Implementation of an Elliptic Curve Scalar Multiplication Method Using Division Polynomials

Naoki KANAYAMA; Yang LIU; Eiji OKAMOTO; Kazutaka SAITO; Tadanori TERUYA; Shigenori UCHIYAMA

doi:10.1587/transfun.E97.A.300

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Online ISSN : 1745-1337
Print ISSN : 0916-8508

Special Section on Cryptography and Information Security

Implementation of an Elliptic Curve Scalar Multiplication Method Using Division Polynomials

Naoki KANAYAMA, Yang LIU, Eiji OKAMOTO, Kazutaka SAITO, Tadanori TERUYA, Shigenori UCHIYAMA

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Keywords: elliptic curve, division polynomial, scalar multiplication, elliptic net

JOURNAL RESTRICTED ACCESS

2014 Volume E97.A Issue 1 Pages 300-302

DOI https://doi.org/10.1587/transfun.E97.A.300

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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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