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

Pierre-Alain Fouque 1, 2, 3 Mehdi Tibouchi 3
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : Let E be a non-supersingular elliptic curve over a finite field Fq . At CRYPTO 2009, Icart introduced a deterministic function from Fq to 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.
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Communication dans un congrès
Michel Abdalla and Paulo S. L. M. Barreto. Progress in Cryptology - LATINCRYPT 2010, First International Conference on Cryptology and Information Security in Latin America, 2010, Puebla, Mexico. Springer, 6212, pp.81-91, 2010, Lecture Notes in Computer Science. 〈10.1007/978-3-642-14712-8〉
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Pierre-Alain Fouque, Mehdi Tibouchi. Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves. Michel Abdalla and Paulo S. L. M. Barreto. Progress in Cryptology - LATINCRYPT 2010, First International Conference on Cryptology and Information Security in Latin America, 2010, Puebla, Mexico. Springer, 6212, pp.81-91, 2010, Lecture Notes in Computer Science. 〈10.1007/978-3-642-14712-8〉. 〈inria-00556676〉

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