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Journal Articles Mathematics of Computation Year : 2015

Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves

Abstract

In this paper, we compute l-isogenies between abelian varieties over a field of characteristic different from 2 in polynomial time in l, when l is an odd prime which is coprime to the characteristic. We use level n symmetric theta structure where n = 2 or n = 4. In a second part of this paper we explain how to convert between Mumford coordinates of Jacobians of genus 2 hyperelliptic curves to theta coordinates of level 2 or 4. Combined with the preceding algorithm, this gives a method to compute (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves.
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Dates and versions

hal-00578991 , version 1 (22-03-2011)

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Romain Cosset, Damien Robert. Computing (l,l)-isogenies in polynomial time on Jacobians of genus 2 curves. Mathematics of Computation, 2015, 84 (294), pp.1953-1975 ⟨10.1090/S0025-5718-2014-02899-8⟩. ⟨hal-00578991⟩
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