Skip to Main content Skip to Navigation
Journal articles

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

Romain Cosset 1 Damien Robert 2, 3
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
Document type :
Journal articles
Complete list of metadata

Cited literature [37 references]  Display  Hide  Download
Contributor : Damien Robert <>
Submitted on : Tuesday, March 22, 2011 - 6:53:49 PM
Last modification on : Monday, December 14, 2020 - 3:33:10 PM
Long-term archiving on: : Thursday, March 30, 2017 - 8:34:17 AM


Files produced by the author(s)




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



Record views


Files downloads