  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.
