1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
|
=pod
=head1 NAME
EC_POINT_set_Jprojective_coordinates_GFp, EC_POINT_point2buf,
EC_POINT_new, EC_POINT_free, EC_POINT_clear_free,
EC_POINT_copy, EC_POINT_dup, EC_POINT_method_of,
EC_POINT_set_to_infinity,
EC_POINT_get_Jprojective_coordinates_GFp,
EC_POINT_set_affine_coordinates_GFp,
EC_POINT_get_affine_coordinates_GFp, EC_POINT_set_compressed_coordinates_GFp,
EC_POINT_set_affine_coordinates_GF2m, EC_POINT_get_affine_coordinates_GF2m,
EC_POINT_set_compressed_coordinates_GF2m, EC_POINT_point2oct,
EC_POINT_oct2point, EC_POINT_point2bn, EC_POINT_bn2point, EC_POINT_point2hex,
EC_POINT_hex2point
- Functions for creating, destroying and manipulating EC_POINT objects
=head1 SYNOPSIS
#include <openssl/ec.h>
EC_POINT *EC_POINT_new(const EC_GROUP *group);
void EC_POINT_free(EC_POINT *point);
void EC_POINT_clear_free(EC_POINT *point);
int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
EC_POINT *p,
const BIGNUM *x, const BIGNUM *y,
const BIGNUM *z, BN_CTX *ctx);
int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
const EC_POINT *p,
BIGNUM *x, BIGNUM *y, BIGNUM *z,
BN_CTX *ctx);
int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
const BIGNUM *x, const BIGNUM *y,
BN_CTX *ctx);
int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
const EC_POINT *p,
BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
EC_POINT *p,
const BIGNUM *x, int y_bit,
BN_CTX *ctx);
int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
const BIGNUM *x, const BIGNUM *y,
BN_CTX *ctx);
int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
const EC_POINT *p,
BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group,
EC_POINT *p,
const BIGNUM *x, int y_bit,
BN_CTX *ctx);
size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
point_conversion_form_t form,
unsigned char *buf, size_t len, BN_CTX *ctx);
size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point,
point_conversion_form_t form,
unsigned char **pbuf, BN_CTX *ctx);
int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
const unsigned char *buf, size_t len, BN_CTX *ctx);
BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, const EC_POINT *p,
point_conversion_form_t form, BIGNUM *bn,
BN_CTX *ctx);
EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, const BIGNUM *bn,
EC_POINT *p, BN_CTX *ctx);
char *EC_POINT_point2hex(const EC_GROUP *group, const EC_POINT *p,
point_conversion_form_t form, BN_CTX *ctx);
EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, const char *hex,
EC_POINT *p, BN_CTX *ctx);
=head1 DESCRIPTION
An B<EC_POINT> structure represents a point on a curve. A new point is
constructed by calling the function EC_POINT_new() and providing the
B<group> object that the point relates to.
EC_POINT_free() frees the memory associated with the B<EC_POINT>.
if B<point> is NULL nothing is done.
EC_POINT_clear_free() destroys any sensitive data held within the EC_POINT and
then frees its memory. If B<point> is NULL nothing is done.
EC_POINT_copy() copies the point B<src> into B<dst>. Both B<src> and B<dst>
must use the same B<EC_METHOD>.
EC_POINT_dup() creates a new B<EC_POINT> object and copies the content from
B<src> to the newly created B<EC_POINT> object.
EC_POINT_method_of() obtains the B<EC_METHOD> associated with B<point>.
A valid point on a curve is the special point at infinity. A point is set to
be at infinity by calling EC_POINT_set_to_infinity().
The affine co-ordinates for a point describe a point in terms of its x and y
position. The functions EC_POINT_set_affine_coordinates_GFp() and
EC_POINT_set_affine_coordinates_GF2m() set the B<x> and B<y> co-ordinates for
the point B<p> defined over the curve given in B<group>.
