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Hashing into Hessian 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

We describe a hashing function from the elements of the finite field \(\mathbb{F}_q\) into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. For ordinary Hessian curves, this function is 2 : 1 for almost all points. More precisely, for odd q, the cardinality of the image set of the function is exactly given by (q + i + 2)/2 for some i = − 1,1.

Next, we present an injective hashing function from the elements of ℤ m into points on a Hessian curve over \(\mathbb{F}_q\) with odd q and m = (q + i)/2 for some i = − 1,1,3.

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Author information

Authors and Affiliations

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

    Reza Rezaeian Farashahi

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  1. Reza Rezaeian Farashahi
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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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Farashahi, R.R. (2011). Hashing into Hessian 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_17

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  • DOI: https://doi.org/10.1007/978-3-642-21969-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21968-9

  • Online ISBN: 978-3-642-21969-6

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