International Workshop on Cryptographic Hardware and Embedded Systems

CHES 2010: Cryptographic Hardware and Embedded Systems, CHES 2010 pp 80-94

Efficient Techniques for High-Speed Elliptic Curve Cryptography

  • Patrick Longa
  • Catherine Gebotys
Conference paper

DOI: 10.1007/978-3-642-15031-9_6

Volume 6225 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Longa P., Gebotys C. (2010) Efficient Techniques for High-Speed Elliptic Curve Cryptography. In: Mangard S., Standaert FX. (eds) Cryptographic Hardware and Embedded Systems, CHES 2010. CHES 2010. Lecture Notes in Computer Science, vol 6225. Springer, Berlin, Heidelberg


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.


Elliptic curve cryptosystempoint multiplicationpoint operationfield arithmeticincomplete reductionsoftware implementation
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Patrick Longa
    • 1
  • Catherine Gebotys
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of WaterlooCanada