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1.\" $OpenBSD: EC_POINT_add.3,v 1.11 2018/07/16 17:37:25 tb Exp $
2.\" OpenSSL b97fdb57 Nov 11 09:33:09 2016 +0100
3.\"
4.\" This file was written by Matt Caswell <matt@openssl.org>.
5.\" Copyright (c) 2013 The OpenSSL Project. All rights reserved.
6.\"
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8.\" modification, are permitted provided that the following conditions
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51.Dd $Mdocdate: July 16 2018 $
52.Dt EC_POINT_ADD 3
53.Os
54.Sh NAME
55.Nm EC_POINT_add ,
56.Nm EC_POINT_dbl ,
57.Nm EC_POINT_invert ,
58.Nm EC_POINT_is_at_infinity ,
59.Nm EC_POINT_is_on_curve ,
60.Nm EC_POINT_cmp ,
61.Nm EC_POINT_make_affine ,
62.Nm EC_POINTs_make_affine ,
63.Nm EC_POINTs_mul ,
64.Nm EC_POINT_mul ,
65.Nm EC_GROUP_precompute_mult ,
66.Nm EC_GROUP_have_precompute_mult
67.Nd perform mathematical operations and tests on EC_POINT objects
68.Sh SYNOPSIS
69.In openssl/ec.h
70.In openssl/bn.h
71.Ft int
72.Fo EC_POINT_add
73.Fa "const EC_GROUP *group"
74.Fa "EC_POINT *r"
75.Fa "const EC_POINT *a"
76.Fa "const EC_POINT *b"
77.Fa "BN_CTX *ctx"
78.Fc
79.Ft int
80.Fo EC_POINT_dbl
81.Fa "const EC_GROUP *group"
82.Fa "EC_POINT *r"
83.Fa "const EC_POINT *a"
84.Fa "BN_CTX *ctx"
85.Fc
86.Ft int
87.Fo EC_POINT_invert
88.Fa "const EC_GROUP *group"
89.Fa "EC_POINT *a"
90.Fa "BN_CTX *ctx"
91.Fc
92.Ft int
93.Fo EC_POINT_is_at_infinity
94.Fa "const EC_GROUP *group"
95.Fa "const EC_POINT *p"
96.Fc
97.Ft int
98.Fo EC_POINT_is_on_curve
99.Fa "const EC_GROUP *group"
100.Fa "const EC_POINT *point"
101.Fa "BN_CTX *ctx"
102.Fc
103.Ft int
104.Fo EC_POINT_cmp
105.Fa "const EC_GROUP *group"
106.Fa "const EC_POINT *a"
107.Fa "const EC_POINT *b"
108.Fa "BN_CTX *ctx"
109.Fc
110.Ft int
111.Fo EC_POINT_make_affine
112.Fa "const EC_GROUP *group"
113.Fa "EC_POINT *point"
114.Fa "BN_CTX *ctx"
115.Fc
116.Ft int
117.Fo EC_POINTs_make_affine
118.Fa "const EC_GROUP *group"
119.Fa "size_t num"
120.Fa "EC_POINT *points[]"
121.Fa "BN_CTX *ctx"
122.Fc
123.Ft int
124.Fo EC_POINTs_mul
125.Fa "const EC_GROUP *group"
126.Fa "EC_POINT *r"
127.Fa "const BIGNUM *n"
128.Fa "size_t num"
129.Fa "const EC_POINT *p[]"
130.Fa "const BIGNUM *m[]"
131.Fa "BN_CTX *ctx"
132.Fc
133.Ft int
134.Fo EC_POINT_mul
135.Fa "const EC_GROUP *group"
136.Fa "EC_POINT *r"
137.Fa "const BIGNUM *n"
138.Fa "const EC_POINT *q"
139.Fa "const BIGNUM *m"
140.Fa "BN_CTX *ctx"
141.Fc
142.Ft int
143.Fo EC_GROUP_precompute_mult
144.Fa "EC_GROUP *group"
145.Fa "BN_CTX *ctx"
146.Fc
147.Ft int
148.Fo EC_GROUP_have_precompute_mult
149.Fa "const EC_GROUP *group"
150.Fc
151.Sh DESCRIPTION
152These functions operate on
153.Vt EC_POINT
154objects created by
155.Xr EC_POINT_new 3 .
156.Pp
157.Fn EC_POINT_add
158adds the two points
159.Fa a
160and
161.Fa b
162and places the result in
163.Fa r .
