Abstract
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.
Highlights
On NP-hard problems, the time taken to produce an algorithm to solve such problems is often vast
If the performance improves over that of previous heuristic chains, it is run with the testing set (50 random instances)
If the performance over this set improves over that of previous heuristic chains, the current chain is assigned as the new best chain
Summary
On NP-hard problems, the time taken to produce an algorithm to solve such problems is often vast. We take a different approach and attempt to design an algorithm in response to feedback from similar instances of the problem Examples of such problems are those in group-theoretic cryptology (multiple conjugacy, Anshel–Anshel–Goldfeld [AAG, [1]] and word decomposition, for instance). These problems have been posed over varying types of groups serving as the base problems for key exchange protocols (KEPs) [1,2,3,4,5] and subsequently attacked [6,7,8,9,10,11,12,13,14].
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