Untitled
ROBERT, Damien
Cryptology, Arithmetic: Hardware and Software [CARAMEL]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Cryptology, Arithmetic: Hardware and Software [CARAMEL]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
ROBERT, Damien
Cryptology, Arithmetic: Hardware and Software [CARAMEL]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Cryptology, Arithmetic: Hardware and Software [CARAMEL]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Compositio Mathematica. 2012-09-01, vol. 148, n° 05, p. 1483--1515
Foundation Compositio Mathematica
English Abstract
We describe an efficient algorithm for the computation of isogenies between abelian varieties represented in the coordinate system provided by algebraic theta functions. We explain how to compute all the isogenies from an ...Read more >
We describe an efficient algorithm for the computation of isogenies between abelian varieties represented in the coordinate system provided by algebraic theta functions. We explain how to compute all the isogenies from an abelian variety whose kernel is isomorphic to a given abstract group. We also describe an analog of Vélu's formulas to compute an isogenis with prescribed kernels. All our algorithms rely in an essential manner on a generalization of the Riemann formulas. In order to improve the efficiency of our algorithms, we introduce a point compression algorithm that represents a point of level $4\ell$ of a $g$ dimensional abelian variety using only $g(g+1)/2\cdot 4^g$ coordinates. We also give formulas to compute the Weil and commutator pairing given input points in theta coordinates. All the algorithms presented in this paper work in general for any abelian variety defined over a field of odd characteristic.Read less <
European Project
Algorithmic Number Theory in Computer Science
ANR Project
Courbes Hyperelliptiques : Isogénies et Comptage - ANR-09-BLAN-0020
Origin
Hal imported