Huff's Model for Elliptic Curves

Marc Joye 1 Mehdi Tibouchi 2, 3 Damien Vergnaud 2, 3
3 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 : This paper revisits a model for elliptic curves over Q introduced by Huff in 1948 to study a diophantine problem. Huff's model readily extends over fields of odd characteristic. Every elliptic curve over such a field and containing a copy of Z/4Z x Z/2Z is birationally equivalent to a Huff curve over the original field. This paper extends and generalizes Huff's model. It presents fast ex- plicit formulae for point addition and doubling on Huff curves. It also addresses the problem of the efficient evaluation of pairings over Huff curves. Remarkably, the so-obtained formulae feature some useful properties, including completeness and independence of the curve parameters.
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Communication dans un congrès
Guillaume Hanrot and François Morain and Emmanuel Thomé. Algorithmic Number Theory, 9th International Symposium, ANTS-IX, Jul 2010, Nancy, France. Springer, 6197, pp.234-250, 2010, Lecture Notes in Computer Science. 〈10.1007/978-3-642-14518-6_20〉
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Marc Joye, Mehdi Tibouchi, Damien Vergnaud. Huff's Model for Elliptic Curves. Guillaume Hanrot and François Morain and Emmanuel Thomé. Algorithmic Number Theory, 9th International Symposium, ANTS-IX, Jul 2010, Nancy, France. Springer, 6197, pp.234-250, 2010, Lecture Notes in Computer Science. 〈10.1007/978-3-642-14518-6_20〉. 〈inria-00577140〉

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