#include <openssl/ec.h>
- int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
+ int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
+ const EC_POINT *b, BN_CTX *ctx);
int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);
int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
- int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx);
- int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num, const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx);
- int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
+ int EC_POINTs_make_affine(const EC_GROUP *group, size_t num,
+ EC_POINT *points[], BN_CTX *ctx);
+ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num,
+ const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx);
+ int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n,
+ const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
co-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
forced.
-EC_POINT_mul calculates the value generator * B<n> + B<q> * B<m> and stores the result in B<r>. The value B<n> may be NULL in which case the result is just B<q> * B<m>.
+EC_POINT_mul is a convenient interface to EC_POINTs_mul: it calculates the value generator * B<n> + B<q> * B<m> and stores the result in B<r>.
+The 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).
+When 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).
-EC_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.
+EC_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.
+When 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).
The function EC_GROUP_precompute_mult stores multiples of the generator for faster point multiplication, whilst
EC_GROUP_have_precompute_mult tests whether precomputation has already been done. See L<EC_GROUP_copy(3)> for information
=head1 SEE ALSO
-L<crypto(3)>, L<ec(3)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>,
+L<crypto(7)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>,
L<EC_POINT_new(3)>, L<EC_KEY_new(3)>,
L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
=head1 COPYRIGHT
-Copyright 2013-2016 The OpenSSL Project Authors. All Rights Reserved.
+Copyright 2013-2018 The OpenSSL Project Authors. All Rights Reserved.
-Licensed under the OpenSSL license (the "License"). You may not use
+Licensed under the Apache License 2.0 (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>.