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
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
|
.\" Automatically generated by Pod::Man 2.28 (Pod::Simple 3.30)
.\"
.\" Standard preamble:
.\" ========================================================================
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.de Vb \" Begin verbatim text
.ft CW
.nf
.ne \\$1
..
.de Ve \" End verbatim text
.ft R
.fi
..
.\" Set up some character translations and predefined strings. \*(-- will
.\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left
.\" double quote, and \*(R" will give a right double quote. \*(C+ will
.\" give a nicer C++. Capital omega is used to do unbreakable dashes and
.\" therefore won't be available. \*(C` and \*(C' expand to `' in nroff,
.\" nothing in troff, for use with C<>.
.tr \(*W-
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
.ie n \{\
. ds -- \(*W-
. ds PI pi
. if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
. if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch
. ds L" ""
. ds R" ""
. ds C` ""
. ds C' ""
'br\}
.el\{\
. ds -- \|\(em\|
. ds PI \(*p
. ds L" ``
. ds R" ''
. ds C`
. ds C'
'br\}
.\"
.\" Escape single quotes in literal strings from groff's Unicode transform.
.ie \n(.g .ds Aq \(aq
.el .ds Aq '
.\"
.\" If the F register is turned on, we'll generate index entries on stderr for
.\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
.\" entries marked with X<> in POD. Of course, you'll have to process the
.\" output yourself in some meaningful fashion.
.\"
.\" Avoid warning from groff about undefined register 'F'.
.de IX
..
.nr rF 0
.if \n(.g .if rF .nr rF 1
.if (\n(rF:(\n(.g==0)) \{
. if \nF \{
. de IX
. tm Index:\\$1\t\\n%\t"\\$2"
..
. if !\nF==2 \{
. nr % 0
. nr F 2
. \}
. \}
.\}
.rr rF
.\"
.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
.\" Fear. Run. Save yourself. No user-serviceable parts.
. \" fudge factors for nroff and troff
.if n \{\
. ds #H 0
. ds #V .8m
. ds #F .3m
. ds #[ \f1
. ds #] \fP
.\}
.if t \{\
. ds #H ((1u-(\\\\n(.fu%2u))*.13m)
. ds #V .6m
. ds #F 0
. ds #[ \&
. ds #] \&
.\}
. \" simple accents for nroff and troff
.if n \{\
. ds ' \&
. ds ` \&
. ds ^ \&
. ds , \&
. ds ~ ~
. ds /
.\}
.if t \{\
. ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u"
. ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u'
. ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u'
. ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u'
. ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u'
. ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
.\}
. \" troff and (daisy-wheel) nroff accents
.ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
.ds 8 \h'\*(#H'\(*b\h'-\*(#H'
.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
.ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
.ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
.ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
.ds ae a\h'-(\w'a'u*4/10)'e
.ds Ae A\h'-(\w'A'u*4/10)'E
. \" corrections for vroff
.if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
.if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
. \" for low resolution devices (crt and lpr)
.if \n(.H>23 .if \n(.V>19 \
\{\
. ds : e
. ds 8 ss
. ds o a
. ds d- d\h'-1'\(ga
. ds D- D\h'-1'\(hy
. ds th \o'bp'
. ds Th \o'LP'
. ds ae ae
. ds Ae AE
.\}
.rm #[ #] #H #V #F C
.\" ========================================================================
.\"
.IX Title "EC_POINT_new 3"
.TH EC_POINT_new 3 "2016-05-03" "1.0.2h" "OpenSSL"
.\" For nroff, turn off justification. Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
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_set_Jprojective_coordinates, 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.
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 2
\& #include <openssl/ec.h>
\& #include <openssl/bn.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);
\& 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 *, const EC_POINT *,
\& point_conversion_form_t form, BIGNUM *, BN_CTX *);
\& EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
\& EC_POINT *, BN_CTX *);
\& char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
\& point_conversion_form_t form, BN_CTX *);
\& EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
\& EC_POINT *, BN_CTX *);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
An \s-1EC_POINT\s0 represents a point on a curve. A new point is constructed by calling the function EC_POINT_new and providing the \fBgroup\fR
object that the point relates to.
.PP
EC_POINT_free frees the memory associated with the \s-1EC_POINT.\s0
.PP
EC_POINT_clear_free destroys any sensitive data held within the \s-1EC_POINT\s0 and then frees its memory.
.PP
EC_POINT_copy copies the point \fBsrc\fR into \fBdst\fR. Both \fBsrc\fR and \fBdst\fR must use the same \s-1EC_METHOD.\s0
.PP
EC_POINT_dup creates a new \s-1EC_POINT\s0 object and copies the content from \fBsrc\fR to the newly created
\&\s-1EC_POINT\s0 object.
.PP
EC_POINT_method_of obtains the \s-1EC_METHOD\s0 associated with \fBpoint\fR.
.PP
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.
.PP
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 \fBx\fR and \fBy\fR co-ordinates for the point
\&\fBp\fR defined over the curve given in \fBgroup\fR.
.PP
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 to 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.
.PP
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 \fBx\fR is the x co-ordinate and \fBy_bit\fR is a value 0 or 1 to identify which of
the two possible values for y should be used.
.PP
In addition EC_POINTs can be converted to and from various external
representations. Supported representations are octet strings, BIGNUMs and
hexadecimal. Octet strings are stored in a buffer along with an associated
buffer length. A point held in a \s-1BIGNUM\s0 is calculated by converting the point to
an octet string and then converting that octet string into a \s-1BIGNUM\s0 integer.
Points in hexadecimal format are stored in a \s-1NULL\s0 terminated character string
where each character is one of the printable values 0\-9 or A\-F (or a\-f).
.PP
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 string, \s-1BIGNUM\s0 and hexadecimal respectively.
.PP
The function EC_POINT_point2oct must be supplied with a buffer long enough to store the octet string. The return value provides the number of
octets stored. Calling the function with a \s-1NULL\s0 buffer will not perform the conversion but will still return the required buffer length.
.PP
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 \fIOPENSSL_free()\fR.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
EC_POINT_new and EC_POINT_dup return the newly allocated \s-1EC_POINT\s0 or \s-1NULL\s0 on error.
.PP
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.
.PP
EC_POINT_method_of returns the \s-1EC_METHOD\s0 associated with the supplied \s-1EC_POINT.\s0
.PP
EC_POINT_point2oct returns the length of the required buffer, or 0 on error.
.PP
EC_POINT_point2bn returns the pointer to the \s-1BIGNUM\s0 supplied, or \s-1NULL\s0 on error.
.PP
EC_POINT_bn2point returns the pointer to the \s-1EC_POINT\s0 supplied, or \s-1NULL\s0 on error.
.PP
EC_POINT_point2hex returns a pointer to the hex string, or \s-1NULL\s0 on error.
.PP
EC_POINT_hex2point returns the pointer to the \s-1EC_POINT\s0 supplied, or \s-1NULL\s0 on error.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fIcrypto\fR\|(3), \fIec\fR\|(3), \fIEC_GROUP_new\fR\|(3), \fIEC_GROUP_copy\fR\|(3),
\&\fIEC_POINT_add\fR\|(3), \fIEC_KEY_new\fR\|(3),
\&\fIEC_GFp_simple_method\fR\|(3), \fId2i_ECPKParameters\fR\|(3)
|
