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EC_POINT_ADD(3)			    OpenSSL		       EC_POINT_ADD(3)

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>.

1.1.1a				  2018-11-20		       EC_POINT_ADD(3)

NAME | SYNOPSIS | DESCRIPTION | RETURN VALUES | SEE ALSO | COPYRIGHT

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