Automatically generated by Pod::Man 4.14 (Pod::Simple 3.43)

Standard preamble:
========================================================================
..

..

.. Set up some character translations and predefined strings. \*(-- will
give an unbreakable dash, \*(PI will give pi, \*(L" will give a left
double quote, and \*(R" will give a right double quote. \*(C+ will
give a nicer C++. Capital omega is used to do unbreakable dashes and
therefore won't be available. \*(C` and \*(C' expand to `' in nroff,
nothing in troff, for use with C<>.
.tr \(*W- . ds -- \(*W- . ds PI pi . if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch . if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch . ds L" "" . ds R" "" . ds C` "" . ds C' "" 'br\} . ds -- \|\(em\| . ds PI \(*p . ds L" `` . ds R" '' . ds C` . ds C' 'br\}
Escape single quotes in literal strings from groff's Unicode transform.

If the F register is >0, we'll generate index entries on stderr for
titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
entries marked with X<> in POD. Of course, you'll have to process the
output yourself in some meaningful fashion.

Avoid warning from groff about undefined register 'F'.
.. .nr rF 0 . if \nF \{\ . de IX . tm Index:\\$1\t\\n%\t"\\$2" .. . if !\nF==2 \{\ . nr % 0 . nr F 2 . \} . \} .\} .rr rF
Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
Fear. Run. Save yourself. No user-serviceable parts.
. \" fudge factors for nroff and troff . ds #H 0 . ds #V .8m . ds #F .3m . ds #[ \f1 . ds #] .\} . ds #H ((1u-(\\\\n(.fu%2u))*.13m) . ds #V .6m . ds #F 0 . ds #[ \& . ds #] \& .\} . \" simple accents for nroff and troff . ds ' \& . ds ` \& . ds ^ \& . ds , \& . ds ~ ~ . ds / .\} . ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u" . ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u' . ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u' . ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u' . ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u' . ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u' .\} . \" troff and (daisy-wheel) nroff accents . \" corrections for vroff . \" for low resolution devices (crt and lpr) \{\ . ds : e . ds 8 ss . ds o a . ds d- d\h'-1'\(ga . ds D- D\h'-1'\(hy . ds th \o'bp' . ds Th \o'LP' . ds ae ae . ds Ae AE .\} ========================================================================

Title "EC_POINT_ADD 3" For nroff, turn off justification. Always turn off hyphenation; it makes
way too many mistakes in technical documents.
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 Header "SYNOPSIS" .Vb 1 #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); .Ve Header "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 \s-1EC_POINT\s0(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 \s-1NULL\s0 in which case the result is just q * m (variable point multiplication). Alternatively, both q and m may be \s-1NULL,\s0 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 \s-1NULL\s0 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 \s-1NULL\s0 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.

Header "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.

Header "SEE ALSO" \fBcrypto\|(7), EC_GROUP_new\|(3), EC_GROUP_copy\|(3), \fBEC_POINT_new\|(3), EC_KEY_new\|(3), \fBEC_GFp_simple_method\|(3), d2i_ECPKParameters\|(3) Header "COPYRIGHT" Copyright 2013-2018 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the OpenSSL license (the \*(L"License\*(R"). You may not use this file except in compliance with the License. You can obtain a copy in the file \s-1LICENSE\s0 in the source distribution or at <https://www.openssl.org/source/license.html>.