66 citations · 90 across the 9 of their papers we have counts for
9 papers · 1 filter
On the computation of endomorphism rings of abelian surfaces over finite fields
Samuele Anni, Gaetan Bisson, Annamaria Iezzi +2
We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address th…
Iterative constructions of irreducible polynomials from isogenies
Alp Bassa, Gaetan Bisson, Roger Oyono
Let be a rational fraction and let be a polynomial over a finite field. Consider the transform . In certain cases, the polynomials ,…
Constructing Permutation Rational Functions From Isogenies
Gaetan Bisson, Mehdi Tibouchi
A permutation rational function is a rational function that induces a bijection on , that is, for all there exists exactly o…
On polarised class groups of orders in quartic CM-fields
Gaetan Bisson, Marco Streng
We give an explicit necessary condition for pairs of orders in a quartic CM-field to have the same polarised class group. This generalises a simpler result for imaginary quadratic…
Computing endomorphism rings of abelian varieties of dimension two
Gaetan Bisson
Generalizing a method of Sutherland and the author for elliptic curves, we design a subexponential algorithm for computing the endomorphism rings of ordinary abelian varieties of d…
Computing endomorphism rings of elliptic curves under the GRH
Gaetan Bisson
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size o…
A low-memory algorithm for finding short product representations in finite groups
Gaetan Bisson, Andrew V. Sutherland
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-rho approach. Given an element z and a sequence…
Computing the endomorphism ring of an ordinary elliptic curve over a finite field
Gaetan Bisson, Andrew V. Sutherland
We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field F_q. Under suitable heuristic assumptions, both have subexpon…
More Discriminants with the Brezing-Weng Method
Gaetan Bisson, Takakazu Satoh
The Brezing-Weng method is a general framework to generate families of pairing-friendly elliptic curves. Here, we introduce an improvement which can be used to generate more curves…