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 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
42 int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *p,
43                                     const BIGNUM *x, const BIGNUM *y,
44                                     BN_CTX *ctx);
45 int EC_POINT_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *p,
46                                     BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
47 int EC_POINT_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p,
48                                         const BIGNUM *x, int y_bit,
49                                         BN_CTX *ctx);
50 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
51                           point_conversion_form_t form,
52                           unsigned char *buf, size_t len, BN_CTX *ctx);
53 size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point,
54                           point_conversion_form_t form,
55                           unsigned char **pbuf, BN_CTX *ctx);
56 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
57                        const unsigned char *buf, size_t len, BN_CTX *ctx);
58 char *EC_POINT_point2hex(const EC_GROUP *group, const EC_POINT *p,
59                          point_conversion_form_t form, BN_CTX *ctx);
60 EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, const char *hex,
61                              EC_POINT *p, BN_CTX *ctx);
62
63Deprecated since OpenSSL 3.0:
64
65 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
66 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
67                                              EC_POINT *p,
68                                              const BIGNUM *x, const BIGNUM *y,
69                                              const BIGNUM *z, BN_CTX *ctx);
70 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
71                                              const EC_POINT *p,
72                                              BIGNUM *x, BIGNUM *y, BIGNUM *z,
73                                              BN_CTX *ctx);
74 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
75                                         const BIGNUM *x, const BIGNUM *y,
76                                         BN_CTX *ctx);
77 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
78                                         const EC_POINT *p,
79                                         BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
80 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
81                                             EC_POINT *p,
82                                             const BIGNUM *x, int y_bit,
83                                             BN_CTX *ctx);
84 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
85                                          const BIGNUM *x, const BIGNUM *y,
86                                          BN_CTX *ctx);
87 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
88                                          const EC_POINT *p,
89                                          BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
90 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group,
91                                              EC_POINT *p,
92                                              const BIGNUM *x, int y_bit,
93                                              BN_CTX *ctx);
94 BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, const EC_POINT *p,
95                           point_conversion_form_t form, BIGNUM *bn,
96                           BN_CTX *ctx);
97 EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, const BIGNUM *bn,
98                             EC_POINT *p, BN_CTX *ctx);
99
100=head1 DESCRIPTION
101
102An B<EC_POINT> structure represents a point on a curve. A new point is
103constructed by calling the function EC_POINT_new() and providing the
104B<group> object that the point relates to.
105
106EC_POINT_free() frees the memory associated with the B<EC_POINT>.
107if B<point> is NULL nothing is done.
108
109EC_POINT_clear_free() destroys any sensitive data held within the EC_POINT and
110then frees its memory. If B<point> is NULL nothing is done.
111
112EC_POINT_copy() copies the point B<src> into B<dst>. Both B<src> and B<dst>
113must use the same B<EC_METHOD>.
114
115EC_POINT_dup() creates a new B<EC_POINT> object and copies the content from
116B<src> to the newly created B<EC_POINT> object.
117
118EC_POINT_method_of() obtains the B<EC_METHOD> associated with B<point>.
119This function was deprecated in OpenSSL 3.0, since EC_METHOD is no longer a
120public concept.
121
122A valid point on a curve is the special point at infinity. A point is set to
123be at infinity by calling EC_POINT_set_to_infinity().
124
125The affine co-ordinates for a point describe a point in terms of its x and y
126position. The function EC_POINT_set_affine_coordinates() sets the B<x> and B<y>
127co-ordinates for the point B<p> defined over the curve given in B<group>. The
128function EC_POINT_get_affine_coordinates() sets B<x> and B<y>, either of which
129may be NULL, to the corresponding coordinates of B<p>.
130
131The functions EC_POINT_set_affine_coordinates_GFp() and
132EC_POINT_set_affine_coordinates_GF2m() are synonyms for
133EC_POINT_set_affine_coordinates(). They are defined for backwards compatibility
134only and should not be used.
135
136The functions EC_POINT_get_affine_coordinates_GFp() and
137EC_POINT_get_affine_coordinates_GF2m() are synonyms for
138EC_POINT_get_affine_coordinates(). They are defined for backwards compatibility
139only and should not be used.
140
141As well as the affine co-ordinates, a point can alternatively be described in
142terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian
143projective co-ordinates are expressed as three values x, y and z. Working in
144this co-ordinate system provides more efficient point multiplication
145operations.  A mapping exists between Jacobian projective co-ordinates and
146affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written
147as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian
148projective from affine co-ordinates is simple. The co-ordinate (x, y) is mapped
149to (x, y, 1). Although deprecated in OpenSSL 3.0 and should no longer be used,
150to set or get the projective co-ordinates in older versions use
151EC_POINT_set_Jprojective_coordinates_GFp() and
152EC_POINT_get_Jprojective_coordinates_GFp() respectively.
153Modern versions should instead use EC_POINT_set_affine_coordinates() and
154EC_POINT_get_affine_coordinates(), performing the conversion manually using the
155above maps in such rare circumstances.
156
157Points can also be described in terms of their compressed co-ordinates. For a
158point (x, y), for any given value for x such that the point is on the curve
159there will only ever be two possible values for y. Therefore, a point can be set
160using the EC_POINT_set_compressed_coordinates() function where B<x> is the x
161co-ordinate and B<y_bit> is a value 0 or 1 to identify which of the two
162possible values for y should be used.
