✏ 编辑: EC_POINTs_mul.3

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.\" ========================================================================
.\"
.IX Title "EC_POINT_ADD 3"
.TH EC_POINT_ADD 3 "2023-09-11" "1.1.1w" "OpenSSL"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
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.if n .ad l
.nh
.SH "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
.SH "SYNOPSIS"
.IX 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
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
EC_POINT_add adds the two points \fBa\fR and \fBb\fR and places the result in \fBr\fR. Similarly EC_POINT_dbl doubles the point \fBa\fR and places the
result in \fBr\fR. In both cases it is valid for \fBr\fR to be one of \fBa\fR or \fBb\fR.
.PP
EC_POINT_invert calculates the inverse of the supplied point \fBa\fR. The result is placed back in \fBa\fR.
.PP
The function EC_POINT_is_at_infinity tests whether the supplied point is at infinity or not.
.PP
EC_POINT_is_on_curve tests whether the supplied point is on the curve or not.
.PP
EC_POINT_cmp compares the two supplied points and tests whether or not they are equal.
.PP
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 \fBnum\fR provides the number of points in the array \fBpoints\fR to be
forced.
.PP
EC_POINT_mul is a convenient interface to EC_POINTs_mul: it calculates the value generator * \fBn\fR + \fBq\fR * \fBm\fR and stores the result in \fBr\fR.
The value \fBn\fR may be \s-1NULL\s0 in which case the result is just \fBq\fR * \fBm\fR (variable point multiplication). Alternatively, both \fBq\fR and \fBm\fR may be \s-1NULL,\s0 and \fBn\fR non-NULL, in which case the result is just generator * \fBn\fR (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 \fBn\fR or \fBm\fR) is in the range [0, ec_group_order).
.PP
EC_POINTs_mul calculates the value generator * \fBn\fR + \fBq[0]\fR * \fBm[0]\fR + ... + \fBq[num\-1]\fR * \fBm[num\-1]\fR. As for EC_POINT_mul the value \fBn\fR may be \s-1NULL\s0 or \fBnum\fR may be zero.
When performing a fixed point multiplication (\fBn\fR is non-NULL and \fBnum\fR is 0) or a variable point multiplication (\fBn\fR is \s-1NULL\s0 and \fBnum\fR is 1), the underlying implementation uses a constant time algorithm, when the input scalar (either \fBn\fR or \fBm[0]\fR) is in the range [0, ec_group_order).
.PP
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 \fIEC_GROUP_copy\fR\|(3) for information
about the generator.
.SH "RETURN VALUES"
.IX 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.
.PP
EC_POINT_is_at_infinity returns 1 if the point is at infinity, or 0 otherwise.
.PP
EC_POINT_is_on_curve returns 1 if the point is on the curve, 0 if not, or \-1 on error.
.PP
EC_POINT_cmp returns 1 if the points are not equal, 0 if they are, or \-1 on error.
.PP
EC_GROUP_have_precompute_mult return 1 if a precomputation has been done, or 0 if not.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fIcrypto\fR\|(7), \fIEC_GROUP_new\fR\|(3), \fIEC_GROUP_copy\fR\|(3),
\&\fIEC_POINT_new\fR\|(3), \fIEC_KEY_new\fR\|(3),
\&\fIEC_GFp_simple_method\fR\|(3), \fId2i_ECPKParameters\fR\|(3)
.SH "COPYRIGHT"
.IX Header "COPYRIGHT"
Copyright 2013\-2018 The OpenSSL Project Authors. All Rights Reserved.
.PP
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>.

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