# Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic

## TL;DR

This paper demonstrates that the discrete logarithm problem in finite fields of fixed characteristic can be solved in quasi-polynomial expected time, significantly improving the understanding of its computational complexity.

## Contribution

The authors establish a quasi-polynomial time algorithm for discrete logarithms in finite fields of fixed characteristic, advancing the field of computational number theory.

## Key findings

- Discrete logarithm problem solvable in quasi-polynomial time
- Expected time complexity is $(pn)^{2 ext{log}_2(n) + O(1)}$
- Results impact cryptographic security assumptions

## Abstract

We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality $p^n$ in expected time $(pn)^{2\log_2(n) + O(1)}$.