Efficient Techniques for High-Speed Elliptic Curve Cryptography

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.

• Type: Conference
• Year: 2010
• Where: CHES
• Authors: Patrick Longa, Catherine H. Gebotys
• Keywords: CHES 2010, Cryptology, Elliptic Curve Point, Elliptic Curves, Thorough Bottom-up Optimization