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Springer Verlag, Lecture Notes in Computer Science, p. 81-91

DOI: 10.1007/978-3-642-14712-8_5

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

Journal article published in 2010 by Michel Abdalla, Pierre-Alain Fouque, Paulo S. L. M. Barreto, Mehdi Tibouchi
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Let E be a non-supersingular elliptic curve over a nite eld Fq. At CRYPTO 2009, Icart (5) introduced a deterministic function Fq ! E(Fq) which can be computed eciently, and allowed him and Coron (3) to dene 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 (5). We prove this conjecture below as well as analogues for other hash functions. This allows us to prove that a related function is surjective, which is a rst step towards ecient hashing to the whole set of points of elliptic curves.