5 EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy, EC_POINT_dup,
6 EC_POINT_method_of, EC_POINT_set_to_infinity,
7 EC_POINT_set_Jprojective_coordinates, EC_POINT_get_Jprojective_coordinates_GFp,
8 EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp,
9 EC_POINT_set_compressed_coordinates_GFp, EC_POINT_set_affine_coordinates_GF2m,
10 EC_POINT_get_affine_coordinates_GF2m, EC_POINT_set_compressed_coordinates_GF2m,
11 EC_POINT_point2oct, EC_POINT_oct2point, EC_POINT_point2bn, EC_POINT_bn2point,
12 EC_POINT_point2hex, EC_POINT_hex2point - Functions for creating, destroying and
13 manipulating B<EC_POINT> objects.
17 #include <openssl/ec.h>
18 #include <openssl/bn.h>
20 EC_POINT *EC_POINT_new(const EC_GROUP *group);
21 void EC_POINT_free(EC_POINT *point);
22 void EC_POINT_clear_free(EC_POINT *point);
23 int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
24 EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
25 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
26 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
27 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
29 const BIGNUM *x, const BIGNUM *y,
30 const BIGNUM *z, BN_CTX *ctx);
31 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
33 BIGNUM *x, BIGNUM *y, BIGNUM *z,
35 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
36 const BIGNUM *x, const BIGNUM *y,
38 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
40 BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
41 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
43 const BIGNUM *x, int y_bit,
45 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
46 const BIGNUM *x, const BIGNUM *y,
48 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
50 BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
51 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group,
53 const BIGNUM *x, int y_bit,
55 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
56 point_conversion_form_t form,
57 unsigned char *buf, size_t len, BN_CTX *ctx);
58 size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point,
59 point_conversion_form_t form,
60 unsigned char **pbuf, BN_CTX *ctx);
61 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
62 const unsigned char *buf, size_t len, BN_CTX *ctx);
63 BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, const EC_POINT *p,
64 point_conversion_form_t form, BIGNUM *bn,
66 EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, const BIGNUM *bn,
67 EC_POINT *p, BN_CTX *ctx);
68 char *EC_POINT_point2hex(const EC_GROUP *group, const EC_POINT *p,
69 point_conversion_form_t form, BN_CTX *ctx);
70 EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, const char *hex,
71 EC_POINT *p, BN_CTX *ctx);
76 An B<EC_POINT> structure represents a point on a curve. A new point is
77 constructed by calling the function EC_POINT_new() and providing the
78 B<group> object that the point relates to.
80 EC_POINT_free() frees the memory associated with the B<EC_POINT>.
81 if B<point> is NULL nothing is done.
83 EC_POINT_clear_free() destroys any sensitive data held within the EC_POINT and
84 then frees its memory. If B<point> is NULL nothing is done.
86 EC_POINT_copy() copies the point B<src> into B<dst>. Both B<src> and B<dst>
87 must use the same B<EC_METHOD>.
89 EC_POINT_dup() creates a new B<EC_POINT> object and copies the content from
90 B<src> to the newly created B<EC_POINT> object.
92 EC_POINT_method_of() obtains the B<EC_METHOD> associated with B<point>.
94 A valid point on a curve is the special point at infinity. A point is set to
95 be at infinity by calling EC_POINT_set_to_infinity().
97 The affine co-ordinates for a point describe a point in terms of its x and y
98 position. The functions EC_POINT_set_affine_coordinates_GFp() and
99 EC_POINT_set_affine_coordinates_GF2m() set the B<x> and B<y> co-ordinates for
100 the point B<p> defined over the curve given in B<group>.
