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New Formulae for Efficient Elliptic Curve Arithmetic

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Progress in Cryptology – INDOCRYPT 2007 (INDOCRYPT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4859))

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Abstract

This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings for Jacobi-quartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobi-quartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d), Jacobi-intersection (4M+10S+5d or 7M+7S+3d), Edwards (9M+4S) and Hessian (8M+6S+1d) forms. We show that Hessian tripling costs 6M+4C+1d for Hessian curves defined over a field of characteristic 3. We discuss an alternative way of choosing the base point in successive squaring based scalar multiplication algorithms. Using this technique, we improve the latest mixed-addition formulae for Jacobi-intersection (10M+2S+1d), Hessian (5M+6S) and Edwards (9M+1S+ 1d+4a) forms. We discuss the significance of these optimizations for elliptic curve cryptography.

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Authors and Affiliations

  1. Information Security Institute, Queensland University of Technology,  

    Huseyin Hisil, Gary Carter & Ed Dawson

Authors
  1. Huseyin Hisil
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  2. Gary Carter
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  3. Ed Dawson
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K. Srinathan C. Pandu Rangan Moti Yung

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Hisil, H., Carter, G., Dawson, E. (2007). New Formulae for Efficient Elliptic Curve Arithmetic. In: Srinathan, K., Rangan, C.P., Yung, M. (eds) Progress in Cryptology – INDOCRYPT 2007. INDOCRYPT 2007. Lecture Notes in Computer Science, vol 4859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77026-8_11

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  • DOI: https://doi.org/10.1007/978-3-540-77026-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77025-1

  • Online ISBN: 978-3-540-77026-8

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