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 y1 and y2 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.
Digital Object Identifier (DOI)
Kareem K. Ajeena, Ruma and Kamarulhaili, Hailiza
"Point Multiplication using Integer Sub-Decomposition for Elliptic Curve Cryptography,"
Applied Mathematics & Information Sciences: Vol. 08:
2, Article 9.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss2/9