Fast algorithms for ell-adic towers over finite fields

TL;DR

This paper introduces efficient algorithms for computations within the ell-adic closure of finite fields, achieving near-linear complexity in many cases, inspired by prior foundational work.

Contribution

It presents new fast algorithms for ell-adic tower computations over finite fields with quasi-linear complexity, improving efficiency over previous methods.

Findings

Algorithms achieve quasi-linear complexity in many cases

Significant speed-up in computations within ell-adic closures

Builds on and extends prior foundational work in the field

Abstract

Inspired by previous work of Shoup, Lenstra-De Smit and Couveignes-Lercier, we give fast algorithms to compute in (the first levels of) the ell-adic closure of a finite field. In many cases, our algorithms have quasi-linear complexity.