Substitution Boxes (S-boxes) play an important role in many modern-day cryptography algorithms. Indeed, without carefully chosen S-boxes many ciphers would be easy to break. The design of suitable S-boxes attracts a lot of attention in cryptography community. The evolutionary algorithms (EAs) community also had several attempts to evolve Sboxes with good cryptographic properties. When using EAs one usually uses permutation representation in order to preserve the bijectivity of the resulting S-boxes. In this paper we experiment with Cartesian Genetic Programming (CGP) and Genetic Programming (GP) in order to evolve bijective S-boxes of various sizes that have good cryptographic properties. Besides the standard CGP representation, we use an approach that allows CGP and GP to be mapped to the permutation encoding.
Picek et al. used Cartesian Genetic Programming and Genetic Programming to evolve S-boxes and discussed how to obtain permutation based encoding with those algorithms REF .
Cartesian Genetic Programming Approach for Generating Substitution Boxes of Different Sizes
GECCO Companion '15
Computer Science