between said elliptic curve and another elliptic curve said parameterization defining some configuration parameters each configuration parameter having a range of possible values determining in function of values of coordinates of said at least two points said configuration parameters delivering determined configuration parameters and obtaining coordinates of another point corresponding to an image of an addition of said at least two points through said isomorphism said another point belonging to said another elliptic curve and said obtaining being performed without an inversion operation in said algebraic structure due to said determined configuration parameters application_number US 201514634998 A description before describing the proposed method in its full generality we first make a couple of observations on the weierstra u03b2 model to simplify the exposition we focus on elliptic curves defined over a ring of characteristic different of 2 or 3 as is customary we let denote the multiplicative group of and char the characteristic of consider the elliptic curve e 1 over a ring char u2260 2 3 given by for any u u03b5 elliptic curve e 1 is isomorphic to elliptic curve given two finite point points p 1 x 1 y 1 and p 2 x 2 y 2 on e 1 such that p 1 u2260 u00b1 p 2 i e such that x 1 u2260 x 2 provided that x 1 u2212 x 2 u03b5 their sum is given by p 3 p 1 p 2 x 3 y 3 where the double of p 1 x 1 y 1 provided that.