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On Randomness Extraction in Elliptic Curves

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Progress in Cryptology – AFRICACRYPT 2011 (AFRICACRYPT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6737))

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Abstract

A deterministic extractor for an elliptic curve, that converts a uniformly random point on the curve to a random k-bit-string with a distribution close to uniform, is an important tool in cryptography. Such extractors can be used for example in key derivation functions, in key exchange protocols and to design cryptographically secure pseudorandom number generator.

In this paper, we present a simple and efficient deterministic extractor for an elliptic curve E defined over \(\mathbb{F}_{q^n}\), where q is prime and n is a positive integer. Our extractor, denoted by \(\mathcal{D}_k\), for a given random point P on E, outputs the k-first \(\mathbb{F}_{q}\)-coordinates of the abscissa of the point P. This extractor confirms the two conjectures stated by R. R. Farashahi and R. Pellikaan in [6] and by R. R. Farashahi, A. Sidorenko and R. Pellikaan in [7], related to the extraction of bits from coordinates of a point of an elliptic curve.

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Author information

Authors and Affiliations

  1. École doctorale de Mathématiques et d’Informatique, Université Cheikh Anta Diop de Dakar, Sénégal, BP: 5005, Dakar Fann

    Abdoul Aziz Ciss & Djiby Sow

Authors
  1. Abdoul Aziz Ciss
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  2. Djiby Sow
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Editor information

Editors and Affiliations

  1. Département de Mathématiques, Université de Caen, Campus II, Boulevard Maréchal Juin, BP 5186, 14032, Caen Cedex, France

    Abderrahmane Nitaj

  2. École normale supérieure - CNRS - INRIA, Paris, France

    David Pointcheval

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Ciss, A.A., Sow, D. (2011). On Randomness Extraction in Elliptic Curves. In: Nitaj, A., Pointcheval, D. (eds) Progress in Cryptology – AFRICACRYPT 2011. AFRICACRYPT 2011. Lecture Notes in Computer Science, vol 6737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21969-6_18

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  • DOI: https://doi.org/10.1007/978-3-642-21969-6_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21968-9

  • Online ISBN: 978-3-642-21969-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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