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Cryptographers’ Track at the RSA Conference

CT-RSA 2010: Topics in Cryptology - CT-RSA 2010 pp 106–118Cite as

Refinement of Miller’s Algorithm Over Edwards Curves

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 5985))

Abstract

Edwards gave a new form of elliptic curves in [1], and these curves were introduced to cryptography by Bernstein and Lange in [2]. The Edwards curves enjoy faster addition and doubling operations, so they are very attractive for elliptic curve cryptography.

In 2006, Blake, Murty and Xu proposed three refinements to Millers algorithm for computing Weil/Tate pairings over Weierstraß curves. In this paper we extend their method to Edwards curve and propose a faster algorithm for computing pairings with Edwards coordinates, which comes from the analysis of divisors of rational functions.

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References

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Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Lei Xu & Dongdai Lin

  2. Graduate University of Chinese Academy of Sciences, Beijing, China

    Lei Xu

Authors
  1. Lei Xu
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  2. Dongdai Lin
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Editor information

Editors and Affiliations

  1. Department of Computing, Macquarie University, NSW 2109, Sydney, Australia

    Josef Pieprzyk

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Xu, L., Lin, D. (2010). Refinement of Miller’s Algorithm Over Edwards Curves. In: Pieprzyk, J. (eds) Topics in Cryptology - CT-RSA 2010. CT-RSA 2010. Lecture Notes in Computer Science, vol 5985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11925-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-11925-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11924-8

  • Online ISBN: 978-3-642-11925-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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