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Paper: Deterministic Encoding and Hashing to Odd Hyperelliptic Curves

Authors:
Pierre-Alain Fouque
Mehdi Tibouchi
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URL: http://eprint.iacr.org/2010/382
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Abstract: In this paper we propose a very simple and efficient encoding function from F_q to points of a hyperelliptic curve over F_q of the form H: y^2=f(x) where f is an odd polynomial. Hyperelliptic curves of this type have been frequently considered in the literature to obtain Jacobians of good order and pairing-friendly curves. Our new encoding is nearly a bijection to the set of F_q-rational points on H. This makes it easy to construct well-behaved hash functions to the Jacobian J of H, as well as injective maps to J(F_q) which can be used to encode scalars for such applications as ElGamal encryption. The new encoding is already interesting in the genus 1 case, where it provides a well-behaved encoding to Joux's supersingular elliptic curves.
BibTeX
@misc{eprint-2010-23283,
  title={Deterministic Encoding and Hashing to Odd Hyperelliptic Curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Hyperelliptic Curve Cryptography, Deterministic Encoding, Hashing},
  url={http://eprint.iacr.org/2010/382},
  note={(in submission) mehdi.tibouchi@normalesup.org 14798 received 6 Jul 2010, last revised 8 Jul 2010},
  author={Pierre-Alain Fouque and Mehdi Tibouchi},
  year=2010
}