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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. The different implementations include elliptic curves using Jacobian coordinates, extended Twisted Ed-wards coordinates and the recently proposed Galbraith-Lin-Scott (GLS) method. Compared to state-of-the-art implementations on identical plat-forms 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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