Computing discrete logarithms using Joux's algorithm

Abstract

In 2013, Joux presented a new algorithm for solving the discrete logarithm problem in finite fields of small characteristic with a main novelty involving the resolution of bilinear equation systems. The algorithm improved significantly all previous methods for this purpose. We used Joux’s algorithm to compute discrete logarithms in the 1303-bit finite field F36·137 and illustrated for the first time its effectiveness in ‘general’ small-characteristic finite fields with very modest computational resources.