Applied Mathematics & Information Sciences

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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.

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