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New Formulae for Efficient Elliptic Curve Arithmetic

Hisil, Huseyin, Carter, Gary P., & Dawson, Edward P. (2007) New Formulae for Efficient Elliptic Curve Arithmetic. Progress in Cryptology – INDOCRYPT 2007 (LNCS), 4859, pp. 138-151.

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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.

Impact and interest:

18 citations in Scopus
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11 citations in Web of Science®

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ID Code: 15234
Item Type: Journal Article
Keywords: Elliptic curve, efficient point multiplication, doubling, tripling, DBNS
DOI: 10.1007/978-3-540-77026-8_11
ISBN: 9783540770251
ISSN: 1611-3349
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > DATA FORMAT (080400) > Data Encryption (080402)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Institutes > Information Security Institute
Copyright Owner: Copyright 2007 Springer
Copyright Statement: This is the author-version of the work. Conference proceedings published, by Springer Verlag, will be available via SpringerLink. http://www.springer.de/comp/lncs/ Lecture Notes in Computer Science
Deposited On: 17 Oct 2008
Last Modified: 29 Feb 2012 23:33

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