Comparative study on four dimensional GLV method and ISD method in elliptic scalar multiplication

Abstract

In this paper, we reviewed and revisited two integer decomposition methods, namely the four dimensional GLV method and the ISD method. In 2001, Gallant, Lambert and Vanstone (GLV) introduced the GLV method. Number of variants of GLV methods were developed since then mainly focusing on the extension of the GLV method to higher dimension. Starting with two dimensional GLV up to eight dimensional GLV method was proposed until the year 2014. All these variants adopted single layer decomposition. However, in 2014 the ISD method was proposed where this method employed a two layers decomposition technique. The ISD method is similar to the four dimensional GLV method in terms of number of decompositions performed, but it involved sub-decomposition process. Both methods used similar approaches to compute the decomposed scalars, namely the lattice method, shortest vector problem and efficiently computable endomorphism. In the four dimensional GLV method, two endomorphism were used, Frobenius endomorphism and GLV endomorphism while in the ISD method three GLV endomorphism were used to compute the decomposed scalars.