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