Chapter

Cryptographic Hardware and Embedded Systems, CHES 2010

Volume 6225 of the series Lecture Notes in Computer Science pp 80-94

Efficient Techniques for High-Speed Elliptic Curve Cryptography

  • Patrick LongaAffiliated withDepartment of Electrical and Computer Engineering, University of Waterloo
  • , Catherine GebotysAffiliated withDepartment of Electrical and Computer Engineering, University of Waterloo

Abstract

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.

Keywords

Elliptic curve cryptosystem point multiplication point operation field arithmetic incomplete reduction software implementation