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Binary Edwards Curves Revisited

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Progress in Cryptology -- INDOCRYPT 2014 (INDOCRYPT 2014)

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Abstract

We present new formulas for the arithmetic on the binary Edwards curves which are much faster than the-state-of-the-art. The representative speedup are \(3M+2D+S\) for a point addition, \(D+S\) for a mixed point addition, \(S\) for a point doubling, \(M+D\) for a differential addition and doubling. Here \(M,S\) and \(D\) are the cost of a multiplication, a squaring and a multiplication by a constant respectively. Notably, the new complete differential addition and doubling for complete binary Edwards curves with 4-torsion points need only \(5M+D+4S\) which is just the cost of the fastest (but incomplete) formulas among various forms of elliptic curves over finite fields of characteristic 2 in the literature. As a result the binary Edwards form becomes definitely the best option for elliptic curve cryptosytems over binary fields in view of both efficiency and resistance against side channel attack

Date of this document: 2014.09.16. This work has been supported by the National Academy of Sciences, D.P.R. of Korea.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Institute of Mathematics, National Academy of Sciences, Pyongyang, D.P.R. of Korea

    Kwang Ho Kim & Chol Ok Lee

  2. Team DALI, Université de Perpignan, Perpignan, France

    Christophe Negre

  3. LIRMM, UMR 5506, Université Montpellier 2 and CNRS, Perpignan, France

    Christophe Negre

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  1. Kwang Ho Kim
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  2. Chol Ok Lee
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  3. Christophe Negre
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Correspondence to Kwang Ho Kim .

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Editors and Affiliations

  1. Hochschule für Technik, Fachhochschule Nordwestschweiz, Windisch, Switzerland

    Willi Meier

  2. Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India

    Debdeep Mukhopadhyay

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Kim, K.H., Lee, C.O., Negre, C. (2014). Binary Edwards Curves Revisited. In: Meier, W., Mukhopadhyay, D. (eds) Progress in Cryptology -- INDOCRYPT 2014. INDOCRYPT 2014. Lecture Notes in Computer Science(), vol 8885. Springer, Cham. https://doi.org/10.1007/978-3-319-13039-2_23

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  • DOI: https://doi.org/10.1007/978-3-319-13039-2_23

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