102 As well as the affine co-ordinates, a point can alternatively be described in
103 terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian
104 projective co-ordinates are expressed as three values x, y and z. Working in
105 this co-ordinate system provides more efficient point multiplication
106 operations. A mapping exists between Jacobian projective co-ordinates and
107 affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written
108 as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian
109 projective to affine co-ordinates is simple. The co-ordinate (x, y) is mapped
110 to (x, y, 1). To set or get the projective co-ordinates use
111 EC_POINT_set_Jprojective_coordinates_GFp() and
112 EC_POINT_get_Jprojective_coordinates_GFp() respectively.
114 Points can also be described in terms of their compressed co-ordinates. For a
115 point (x, y), for any given value for x such that the point is on the curve
116 there will only ever be two possible values for y. Therefore a point can be set
117 using the EC_POINT_set_compressed_coordinates_GFp() and
118 EC_POINT_set_compressed_coordinates_GF2m() functions where B<x> is the x
119 co-ordinate and B<y_bit> is a value 0 or 1 to identify which of the two
120 possible values for y should be used.
122 In addition B<EC_POINT> can be converted to and from various external
123 representations. The octet form is the binary encoding of the B<ECPoint>
124 structure (as defined in RFC5480 and used in certificates and TLS records):
125 only the content octets are present, the B<OCTET STRING> tag and length are
126 not included. B<BIGNUM> form is the octet form interpreted as a big endian
127 integer converted to a B<BIGNUM> structure. Hexadecimal form is the octet
128 form converted to a NULL terminated character string where each character
129 is one of the printable values 0-9 or A-F (or a-f).
131 The functions EC_POINT_point2oct(), EC_POINT_oct2point(), EC_POINT_point2bn(),
132 EC_POINT_bn2point(), EC_POINT_point2hex() and EC_POINT_hex2point() convert from
133 and to EC_POINTs for the formats: octet, BIGNUM and hexadecimal respectively.
135 The function EC_POINT_point2oct() must be supplied with a buffer long enough to
136 store the octet form. The return value provides the number of octets stored.
137 Calling the function with a NULL buffer will not perform the conversion but
138 will still return the required buffer length.
140 The function EC_POINT_point2buf() allocates a buffer of suitable length and
141 writes an EC_POINT to it in octet format. The allocated buffer is written to
142 B<*pbuf> and its length is returned. The caller must free up the allocated
143 buffer with a call to OPENSSL_free(). Since the allocated buffer value is
144 written to B<*pbuf> the B<pbuf> parameter B<MUST NOT> be B<NULL>.
146 The function EC_POINT_point2hex() will allocate sufficient memory to store the
147 hexadecimal string. It is the caller's responsibility to free this memory with
148 a subsequent call to OPENSSL_free().
152 EC_POINT_new() and EC_POINT_dup() return the newly allocated EC_POINT or NULL
155 The following functions return 1 on success or 0 on error: EC_POINT_copy(),
156 EC_POINT_set_to_infinity(), EC_POINT_set_Jprojective_coordinates_GFp(),
157 EC_POINT_get_Jprojective_coordinates_GFp(),
158 EC_POINT_set_affine_coordinates_GFp(), EC_POINT_get_affine_coordinates_GFp(),
159 EC_POINT_set_compressed_coordinates_GFp(),
160 EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(),
161 EC_POINT_set_compressed_coordinates_GF2m() and EC_POINT_oct2point().
163 EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT.
165 EC_POINT_point2oct() and EC_point2buf() return the length of the required
166 buffer or 0 on error.
168 EC_POINT_point2bn() returns the pointer to the BIGNUM supplied, or NULL on
171 EC_POINT_bn2point() returns the pointer to the EC_POINT supplied, or NULL on
174 EC_POINT_point2hex() returns a pointer to the hex string, or NULL on error.
176 EC_POINT_hex2point() returns the pointer to the EC_POINT supplied, or NULL on
181 L<crypto(3)>, L<ec(3)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>,
182 L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
183 L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
189 Copyright 2013-2016 The OpenSSL Project Authors. All Rights Reserved.
191 Licensed under the OpenSSL license (the "License"). You may not use
192 this file except in compliance with the License. You can obtain a copy
193 in the file LICENSE in the source distribution or at
194 L<https://www.openssl.org/source/license.html>.