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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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Contributor : Benjamin Smith <>
Submitted on : Friday, November 19, 2010 - 3:52:11 PM
Last modification on : Monday, December 28, 2020 - 3:54:02 PM

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David Kohel, Benjamin Smith. Efficiently Computable Endomorphisms for Hyperelliptic Curves. Algorithmic Number Theory Symposium: ANTS-VII, Jul 2006, Berlin, Germany. pp.495-509, ⟨10.1007/11792086_35⟩. ⟨inria-00537882⟩



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