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)
Short URL: ia.cr/2010/037
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