NAME

       EC_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

SYNOPSIS

        #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_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_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
        int EC_GROUP_have_precompute_mult(const EC_GROUP *group);

DESCRIPTION

       EC_POINT_add adds the two points a and b and places the result in r. Similarly
       EC_POINT_dbl doubles the point a and places the result in r. In both cases it is valid for
       r to be one of a or b.

       EC_POINT_invert calculates the inverse of the supplied point a. The result is placed back
       in a.

       The function EC_POINT_is_at_infinity tests whether the supplied point is at infinity or
       not.

       EC_POINT_is_on_curve tests whether the supplied point is on the curve or not.

       EC_POINT_cmp compares the two supplied points and tests whether or not they are equal.

       The functions EC_POINT_make_affine and EC_POINTs_make_affine force the internal
       representation of the EC_POINT(s) into the affine co-ordinate system. In the case of
       EC_POINTs_make_affine the value num provides the number of points in the array points to
       be forced.

       EC_POINT_mul is a convenient interface to EC_POINTs_mul: it calculates the value generator
       * n + q * m and stores the result in r.  The value n may be NULL in which case the result
       is just q * m (variable point multiplication). Alternatively, both q and m may be NULL,
       and n non-NULL, in which case the result is just generator * 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 n
       or m) is in the range [0, ec_group_order).

       EC_POINTs_mul calculates the value generator * n + q[0] * m[0] + ... + q[num-1] *
       m[num-1]. As for EC_POINT_mul the value n may be NULL or num may be zero.  When performing
       a fixed point multiplication (n is non-NULL and num is 0) or a variable point
       multiplication (n is NULL and num is 1), the underlying implementation uses a constant
       time algorithm, when the input scalar (either n or 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 EC_GROUP_copy(3) for information about the generator.

RETURN VALUES

       The following functions return 1 on success or 0 on error: EC_POINT_add, EC_POINT_dbl,
       EC_POINT_invert, EC_POINT_make_affine, EC_POINTs_make_affine, EC_POINTs_make_affine,
       EC_POINT_mul, EC_POINTs_mul and EC_GROUP_precompute_mult.

       EC_POINT_is_at_infinity returns 1 if the point is at infinity, or 0 otherwise.

       EC_POINT_is_on_curve returns 1 if the point is on the curve, 0 if not, or -1 on error.

       EC_POINT_cmp returns 1 if the points are not equal, 0 if they are, or -1 on error.

       EC_GROUP_have_precompute_mult return 1 if a precomputation has been done, or 0 if not.

SEE ALSO

       crypto(7), EC_GROUP_new(3), EC_GROUP_copy(3), EC_POINT_new(3), EC_KEY_new(3),
       EC_GFp_simple_method(3), d2i_ECPKParameters(3)

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 <https://www.openssl.org/source/license.html>.