Cryptology ePrint Archive: Report 2010/037

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

Pierre-Alain Fouque and Mehdi Tibouchi

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.

Category / Keywords: public-key cryptography / Elliptic Curves, Function Fields, Hash Functions

Publication Info: Latincrypt 2010

Date: received 24 Jan 2010, last revised 4 Aug 2010

Contact author: mehdi tibouchi at ens fr

Available format(s): PDF | BibTeX Citation

Note: Fixed an error in Prop. 4

Version: 20100804:114029 (All versions of this report)

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