Estimating the size of the image of deterministic hash functions to elliptic curves

Authors:
Pierre-Alain Fouque;Mehdi Tibouchi
Affiliations:
École normale supérieure, Déartement d'informatique, Paris CEDEX 05, France;École normale supérieure, Département d'informatique, Paris CEDEX 05, France
Venue:
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Year:
2010

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Abstract

Let E be a non-supersingular elliptic curve over a finite field Fq. At CRYPTO 2009, Icart introduced a deterministic function Fq → E(Fq) which can be computed efficiently, and allowed him and Coron to define well-behaved hash functions with values in E(Fq). Some properties of this function rely on a conjecture which was left as an open problem in Icart's paper. We prove this conjecture below as well as analogues for other hash functions.