66 citations · 90 across the 9 of their papers we have counts for
11 papers
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…
On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation
Samir M. Perlaza, Iñaki Esnaola, Gaetan Bisson +1
The dependence on training data of the Gibbs algorithm (GA) is analytically characterized. By adopting the expected empirical risk as the performance metric, the sensitivity of the…
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 ,…
Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis
Samir M. Perlaza, Gaetan Bisson, Iñaki Esnaola +2
The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a s…
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…