Evolution of Group-Theoretic Cryptology Attacks using Hyper-heuristics

TL;DR

This paper introduces a hyper-heuristic framework that automatically generates and optimizes algorithms, improving the solution of group-theoretic cryptology problems like the AAG key exchange over polycyclic groups.

Contribution

It presents the first application of hyper-heuristics in group-theoretic cryptology, creating novel heuristic chains that outperform existing evolutionary algorithms.

Findings

Hyper-heuristics generate algorithms that solve more complex AAG instances.

New heuristic chains outperform the original EA in solving difficult problems.

Framework can be adapted to various cryptology problems over groups.

Abstract

In previous work, we developed a single Evolutionary Algorithm (EA) to solve random instances of the Anshel-Anshel-Goldfeld (AAG) key exchange protocol over polycyclic groups. The EA consisted of six simple heuristics which manipulated strings. The present work extends this by exploring the use of hyper-heuristics in group-theoretic cryptology for the first time. Hyper-heuristics are a way to generate new algorithms from existing algorithm components (in this case the simple heuristics), with the EAs being one example of the type of algorithm which can be generated by our hyper-heuristic framework. We take as a starting point the above EA and allow hyper-heuristics to build on it by making small tweaks to it. This adaptation is through a process of taking the EA and injecting chains of heuristics built from the simple heuristics. We demonstrate we can create novel heuristic chains, which when placed in the EA create algorithms which out-perform the existing EA. The new algorithms solve a markedly greater number of random AAG instances than the EA for harder instances. This suggests the approach could be applied to many of the same kinds of problems, providing a framework for the solution of cryptology problems over groups. The contribution of this paper is thus a framework to automatically build algorithms to attack cryptology problems.