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New Formulae for Efficient Elliptic Curve Arithmetic

By Huseyin Hisil, Gary P. Carter and Edward P. Dawson

Abstract

This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings for Jacobi-quartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobi-quartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d), Jacobi-intersection (4M+10S+5d or 7M+7S+3d), Edwards (9M+4S) and Hessian (8M+6S+1d) forms. We show that Hessian tripling costs 6M+4C+1d for Hessian curves defined over a field of characteristic 3. We discuss an alternative way of choosing the base point in successive squaring based scalar multiplication algorithms. Using this technique, we improve the latest mixed-addition formulae for Jacobi-intersection (10M+2S+1d), Hessian (5M+6S) and Edwards (9M+1S+ 1d+4a) forms. We discuss the significance of these optimizations for elliptic curve cryptography

Topics: 080402 Data Encryption, Elliptic curve, efficient point multiplication, doubling, tripling, DBNS
Publisher: Springer
Year: 2007
DOI identifier: 10.1007/978-3-540-77026-8_11
OAI identifier: oai:eprints.qut.edu.au:15234

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