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