164Similarly
165.Fn EC_POINT_dbl
166doubles the point
167.Fa a
168and places the result in
169.Fa r .
170In both cases it is valid for
171.Fa r
172to be one of
173.Fa a
174or
175.Fa b .
176.Pp
177.Fn EC_POINT_invert
178calculates the inverse of the supplied point
179.Fa a .
180The result is placed back in
181.Fa a .
182.Pp
183The function
184.Fn EC_POINT_is_at_infinity
185tests whether the supplied point is at infinity or not.
186.Pp
187.Fn EC_POINT_is_on_curve
188tests whether the supplied point is on the curve or not.
189.Pp
190.Fn EC_POINT_cmp
191compares the two supplied points and tests whether or not they are
192equal.
193.Pp
194The functions
195.Fn EC_POINT_make_affine
196and
197.Fn EC_POINTs_make_affine
198force the internal representation of the
199.Vt EC_POINT Ns s
200into the affine coordinate system.
201In the case of
202.Fn EC_POINTs_make_affine ,
203the value
204.Fa num
205provides the number of points in the array
206.Fa points
207to be forced.
208.Pp
209.Fn EC_POINT_mul
210calculates the value
211.Pp
212.D1 generator * n + q * m
213.Pp
214and stores the result in
215.Fa r .
216The value
217.Fa n
218may be
219.Dv NULL ,
220in which case the result is just
221.Pp
222.Dl q * m.
223.Pp
224.Fn EC_POINTs_mul
225only supports the values 0 and 1 for
226.Fa num .
227If it is 1, then
228.Fn EC_POINTs_mul
229calculates the value
230.Pp
231.Dl generator * n + q[0] * m[0].
232.Pp
233If
234.Fa num
235is 0 then
236.Fa q
237and
238.Fa m
239must be
240.Dv NULL ,
241and the result is just
242.Pp
243.Dl generator * n .
244.Pp
245As for
246.Fn EC_POINT_mul ,
247the value
248.Fa n
249may be
250.Dv NULL .
251.Pp
252The function
253.Fn EC_GROUP_precompute_mult
254stores multiples of the generator for faster point multiplication,
255whilst
256.Fn EC_GROUP_have_precompute_mult
257tests whether precomputation has already been done.
258See
259.Xr EC_GROUP_copy 3
260for information about the generator.
261.Sh RETURN VALUES
262The following functions return 1 on success or 0 on error:
263.Fn EC_POINT_add ,
264.Fn EC_POINT_dbl ,
265.Fn EC_POINT_invert ,
266.Fn EC_POINT_make_affine ,
267.Fn EC_POINTs_make_affine ,
268.Fn EC_POINTs_make_affine ,
269.Fn EC_POINT_mul ,
270.Fn EC_POINTs_mul ,
271and
272.Fn EC_GROUP_precompute_mult .
273.Pp
274.Fn EC_POINT_is_at_infinity
275returns 1 if the point is at infinity or 0 otherwise.
276.Pp
277.Fn EC_POINT_is_on_curve
278returns 1 if the point is on the curve, 0 if not, or -1 on error.
279.Pp
280.Fn EC_POINT_cmp
281returns 1 if the points are not equal, 0 if they are, or -1 on error.
282.Pp
283.Fn EC_GROUP_have_precompute_mult
284returns 1 if a precomputation has been done or 0 if not.
285.Sh SEE ALSO
286.Xr d2i_ECPKParameters 3 ,
287.Xr EC_GFp_simple_method 3 ,
288.Xr EC_GROUP_copy 3 ,
289.Xr EC_GROUP_new 3 ,
290.Xr EC_KEY_new 3 ,
291.Xr EC_POINT_new 3
292.Sh HISTORY
293.Fn EC_POINT_add ,
294.Fn EC_POINT_dbl ,
295.Fn EC_POINT_invert ,
296.Fn EC_POINT_is_at_infinity ,
297.Fn EC_POINT_is_on_curve ,
298.Fn EC_POINT_cmp ,
299.Fn EC_POINT_make_affine ,
300.Fn EC_POINTs_make_affine ,
301.Fn EC_POINTs_mul ,
302.Fn EC_POINT_mul ,
303and
304.Fn EC_GROUP_precompute_mult
305first appeared in OpenSSL 0.9.7 and have been available since
306.Ox 3.2 .
307.Pp
308.Fn EC_GROUP_have_precompute_mult
309first appeared in OpenSSL 0.9.8 and has been available since
310.Ox 4.5 .
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