Hashing into Hessian Curves

  • Reza Rezaeian Farashahi
Conference paper

DOI: 10.1007/978-3-642-21969-6_17

Volume 6737 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
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

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 ℤm into points on a Hessian curve over \(\mathbb{F}_q\) with odd q and m = (q + i)/2 for some i = − 1,1,3.

Keywords

Elliptic curve cryptography Hessian curve hashing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Reza Rezaeian Farashahi
    • 1
  1. 1.Department of ComputingMacquarie UniversitySydneyAustralia