1=pod
2
3=head1 NAME
4
5EC_POINT_add, EC_POINT_dbl, EC_POINT_invert, EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp, EC_POINT_make_affine, EC_POINTs_make_affine, EC_POINTs_mul, EC_POINT_mul, EC_GROUP_precompute_mult, EC_GROUP_have_precompute_mult - Functions for performing mathematical operations and tests on EC_POINT objects
6
7=head1 SYNOPSIS
8
9 #include <openssl/ec.h>
10
11 int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
12                  const EC_POINT *b, BN_CTX *ctx);
13 int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);
14 int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
15 int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
16 int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
17 int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
18 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n,
19                  const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
20
21Deprecated since OpenSSL 3.0:
22
23 int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
24 int EC_POINTs_make_affine(const EC_GROUP *group, size_t num,
25                           EC_POINT *points[], BN_CTX *ctx);
26 int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num,
27                   const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx);
28 int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
29 int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
30
31=head1 DESCRIPTION
32
33EC_POINT_add adds the two points B<a> and B<b> and places the result in B<r>. Similarly EC_POINT_dbl doubles the point B<a> and places the
34result in B<r>. In both cases it is valid for B<r> to be one of B<a> or B<b>.
35
36EC_POINT_invert calculates the inverse of the supplied point B<a>. The result is placed back in B<a>.
37
38The function EC_POINT_is_at_infinity tests whether the supplied point is at infinity or not.
39
40EC_POINT_is_on_curve tests whether the supplied point is on the curve or not.
41
42EC_POINT_cmp compares the two supplied points and tests whether or not they are equal.
43
44The functions EC_POINT_make_affine and EC_POINTs_make_affine force the internal representation of the EC_POINT(s) into the affine
45co-ordinate system. In the case of EC_POINTs_make_affine the value B<num> provides the number of points in the array B<points> to be
46forced. These functions were deprecated in OpenSSL 3.0 and should no longer be used.
47Modern versions automatically perform this conversion when needed.
48
49EC_POINT_mul calculates the value generator * B<n> + B<q> * B<m> and stores the result in B<r>.
50The value B<n> may be NULL in which case the result is just B<q> * B<m> (variable point multiplication). Alternatively, both B<q> and B<m> may be NULL, and B<n> non-NULL, in which case the result is just generator * B<n> (fixed point multiplication).
51When performing a single fixed or variable point multiplication, the underlying implementation uses a constant time algorithm, when the input scalar (either B<n> or B<m>) is in the range [0, ec_group_order).
52
53Although deprecated in OpenSSL 3.0 and should no longer be used,
54EC_POINTs_mul calculates the value generator * B<n> + B<q[0]> * B<m[0]> + ... + B<q[num-1]> * B<m[num-1]>. As for EC_POINT_mul the value B<n> may be NULL or B<num> may be zero.
55When performing a fixed point multiplication (B<n> is non-NULL and B<num> is 0) or a variable point multiplication (B<n> is NULL and B<num> is 1), the underlying implementation uses a constant time algorithm, when the input scalar (either B<n> or B<m[0]>) is in the range [0, ec_group_order).
56Modern versions should instead use EC_POINT_mul(), combined (if needed) with EC_POINT_add() in such rare circumstances.
57
58The function EC_GROUP_precompute_mult stores multiples of the generator for faster point multiplication, whilst
59EC_GROUP_have_precompute_mult tests whether precomputation has already been done. See L<EC_GROUP_copy(3)> for information
60about the generator. Precomputation functionality was deprecated in OpenSSL 3.0.
61Users of EC_GROUP_precompute_mult() and EC_GROUP_have_precompute_mult() should
62switch to named curves which OpenSSL has hardcoded lookup tables for.
63
64=head1 RETURN VALUES
65
66The following functions return 1 on success or 0 on error: EC_POINT_add, EC_POINT_dbl, EC_POINT_invert, EC_POINT_make_affine,
67EC_POINTs_make_affine, EC_POINTs_make_affine, EC_POINT_mul, EC_POINTs_mul and EC_GROUP_precompute_mult.
68
69EC_POINT_is_at_infinity returns 1 if the point is at infinity, or 0 otherwise.
70
71EC_POINT_is_on_curve returns 1 if the point is on the curve, 0 if not, or -1 on error.
72
73EC_POINT_cmp returns 1 if the points are not equal, 0 if they are, or -1 on error.
74
75EC_GROUP_have_precompute_mult return 1 if a precomputation has been done, or 0 if not.
76
77=head1 SEE ALSO
78
79L<crypto(7)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>,
80L<EC_POINT_new(3)>, L<EC_KEY_new(3)>,
81L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
82
83=head1 HISTORY
84
85EC_POINT_make_affine(), EC_POINTs_make_affine(), EC_POINTs_mul(),
86EC_GROUP_precompute_mult(), and EC_GROUP_have_precompute_mult()
87were deprecated in OpenSSL 3.0.
88
89=head1 COPYRIGHT
90
91Copyright 2013-2020 The OpenSSL Project Authors. All Rights Reserved.
92
93Licensed under the Apache License 2.0 (the "License").  You may not use
94this file except in compliance with the License.  You can obtain a copy
95in the file LICENSE in the source distribution or at
96L<https://www.openssl.org/source/license.html>.
97
98=cut
99