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Title:
Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves
Authors: Pierre-Alain Fouque, 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.
ePrint: https://eprint.iacr.org/2010/037
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