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_Jprojective_coordinates_GFp(const EC_GROUP *group,
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,
49 BIGNUM *x, BIGNUM *y, BIGNUM *z,
51 int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *p,
52 const BIGNUM *x, const BIGNUM *y,
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,
59 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
60 const BIGNUM *x, const BIGNUM *y,
62 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
64 BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
65 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
67 const BIGNUM *x, int y_bit,
69 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
70 const BIGNUM *x, const BIGNUM *y,
72 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
74 BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
75 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group,
77 const BIGNUM *x, int y_bit,
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,
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);
100 An B<EC_POINT> structure represents a point on a curve. A new point is
101 constructed by calling the function EC_POINT_new() and providing the
102 B<group> object that the point relates to.
104 EC_POINT_free() frees the memory associated with the B<EC_POINT>.
105 if B<point> is NULL nothing is done.
107 EC_POINT_clear_free() destroys any sensitive data held within the EC_POINT and
108 then frees its memory. If B<point> is NULL nothing is done.
110 EC_POINT_copy() copies the point B<src> into B<dst>. Both B<src> and B<dst>
111 must use the same B<EC_METHOD>.
113 EC_POINT_dup() creates a new B<EC_POINT> object and copies the content from
114 B<src> to the newly created B<EC_POINT> object.
116 EC_POINT_method_of() obtains the B<EC_METHOD> associated with B<point>.
118 A valid point on a curve is the special point at infinity. A point is set to
119 be at infinity by calling EC_POINT_set_to_infinity().
121 The affine co-ordinates for a point describe a point in terms of its x and y
122 position. The function EC_POINT_set_affine_coordinates() sets the B<x> and B<y>
123 co-ordinates for the point B<p> defined over the curve given in B<group>. The
124 function EC_POINT_get_affine_coordinates() sets B<x> and B<y>, either of which
125 may be NULL, to the corresponding coordinates of B<p>.
127 The functions EC_POINT_set_affine_coordinates_GFp() and
128 EC_POINT_set_affine_coordinates_GF2m() are synonyms for
129 EC_POINT_set_affine_coordinates(). They are defined for backwards compatibility
130 only and should not be used.
132 The functions EC_POINT_get_affine_coordinates_GFp() and
133 EC_POINT_get_affine_coordinates_GF2m() are synonyms for
134 EC_POINT_get_affine_coordinates(). They are defined for backwards compatibility
135 only and should not be used.
137 As well as the affine co-ordinates, a point can alternatively be described in
138 terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian
139 projective co-ordinates are expressed as three values x, y and z. Working in
140 this co-ordinate system provides more efficient point multiplication
141 operations. A mapping exists between Jacobian projective co-ordinates and
142 affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written
143 as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian
144 projective from affine co-ordinates is simple. The co-ordinate (x, y) is mapped
145 to (x, y, 1). To set or get the projective co-ordinates use
146 EC_POINT_set_Jprojective_coordinates_GFp() and
147 EC_POINT_get_Jprojective_coordinates_GFp() respectively.
149 Points can also be described in terms of their compressed co-ordinates. For a
150 point (x, y), for any given value for x such that the point is on the curve
151 there will only ever be two possible values for y. Therefore a point can be set
152 using the EC_POINT_set_compressed_coordinates() function where B<x> is the x
153 co-ordinate and B<y_bit> is a value 0 or 1 to identify which of the two
154 possible values for y should be used.
156 The functions EC_POINT_set_compressed_coordinates_GFp() and
157 EC_POINT_set_compressed_coordinates_GF2m() are synonyms for
158 EC_POINT_set_compressed_coordinates(). They are defined for backwards
159 compatibility only and should not be used.
161 In addition B<EC_POINT> can be converted to and from various external
162 representations. The octet form is the binary encoding of the B<ECPoint>
163 structure (as defined in RFC5480 and used in certificates and TLS records):
164 only the content octets are present, the B<OCTET STRING> tag and length are
165 not included. B<BIGNUM> form is the octet form interpreted as a big endian
166 integer converted to a B<BIGNUM> structure. Hexadecimal form is the octet
167 form converted to a NULL terminated character string where each character
168 is one of the printable values 0-9 or A-F (or a-f).
