.\"	$OpenBSD: EC_POINT_add.3,v 1.12 2023/04/12 09:55:22 jsg Exp $
.\"	OpenSSL b97fdb57 Nov 11 09:33:09 2016 +0100
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.\" This file was written by Matt Caswell <matt@openssl.org>.
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.Dd $Mdocdate: April 12 2023 $
.Dt EC_POINT_ADD 3
.Os
.Sh NAME
.Nm EC_POINT_add ,
.Nm EC_POINT_dbl ,
.Nm EC_POINT_invert ,
.Nm EC_POINT_is_at_infinity ,
.Nm EC_POINT_is_on_curve ,
.Nm EC_POINT_cmp ,
.Nm EC_POINT_make_affine ,
.Nm EC_POINTs_make_affine ,
.Nm EC_POINTs_mul ,
.Nm EC_POINT_mul ,
.Nm EC_GROUP_precompute_mult ,
.Nm EC_GROUP_have_precompute_mult
.Nd perform mathematical operations and tests on EC_POINT objects
.Sh SYNOPSIS
.In openssl/ec.h
.In openssl/bn.h
.Ft int
.Fo EC_POINT_add
.Fa "const EC_GROUP *group"
.Fa "EC_POINT *r"
.Fa "const EC_POINT *a"
.Fa "const EC_POINT *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_POINT_dbl
.Fa "const EC_GROUP *group"
.Fa "EC_POINT *r"
.Fa "const EC_POINT *a"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_POINT_invert
.Fa "const EC_GROUP *group"
.Fa "EC_POINT *a"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_POINT_is_at_infinity
.Fa "const EC_GROUP *group"
.Fa "const EC_POINT *p"
.Fc
.Ft int
.Fo EC_POINT_is_on_curve
.Fa "const EC_GROUP *group"
.Fa "const EC_POINT *point"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_POINT_cmp
.Fa "const EC_GROUP *group"
.Fa "const EC_POINT *a"
.Fa "const EC_POINT *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_POINT_make_affine
.Fa "const EC_GROUP *group"
.Fa "EC_POINT *point"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_POINTs_make_affine
.Fa "const EC_GROUP *group"
.Fa "size_t num"
.Fa "EC_POINT *points[]"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_POINTs_mul
.Fa "const EC_GROUP *group"
.Fa "EC_POINT *r"
.Fa "const BIGNUM *n"
.Fa "size_t num"
.Fa "const EC_POINT *p[]"
.Fa "const BIGNUM *m[]"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_POINT_mul
.Fa "const EC_GROUP *group"
.Fa "EC_POINT *r"
.Fa "const BIGNUM *n"
.Fa "const EC_POINT *q"
.Fa "const BIGNUM *m"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_GROUP_precompute_mult
.Fa "EC_GROUP *group"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_GROUP_have_precompute_mult
.Fa "const EC_GROUP *group"
.Fc
.Sh DESCRIPTION
These functions operate on
.Vt EC_POINT
objects created by
.Xr EC_POINT_new 3 .
.Pp
.Fn EC_POINT_add
adds the two points
.Fa a
and
.Fa b
and places the result in
.Fa r .
Similarly
.Fn EC_POINT_dbl
doubles the point
.Fa a
and places the result in
.Fa r .
In both cases it is valid for
.Fa r
to be one of
.Fa a
or
.Fa b .
.Pp
.Fn EC_POINT_invert
calculates the inverse of the supplied point
.Fa a .
The result is placed back in
.Fa a .
.Pp
The function
.Fn EC_POINT_is_at_infinity
tests whether the supplied point is at infinity or not.
.Pp
.Fn EC_POINT_is_on_curve
tests whether the supplied point is on the curve or not.
.Pp
.Fn EC_POINT_cmp
compares the two supplied points and tests whether or not they are
equal.
.Pp
The functions
.Fn EC_POINT_make_affine
and
.Fn EC_POINTs_make_affine
force the internal representation of the
.Vt EC_POINT Ns s
into the affine coordinate system.
In the case of
.Fn EC_POINTs_make_affine ,
the value
.Fa num
provides the number of points in the array
.Fa points
to be forced.
.Pp
.Fn EC_POINT_mul
calculates the value
.Pp
.D1 generator * n + q * m
.Pp
and stores the result in
.Fa r .
The value
.Fa n
may be
.Dv NULL ,
in which case the result is just
.Pp
.Dl q * m.
.Pp
.Fn EC_POINTs_mul
only supports the values 0 and 1 for
.Fa num .
If it is 1, then
.Fn EC_POINTs_mul
calculates the value
.Pp
.Dl generator * n + q[0] * m[0].
.Pp
If
.Fa num
is 0 then
.Fa q
and
.Fa m
must be
.Dv NULL ,
and the result is just
.Pp
.Dl generator * n .
.Pp
As for
.Fn EC_POINT_mul ,
the value
.Fa n
may be
.Dv NULL .
.Pp
The function
.Fn EC_GROUP_precompute_mult
stores multiples of the generator for faster point multiplication,
whilst
.Fn EC_GROUP_have_precompute_mult
tests whether precomputation has already been done.
See
.Xr EC_GROUP_copy 3
for information about the generator.
.Sh RETURN VALUES
The following functions return 1 on success or 0 on error:
.Fn EC_POINT_add ,
.Fn EC_POINT_dbl ,
.Fn EC_POINT_invert ,
.Fn EC_POINT_make_affine ,
.Fn EC_POINTs_make_affine ,
.Fn EC_POINT_mul ,
.Fn EC_POINTs_mul ,
and
.Fn EC_GROUP_precompute_mult .
.Pp
.Fn EC_POINT_is_at_infinity
returns 1 if the point is at infinity or 0 otherwise.
.Pp
.Fn EC_POINT_is_on_curve
returns 1 if the point is on the curve, 0 if not, or -1 on error.
.Pp
.Fn EC_POINT_cmp
returns 1 if the points are not equal, 0 if they are, or -1 on error.
.Pp
.Fn EC_GROUP_have_precompute_mult
returns 1 if a precomputation has been done or 0 if not.
.Sh SEE ALSO
.Xr d2i_ECPKParameters 3 ,
.Xr EC_GFp_simple_method 3 ,
.Xr EC_GROUP_copy 3 ,
.Xr EC_GROUP_new 3 ,
.Xr EC_KEY_new 3 ,
.Xr EC_POINT_new 3
.Sh HISTORY
.Fn EC_POINT_add ,
.Fn EC_POINT_dbl ,
.Fn EC_POINT_invert ,
.Fn EC_POINT_is_at_infinity ,
.Fn EC_POINT_is_on_curve ,
.Fn EC_POINT_cmp ,
.Fn EC_POINT_make_affine ,
.Fn EC_POINTs_make_affine ,
.Fn EC_POINTs_mul ,
.Fn EC_POINT_mul ,
and
.Fn EC_GROUP_precompute_mult
first appeared in OpenSSL 0.9.7 and have been available since
.Ox 3.2 .
.Pp
.Fn EC_GROUP_have_precompute_mult
first appeared in OpenSSL 0.9.8 and has been available since
.Ox 4.5 .