Point Multiplication using Integer Sub-Decomposition for Elliptic Curve Cryptography

In this work, we proposed a new approach called integer sub-decomposition (ISD) based on the GLV idea to compute any multiple kP of a point P of order n lying on an elliptic curve E. This approach uses two fast endomorphisms ψ1 and ψ2 of E over prime field Fp to calculate kP. The basic idea of ISD method is to sub-decompose the returned values k1 and k2 lying outside the range √ n from the GLV decomposition of a multiplier k into integers k11,k12,k21 and k22 with − √ n < k11,k12,k21,k22 < √ n. These integers are computed by solving a closest vector problem in lattice. The new proposed algorithms and implementation results are shown and discussed in this study.