163
164The functions EC_POINT_set_compressed_coordinates_GFp() and
165EC_POINT_set_compressed_coordinates_GF2m() are synonyms for
166EC_POINT_set_compressed_coordinates(). They are defined for backwards
167compatibility only and should not be used.
168
169In addition B<EC_POINT> can be converted to and from various external
170representations. The octet form is the binary encoding of the B<ECPoint>
171structure (as defined in RFC5480 and used in certificates and TLS records):
172only the content octets are present, the B<OCTET STRING> tag and length are
173not included. B<BIGNUM> form is the octet form interpreted as a big endian
174integer converted to a B<BIGNUM> structure. Hexadecimal form is the octet
175form converted to a NULL terminated character string where each character
176is one of the printable values 0-9 or A-F (or a-f).
177
178The functions EC_POINT_point2oct(), EC_POINT_oct2point(), EC_POINT_point2bn(),
179EC_POINT_bn2point(), EC_POINT_point2hex() and EC_POINT_hex2point() convert from
180and to EC_POINTs for the formats: octet, BIGNUM and hexadecimal respectively.
181
182The function EC_POINT_point2oct() encodes the given curve point B<p> as an
183octet string into the buffer B<buf> of size B<len>, using the specified
184conversion form B<form>.
185The encoding conforms with Sec. 2.3.3 of the SECG SEC 1 ("Elliptic Curve
186Cryptography") standard.
187Similarly the function EC_POINT_oct2point() decodes a curve point into B<p> from
188the octet string contained in the given buffer B<buf> of size B<len>, conforming
189to Sec. 2.3.4 of the SECG SEC 1 ("Elliptic Curve Cryptography") standard.
190
191The functions EC_POINT_point2hex() and EC_POINT_point2bn() convert a point B<p>,
192respectively, to the hexadecimal or BIGNUM representation of the same
193encoding of the function EC_POINT_point2oct().
194Vice versa, similarly to the function EC_POINT_oct2point(), the functions
195EC_POINT_hex2point() and EC_POINT_point2bn() decode the hexadecimal or
196BIGNUM representation into the EC_POINT B<p>.
197
198Notice that, according to the standard, the octet string encoding of the point
199at infinity for a given curve is fixed to a single octet of value zero and that,
200vice versa, a single octet of size zero is decoded as the point at infinity.
201
202The function EC_POINT_point2oct() must be supplied with a buffer long enough to
203store the octet form. The return value provides the number of octets stored.
204Calling the function with a NULL buffer will not perform the conversion but
205will still return the required buffer length.
206
207The function EC_POINT_point2buf() allocates a buffer of suitable length and
208writes an EC_POINT to it in octet format. The allocated buffer is written to
209B<*pbuf> and its length is returned. The caller must free up the allocated
210buffer with a call to OPENSSL_free(). Since the allocated buffer value is
211written to B<*pbuf> the B<pbuf> parameter B<MUST NOT> be B<NULL>.
212
213The function EC_POINT_point2hex() will allocate sufficient memory to store the
214hexadecimal string. It is the caller's responsibility to free this memory with
215a subsequent call to OPENSSL_free().
216
217=head1 RETURN VALUES
218
219EC_POINT_new() and EC_POINT_dup() return the newly allocated EC_POINT or NULL
220on error.
221
222The following functions return 1 on success or 0 on error: EC_POINT_copy(),
223EC_POINT_set_to_infinity(), EC_POINT_set_Jprojective_coordinates_GFp(),
224EC_POINT_get_Jprojective_coordinates_GFp(),
225EC_POINT_set_affine_coordinates_GFp(), EC_POINT_get_affine_coordinates_GFp(),
226EC_POINT_set_compressed_coordinates_GFp(),
227EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(),
228EC_POINT_set_compressed_coordinates_GF2m() and EC_POINT_oct2point().
229
230EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT.
231
232EC_POINT_point2oct() and EC_POINT_point2buf() return the length of the required
233buffer or 0 on error.
234
235EC_POINT_point2bn() returns the pointer to the BIGNUM supplied, or NULL on
236error.
237
238EC_POINT_bn2point() returns the pointer to the EC_POINT supplied, or NULL on
239error.
240
241EC_POINT_point2hex() returns a pointer to the hex string, or NULL on error.
242
243EC_POINT_hex2point() returns the pointer to the EC_POINT supplied, or NULL on
244error.
245
246=head1 SEE ALSO
247
248L<crypto(7)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>,
249L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
250L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
251
252=head1 HISTORY
253
254EC_POINT_method_of(),
255EC_POINT_set_Jprojective_coordinates_GFp(),
256EC_POINT_get_Jprojective_coordinates_GFp(),
257EC_POINT_set_affine_coordinates_GFp(), EC_POINT_get_affine_coordinates_GFp(),
258EC_POINT_set_compressed_coordinates_GFp(),
259EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(),
260EC_POINT_set_compressed_coordinates_GF2m(),
261EC_POINT_point2bn(), and EC_POINT_bn2point() were deprecated in OpenSSL 3.0.
262
263
264B<EC_POINT_set_affine_coordinates>, B<EC_POINT_get_affine_coordinates>,
265and B<EC_POINT_set_compressed_coordinates> were
266added in OpenSSL 1.1.1.
267
268=head1 COPYRIGHT
269
270Copyright 2013-2020 The OpenSSL Project Authors. All Rights Reserved.
271
272Licensed under the Apache License 2.0 (the "License").  You may not use
273this file except in compliance with the License.  You can obtain a copy
274in the file LICENSE in the source distribution or at
275L<https://www.openssl.org/source/license.html>.
276
277=cut
278