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New Frobenius expansions for elliptic curves with efficient endomorphisms
- Issue Date
- 2002
- Publisher
- SPRINGER-VERLAG BERLIN
- Keywords
- elliptic curve cryptosystem; scalar multiplication; frobenius expansion; endomorphism
- Citation
- IFORMATION SECURITY AND CRYPTOLOGY - ICISC 2002, v.2587, pp 264 - 282
- Pages
- 19
- Journal Title
- IFORMATION SECURITY AND CRYPTOLOGY - ICISC 2002
- Volume
- 2587
- Start Page
- 264
- End Page
- 282
- ISSN
- 0302-9743
- Abstract
- The Robenius expansion is a method to speed up scalar multiplication on elliptic curves. Nigel Smart gave a Robenius 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 axe improved by 7.6 similar to 17.3% using the new expansion method.
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