New Frobenius expansions for elliptic curves with efficient endomorphisms

Authors:
Tae-Jun Park;Mun-Kyu Lee;Kunsoo Park
Affiliations:
School of Computer Science and Engineering, Seoul National University, Seoul, Korea;School of Computer Science and Engineering, Seoul National University, Seoul, Korea;School of Computer Science and Engineering, Seoul National University, Seoul, Korea
Venue:
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Year:
2002

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Abstract

The Frobenius expansion is a method to speed up scalar multiplication on elliptic curves. Nigel Smart gave a Frobenius expansion method for elliptic curves defined over odd prime fields. Gallant, Lambert and Vanstone suggested that efficiently computable endomorphisms other than Frobenius endomorphisms can be used for fast scalar multiplication. In this paper we show that these two kinds of endomorphisms can be used together for a certain class of curves, and we present a new expansion method for elliptic curves over odd prime fields. Our experimental results show that the throughputs of the known scalar multiplication algorithms are improved by 7.6-17.3% using the new expansion method.