Secured performance of an elliptic curve cryptographic process

Abstract

A method for performing an elliptic curve cryptographic process to generate output data based on input data, the elliptic curve cryptographic process based on an elliptic curve over a finite field, wherein the generation of the output data comprises generating, based on a predetermined point V of the elliptic curve and a positive R-bit integer k, a first point of the elliptic curve that is based, at least in part, on the point kV of the elliptic curve, wherein k=Σ2band, for each r=0, 1, . . . , R−1, bis the bit value of k at bit position r of k, wherein the method comprises: storing, according to a partition of the R bit positions for k into T groups of bit positions P(t=0, 1, . . . , T−1), a corresponding lookup table Lhaving, for each of the 2possible options for assigning to the |P| bit positions s∈Pa respective bit value x, a corresponding point of the elliptic curve that is based, at least in part, on the point (Σ2x)V of the elliptic curve; obtaining k; and determining the first point as Σl, where lis the point of the elliptic curve that corresponds, in lookup table L, to the option for assigning to the |P| bit positions s∈Pthe corresponding bit value b.