170 The functions EC_POINT_point2oct(), EC_POINT_oct2point(), EC_POINT_point2bn(),
171 EC_POINT_bn2point(), EC_POINT_point2hex() and EC_POINT_hex2point() convert from
172 and to EC_POINTs for the formats: octet, BIGNUM and hexadecimal respectively.
174 The function EC_POINT_point2oct() encodes the given curve point B<p> as an
175 octet string into the buffer B<buf> of size B<len>, using the specified
176 conversion form B<form>.
177 The encoding conforms with Sec. 2.3.3 of the SECG SEC 1 ("Elliptic Curve
178 Cryptography") standard.
179 Similarly the function EC_POINT_oct2point() decodes a curve point into B<p> from
180 the octet string contained in the given buffer B<buf> of size B<len>, conforming
181 to Sec. 2.3.4 of the SECG SEC 1 ("Elliptic Curve Cryptography") standard.
183 The functions EC_POINT_point2hex() and EC_POINT_point2bn() convert a point B<p>,
184 respectively, to the hexadecimal or BIGNUM representation of the same
185 encoding of the function EC_POINT_point2oct().
186 Vice versa, similarly to the function EC_POINT_oct2point(), the functions
187 EC_POINT_hex2point() and EC_POINT_point2bn() decode the hexadecimal or
188 BIGNUM representation into the EC_POINT B<p>.
190 Notice that, according to the standard, the octet string encoding of the point
191 at infinity for a given curve is fixed to a single octet of value zero and that,
192 vice versa, a single octet of size zero is decoded as the point at infinity.
194 The function EC_POINT_point2oct() must be supplied with a buffer long enough to
195 store the octet form. The return value provides the number of octets stored.
196 Calling the function with a NULL buffer will not perform the conversion but
197 will still return the required buffer length.
199 The function EC_POINT_point2buf() allocates a buffer of suitable length and
200 writes an EC_POINT to it in octet format. The allocated buffer is written to
201 B<*pbuf> and its length is returned. The caller must free up the allocated
202 buffer with a call to OPENSSL_free(). Since the allocated buffer value is
203 written to B<*pbuf> the B<pbuf> parameter B<MUST NOT> be B<NULL>.
205 The function EC_POINT_point2hex() will allocate sufficient memory to store the
206 hexadecimal string. It is the caller's responsibility to free this memory with
207 a subsequent call to OPENSSL_free().
211 EC_POINT_new() and EC_POINT_dup() return the newly allocated EC_POINT or NULL
214 The following functions return 1 on success or 0 on error: EC_POINT_copy(),
215 EC_POINT_set_to_infinity(), EC_POINT_set_Jprojective_coordinates_GFp(),
216 EC_POINT_get_Jprojective_coordinates_GFp(),
217 EC_POINT_set_affine_coordinates_GFp(), EC_POINT_get_affine_coordinates_GFp(),
218 EC_POINT_set_compressed_coordinates_GFp(),
219 EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(),
220 EC_POINT_set_compressed_coordinates_GF2m() and EC_POINT_oct2point().
222 EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT.
224 EC_POINT_point2oct() and EC_POINT_point2buf() return the length of the required
225 buffer or 0 on error.
227 EC_POINT_point2bn() returns the pointer to the BIGNUM supplied, or NULL on
230 EC_POINT_bn2point() returns the pointer to the EC_POINT supplied, or NULL on
233 EC_POINT_point2hex() returns a pointer to the hex string, or NULL on error.
235 EC_POINT_hex2point() returns the pointer to the EC_POINT supplied, or NULL on
240 L<crypto(7)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>,
241 L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
242 L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
246 Copyright 2013-2018 The OpenSSL Project Authors. All Rights Reserved.
248 Licensed under the OpenSSL license (the "License"). You may not use
249 this file except in compliance with the License. You can obtain a copy
250 in the file LICENSE in the source distribution or at
251 L<https://www.openssl.org/source/license.html>.