Publication: Efficient Techniques for High-Speed Elliptic Curve Cryptography

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Title Efficient Techniques for High-Speed Elliptic Curve Cryptography
Authors/Editors* Patrick Longa, Catherine Gebotys
Where published* Workshop on Cryptographic Hardware and Embedded Systems
How published* Proceedings
Year* 2010
Volume 6225/2011
Pages 80-94
Publisher LNCS
Keywords Elliptic curve cryptosystem - point multiplication - point operation - field arithmetic - incomplete reduction - software implementation
In this paper, a thorough bottom-up optimization process (field, point and scalar arithmetic) is used to speed up the computation of elliptic curve point multiplication and report new speed records on modern x86-64 based processors. Our different implementations include elliptic curves using Jacobian coordinates, extended Twisted Edwards coordinates and the recently proposed Galbraith-Lin-Scott (GLS) method. Compared to state-of-the-art implementations on identical platforms the proposed techniques provide up to 30% speed improvements. Additionally, compared to the best previous published results on similar platforms improvements up to 31% are observed. This research is crucial for advancing high speed cryptography on new emerging processor architectures.

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