Evolution of group-theoretic cryptology attacks using hyper-heuristics

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, simple heuristics), with 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 that out perform the existing EA. The new algorithms solve a greater number of random AAG instances than the EA. This suggests the approach may 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 article is thus a framework to automatically build algorithms to attack cryptology problems given an applicable group.</jats:p

Analysis of a Group of Automorphisms of a Free Group as a Platform for Conjugacy-Based Group Cryptography

Let F be a finitely generated free group and Aut(F) its group of automorphisms. In this monograph we discuss potential uses of Aut(F) in group-based cryptography. Our main focus is on using Aut(F) as a platform group for the Anshel-Anshel-Goldfeld protocol, Ko-Lee protocol, and other protocols based on different versions of the conjugacy search problem or decomposition problem, such as Shpilrain-Ushakov protocol. We attack the Anshel-Anshel-Goldfeld and Ko-Lee protocols by adapting the existing types of the length-based attack to the specifics of Aut(F). We also present our own version of the length-based attack that significantly increases the attack\u27 success rate. After discussing attacks, we discuss the ways to make keys from Aut(F) resistant to the different versions of length-based attacks including our own