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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>.