71                                          BN_CTX *ctx);
72 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
73                                          const EC_POINT *p,
74                                          BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
75 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group,
76                                              EC_POINT *p,
77                                              const BIGNUM *x, int y_bit,
78                                              BN_CTX *ctx);
79 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
80                           point_conversion_form_t form,
81                           unsigned char *buf, size_t len, BN_CTX *ctx);
82 size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point,
83                           point_conversion_form_t form,
84                           unsigned char **pbuf, BN_CTX *ctx);
85 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
86                        const unsigned char *buf, size_t len, BN_CTX *ctx);
87 BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, const EC_POINT *p,
88                           point_conversion_form_t form, BIGNUM *bn,
89                           BN_CTX *ctx);
90 EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, const BIGNUM *bn,
91                             EC_POINT *p, BN_CTX *ctx);
92 char *EC_POINT_point2hex(const EC_GROUP *group, const EC_POINT *p,
93                          point_conversion_form_t form, BN_CTX *ctx);
94 EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, const char *hex,
95                              EC_POINT *p, BN_CTX *ctx);
96
97
98=head1 DESCRIPTION
99
100An B<EC_POINT> structure represents a point on a curve. A new point is
101constructed by calling the function EC_POINT_new() and providing the
102B<group> object that the point relates to.
103
104EC_POINT_free() frees the memory associated with the B<EC_POINT>.
105if B<point> is NULL nothing is done.
106
107EC_POINT_clear_free() destroys any sensitive data held within the EC_POINT and
108then frees its memory. If B<point> is NULL nothing is done.
109
110EC_POINT_copy() copies the point B<src> into B<dst>. Both B<src> and B<dst>
111must use the same B<EC_METHOD>.
112
113EC_POINT_dup() creates a new B<EC_POINT> object and copies the content from
114B<src> to the newly created B<EC_POINT> object.
115
116EC_POINT_method_of() obtains the B<EC_METHOD> associated with B<point>.
117
118A valid point on a curve is the special point at infinity. A point is set to
119be at infinity by calling EC_POINT_set_to_infinity().
120
121The affine co-ordinates for a point describe a point in terms of its x and y
122position. The function EC_POINT_set_affine_coordinates() sets the B<x> and B<y>
123co-ordinates for the point B<p> defined over the curve given in B<group>. The
124function EC_POINT_get_affine_coordinates() sets B<x> and B<y>, either of which
125may be NULL, to the corresponding coordinates of B<p>.
126
127The functions EC_POINT_set_affine_coordinates_GFp() and
128EC_POINT_set_affine_coordinates_GF2m() are synonyms for
129EC_POINT_set_affine_coordinates(). They are defined for backwards compatibility
130only and should not be used.
131
132The functions EC_POINT_get_affine_coordinates_GFp() and
133EC_POINT_get_affine_coordinates_GF2m() are synonyms for
134EC_POINT_get_affine_coordinates(). They are defined for backwards compatibility
135only and should not be used.
136
137As well as the affine co-ordinates, a point can alternatively be described in
138terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian
139projective co-ordinates are expressed as three values x, y and z. Working in
140this co-ordinate system provides more efficient point multiplication
141operations.  A mapping exists between Jacobian projective co-ordinates and
142affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written
143as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian
144projective from affine co-ordinates is simple. The co-ordinate (x, y) is mapped
145to (x, y, 1). To set or get the projective co-ordinates use
146EC_POINT_set_Jprojective_coordinates_GFp() and
147EC_POINT_get_Jprojective_coordinates_GFp() respectively.
148
149Points can also be described in terms of their compressed co-ordinates. For a
150point (x, y), for any given value for x such that the point is on the curve
151there will only ever be two possible values for y. Therefore, a point can be set
152using the EC_POINT_set_compressed_coordinates() function where B<x> is the x
153co-ordinate and B<y_bit> is a value 0 or 1 to identify which of the two
154possible values for y should be used.
155
156The functions EC_POINT_set_compressed_coordinates_GFp() and
157EC_POINT_set_compressed_coordinates_GF2m() are synonyms for
158EC_POINT_set_compressed_coordinates(). They are defined for backwards
159compatibility only and should not be used.
