Research should be something of an adventure. There are many ‘Open Questions’ identified in the specific chapters of this thesis. Below is an attempt to summarise very briefly, and hopefully in an entertaining style, some exhortations on how to engage in exciting metaheuristic search-based work in cryptology. Some of these are justified by the research reported here. Some are simply inspired by it.
Watch It! Exploit the computational dynamics of search. The author knows
of no cryptosystem designed to withstand an attack based on analysis of a simulated-annealing run in action.
Achieve Less More Often! There seems to be a general opinion that metaheuristic search will never be able to evolve a secret key for a modern- day crypto-algorithm. This is probably true, but it seems to assume that the only way to break a cryptosystem is to evolve a key. Can metaheuristic search be used to evolve approximations that are better than currently used? Can many but diverse approximations be evolved and combined? Being less ambitious very many times may be a powerful idea.
Measure Everything! 1 Structures abound in cryptology and there may be very subtle interactions and relationships between properties. Be prepared to take advantage of these relationships. Optimisation results may indeed suggest unusual relationships. If you do not look you will not find them.
Profile it! Every cost function achieves something. The issue is ‘What?’
Use of certain cost functions may have unanticipated consequences (as has been seen to considerable effect in this thesis). What patterns are there in the results? Can they be exploited?
Describe it! Patterns or structure in the results may be present but the an-
alyst may be unable to see them. Can techniques such as genetic program- ming be used to evolve descriptions of the results?
Warp it! The best cost functions are those that get you what you want.
Be flexible in your choice of cost function families. Deviate from the stan- dard or obvious cost functions. Can ‘warped’ functions be used? Can ap- proximation families be used? We have seen the use of polynomial-based approximations. What others are there?
Embrace Local Optima! The world seems grossly prejudiced against local
optima! One might be tempted to believe that the only good local optimum is a global optimum. This seems extreme. As argued in Chapter 5 local optima may better be regarded as sources of information and not failures. Stop worrying and learn to love local optima! Just how far can this notion be pushed?
Appendix A
A.1
Example (8,0,6,116,24) Function With Walsh and
AC Zeroes Rank of 8
Here is the support for a (8,0,6,116,24) derived using the NCT method. It has Walsh and AC zeroes of rank 8. These provide linear transformation bases to give CI(1) and PC(1) transformed functions.
B B B B B CB@B B B B B B CB B B B B B B B B B B % B =