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Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves

Authors:
Pierre-Alain Fouque
Mehdi Tibouchi
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URL: http://eprint.iacr.org/2010/037
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Abstract: Let E be a non-supersingular elliptic curve over a finite field F_q. At CRYPTO 2009, Icart introduced a deterministic function F_q->E(F_q) which can be computed efficiently, and allowed him and Coron to define well-behaved hash functions with values in E(F_q). Some properties of this function rely on a conjecture which was left as an open problem in Icart's paper. We prove this conjecture as well as analogues for other hash functions. See also Farahashi, Shparlinski and Voloch, _On Hashing into Elliptic Curves_, for independent results of a similar form.
BibTeX
@misc{eprint-2010-22938,
  title={Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Elliptic Curves, Function Fields, Hash Functions},
  url={http://eprint.iacr.org/2010/037},
  note={Latincrypt 2010 mehdi.tibouchi@ens.fr 14825 received 24 Jan 2010, last revised 4 Aug 2010},
  author={Pierre-Alain Fouque and Mehdi Tibouchi},
  year=2010
}