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>
        #include <openssl/bn.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 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.

       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.

       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(3), ec(3), EC_GROUP_new(3), EC_GROUP_copy(3), EC_POINT_new(3), EC_KEY_new(3),
       EC_GFp_simple_method(3), d2i_ECPKParameters(3)