Efficiently Computable Endomorphisms for Hyperelliptic Curves

Abstract : Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic Jacobians, but one obstruction is the lack of explicit models of curves together with an efficiently computable endomorphism. In the case of hyperelliptic curves there are limited examples, most methods focusing on special CM curves or curves defined over a small field. In this article we describe three infinite families of curves which admit an efficiently computable endomorphism, and give algorithms for their efficient application.
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Hess, Florian and Pauli, Sebastian and Pohst, Michael. Algorithmic Number Theory Symposium: ANTS-VII, Jul 2006, Berlin, Germany. Springer, 4076, pp.495-509, 2006, Lecture Notes in Computer Science. 〈10.1007/11792086_35〉
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Contributeur : Benjamin Smith <>
Soumis le : vendredi 19 novembre 2010 - 15:52:11
Dernière modification le : lundi 20 janvier 2014 - 15:57:59

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David Kohel, Benjamin Smith. Efficiently Computable Endomorphisms for Hyperelliptic Curves. Hess, Florian and Pauli, Sebastian and Pohst, Michael. Algorithmic Number Theory Symposium: ANTS-VII, Jul 2006, Berlin, Germany. Springer, 4076, pp.495-509, 2006, Lecture Notes in Computer Science. 〈10.1007/11792086_35〉. 〈inria-00537882〉

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