160
161In addition B<EC_POINT> can be converted to and from various external
162representations. The octet form is the binary encoding of the B<ECPoint>
163structure (as defined in RFC5480 and used in certificates and TLS records):
164only the content octets are present, the B<OCTET STRING> tag and length are
165not included. B<BIGNUM> form is the octet form interpreted as a big endian
166integer converted to a B<BIGNUM> structure. Hexadecimal form is the octet
167form converted to a NULL terminated character string where each character
168is one of the printable values 0-9 or A-F (or a-f).
169
170The functions EC_POINT_point2oct(), EC_POINT_oct2point(), EC_POINT_point2bn(),
171EC_POINT_bn2point(), EC_POINT_point2hex() and EC_POINT_hex2point() convert from
172and to EC_POINTs for the formats: octet, BIGNUM and hexadecimal respectively.
173
174The function EC_POINT_point2oct() encodes the given curve point B<p> as an
175octet string into the buffer B<buf> of size B<len>, using the specified
176conversion form B<form>.
177The encoding conforms with Sec. 2.3.3 of the SECG SEC 1 ("Elliptic Curve
178Cryptography") standard.
179Similarly the function EC_POINT_oct2point() decodes a curve point into B<p> from
180the octet string contained in the given buffer B<buf> of size B<len>, conforming
181to Sec. 2.3.4 of the SECG SEC 1 ("Elliptic Curve Cryptography") standard.
182
183The functions EC_POINT_point2hex() and EC_POINT_point2bn() convert a point B<p>,
184respectively, to the hexadecimal or BIGNUM representation of the same
185encoding of the function EC_POINT_point2oct().
186Vice versa, similarly to the function EC_POINT_oct2point(), the functions
187EC_POINT_hex2point() and EC_POINT_point2bn() decode the hexadecimal or
188BIGNUM representation into the EC_POINT B<p>.
189
190Notice that, according to the standard, the octet string encoding of the point
191at infinity for a given curve is fixed to a single octet of value zero and that,
192vice versa, a single octet of size zero is decoded as the point at infinity.
193
194The function EC_POINT_point2oct() must be supplied with a buffer long enough to
195store the octet form. The return value provides the number of octets stored.
196Calling the function with a NULL buffer will not perform the conversion but
197will still return the required buffer length.
198
199The function EC_POINT_point2buf() allocates a buffer of suitable length and
200writes an EC_POINT to it in octet format. The allocated buffer is written to
201B<*pbuf> and its length is returned. The caller must free up the allocated
202buffer with a call to OPENSSL_free(). Since the allocated buffer value is
203written to B<*pbuf> the B<pbuf> parameter B<MUST NOT> be B<NULL>.
204
205The function EC_POINT_point2hex() will allocate sufficient memory to store the
206hexadecimal string. It is the caller's responsibility to free this memory with
207a subsequent call to OPENSSL_free().
208
209=head1 RETURN VALUES
210
211EC_POINT_new() and EC_POINT_dup() return the newly allocated EC_POINT or NULL
212on error.
213
214The following functions return 1 on success or 0 on error: EC_POINT_copy(),
215EC_POINT_set_to_infinity(), EC_POINT_set_Jprojective_coordinates_GFp(),
216EC_POINT_get_Jprojective_coordinates_GFp(),
217EC_POINT_set_affine_coordinates_GFp(), EC_POINT_get_affine_coordinates_GFp(),
218EC_POINT_set_compressed_coordinates_GFp(),
219EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(),
220EC_POINT_set_compressed_coordinates_GF2m() and EC_POINT_oct2point().
221
222EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT.
223
224EC_POINT_point2oct() and EC_POINT_point2buf() return the length of the required
225buffer or 0 on error.
226
227EC_POINT_point2bn() returns the pointer to the BIGNUM supplied, or NULL on
228error.
229
230EC_POINT_bn2point() returns the pointer to the EC_POINT supplied, or NULL on
231error.
232
233EC_POINT_point2hex() returns a pointer to the hex string, or NULL on error.
234
235EC_POINT_hex2point() returns the pointer to the EC_POINT supplied, or NULL on
236error.
237
238=head1 SEE ALSO
239
240L<crypto(7)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>,
241L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
242L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
243
244=head1 COPYRIGHT
245
246Copyright 2013-2020 The OpenSSL Project Authors. All Rights Reserved.
247
248Licensed under the OpenSSL license (the "License").  You may not use
249this file except in compliance with the License.  You can obtain a copy
250in the file LICENSE in the source distribution or at
251L<https://www.openssl.org/source/license.html>.
252
253=cut
254