Biblio
The aim of this paper is to find cellular automata (CA) rules that are used to describe S-boxes with good cryptographic properties and low implementation cost. Up to now, CA rules have been used in several ciphers to define an S-box, but in all those ciphers, the same CA rule is used. This CA rule is best known as the one defining the Keccak $\chi$ transformation. Since there exists no straightforward method for constructing CA rules that define S-boxes with good cryptographic/implementation properties, we use a special kind of heuristics for that – Genetic Programming (GP). Although it is not possible to theoretically prove the efficiency of such a method, our experimental results show that GP is able to find a large number of CA rules that define good S-boxes in a relatively easy way. We focus on the 4 x 4 and 5 x 5 sizes and we implement the S-boxes in hardware to examine implementation properties like latency, area, and power. Particularly interesting is the internal encoding of the solutions in the considered heuristics using combinatorial circuits; this makes it easy to approximate S-box implementation properties like latency and area a priori.
Evolutionary Computation (EC) has been used with great success on various real-world problems. One domain abundant with numerous difficult problems is cryptology. Cryptology can be divided into cryptography, that informally speaking considers methods how to ensure secrecy (but also authenticity, privacy, etc.), and cryptanalysis, that deals with methods how to break cryptographic systems. Although not always in an obvious way, EC can be applied to problems from both domains. This tutorial will first give a brief introduction to cryptology intended for general audience (therefore, omitting proofs and mathematics behind many concepts). Afterwards, we concentrate on several topics from cryptography that are successfully tackled up to now with EC and discuss why those topics are suitable to apply EC. However, care must be taken since there exists a number of problems that seem to be impossible to solve with EC and one needs to realize the limitations of the heuristics. We will discuss the choice of appropriate EC techniques (GA, GP, CGP, ES, multi-objective optimization, etc) for various problems and evaluate on the importance of that choice. Furthermore, we will discuss the gap between the cryptographic community and EC community and what does that mean for the results. By doing that, we will give a special emphasis on the perspective that cryptography presents a source of benchmark problems for the EC community. To conclude, we will present a number of topics we consider to be a strong research choice that can have a real-world impact. In that part, we give a special attention to cryptographic problems where cryptographic community successfully applied EC, but where those problems remained out of the focus of EC community. This tutorial will also present some live demos of EC in action when dealing with cryptographic problems. We will present several problems, ways of encoding solutions, impact of the algorithms choice and finally, we will run some experiments to show the results and discuss how to assess them from cryptographic perspective.