2013•IEICE Transactions on Fundamentals of Electronics Communications and Computer SciencesRequires access

Implementation of an Elliptic Curve Scalar Multiplication Method Using Division Polynomials

Naoki Kanayama, Yang Liu, Eiji Okamoto, Kazutaka SAITO, Tadanori Teruya, Shigenori Uchiyama

Abstract

We implemented a scalar multiplication method over elliptic curves using division polynomials. We adapt an algorithm for computing elliptic nets proposed by Stange. According to our experimental results, the scalar multiplication method using division polynomials is faster than the binary method in an affine coordinate system.

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Key concepts: Scalar multiplication, Division (mathematics), Scalar (mathematics), Mathematics, Division polynomials, Elliptic curve point multiplication, Multiplication (music), Elliptic curve