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Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves

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Information Security and Privacy (ACISP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5107))

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Abstract

Extractors are an important ingredient in designing key exchange protocols and secure pseudorandom sequences in the standard model. Elliptic and hyperelliptic curves are gaining more and more interest due to their fast arithmetic and the fact that no subexponential attacks against the discrete logarithm problem are known.

In this paper we propose two simple and efficient deterministic extractors for \(J(\mathbb{F}_q)\), the Jacobian of a genus 2 hyperelliptic curve H defined over \(\mathbb{F}_q\), where q = 2n, called the sum and product extractors.

For non-supersingular hyperelliptic curves having a Jacobian with group order 2m, where m is odd, we propose the modified sum and product extractors for the main subgroup of \(J(\mathbb{F}_q)\). We show that, if \(D\in J(\mathbb{F}_q)\) is chosen uniformly at random, the bits extracted from D are indistinguishable from a uniformly random bit-string of length n.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Reza Rezaeian Farashahi

  2. Dept. of Mathematical Sciences, Isfahan University of Technology, P.O. Box 85145, Isfahan, Iran

    Reza Rezaeian Farashahi

Authors
  1. Reza Rezaeian Farashahi
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Editor information

Yi Mu Willy Susilo Jennifer Seberry

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Farashahi, R.R. (2008). Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves. In: Mu, Y., Susilo, W., Seberry, J. (eds) Information Security and Privacy. ACISP 2008. Lecture Notes in Computer Science, vol 5107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70500-0_33

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  • DOI: https://doi.org/10.1007/978-3-540-70500-0_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69971-2

  • Online ISBN: 978-3-540-70500-0

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