As well as the affine co-ordinates, a point can alternatively be described in
terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian
projective co-ordinates are expressed as three values x, y and z. Working in
this co-ordinate system provides more efficient point multiplication
operations. A mapping exists between Jacobian projective co-ordinates and
affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written
as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian
projective from affine co-ordinates is simple. The co-ordinate (x, y) is mapped
to (x, y, 1). To set or get the projective co-ordinates use
EC_POINT_set_Jprojective_coordinates_GFp() and
EC_POINT_get_Jprojective_coordinates_GFp() respectively.
Points can also be described in terms of their compressed co-ordinates. For a
point (x, y), for any given value for x such that the point is on the curve
there will only ever be two possible values for y. Therefore a point can be set
using the EC_POINT_set_compressed_coordinates_GFp() and
EC_POINT_set_compressed_coordinates_GF2m() functions where B<x> is the x
co-ordinate and B<y_bit> is a value 0 or 1 to identify which of the two
possible values for y should be used.
In addition B<EC_POINT> can be converted to and from various external
representations. The octet form is the binary encoding of the B<ECPoint>
structure (as defined in RFC5480 and used in certificates and TLS records):
only the content octets are present, the B<OCTET STRING> tag and length are
not included. B<BIGNUM> form is the octet form interpreted as a big endian
integer converted to a B<BIGNUM> structure. Hexadecimal form is the octet
form converted to a NULL terminated character string where each character
is one of the printable values 0-9 or A-F (or a-f).
The functions EC_POINT_point2oct(), EC_POINT_oct2point(), EC_POINT_point2bn(),
EC_POINT_bn2point(), EC_POINT_point2hex() and EC_POINT_hex2point() convert from
and to EC_POINTs for the formats: octet, BIGNUM and hexadecimal respectively.
The function EC_POINT_point2oct() must be supplied with a buffer long enough to
store the octet form. The return value provides the number of octets stored.
Calling the function with a NULL buffer will not perform the conversion but
will still return the required buffer length.
The function EC_POINT_point2buf() allocates a buffer of suitable length and
writes an EC_POINT to it in octet format. The allocated buffer is written to
B<*pbuf> and its length is returned. The caller must free up the allocated
buffer with a call to OPENSSL_free(). Since the allocated buffer value is
written to B<*pbuf> the B<pbuf> parameter B<MUST NOT> be B<NULL>.
The function EC_POINT_point2hex() will allocate sufficient memory to store the
hexadecimal string. It is the caller's responsibility to free this memory with
a subsequent call to OPENSSL_free().
=head1 RETURN VALUES
EC_POINT_new() and EC_POINT_dup() return the newly allocated EC_POINT or NULL
on error.
The following functions return 1 on success or 0 on error: EC_POINT_copy(),
EC_POINT_set_to_infinity(), EC_POINT_set_Jprojective_coordinates_GFp(),
EC_POINT_get_Jprojective_coordinates_GFp(),
EC_POINT_set_affine_coordinates_GFp(), EC_POINT_get_affine_coordinates_GFp(),
EC_POINT_set_compressed_coordinates_GFp(),
EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(),
EC_POINT_set_compressed_coordinates_GF2m() and EC_POINT_oct2point().
EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT.
EC_POINT_point2oct() and EC_POINT_point2buf() return the length of the required
buffer or 0 on error.
EC_POINT_point2bn() returns the pointer to the BIGNUM supplied, or NULL on
error.
EC_POINT_bn2point() returns the pointer to the EC_POINT supplied, or NULL on
error.
EC_POINT_point2hex() returns a pointer to the hex string, or NULL on error.
EC_POINT_hex2point() returns the pointer to the EC_POINT supplied, or NULL on
error.
=head1 SEE ALSO
L<crypto(7)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>,
L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
=head1 COPYRIGHT
Copyright 2013-2018 The OpenSSL Project Authors. All Rights Reserved.
Licensed under the OpenSSL license (the "License"). You may not use
this file except in compliance with the License. You can obtain a copy
in the file LICENSE in the source distribution or at
L<https://www.openssl.org/source/license.html>.
=cut
|
