Simulation Model for Investigation of the Behaviour of an Artificial Immune Algorithm for Generation of S-Boxes with Good Cryptographic Properties

Recently applications of a variety of immune algorithms for generation of S-boxes with good cryptographic properties have been used. It is very hard to observe and analyse the work of such algorithms as they have many parallel branches and a big variety of randomly chosen parameters in the hypermutation functions. That is why, we create a simulation model of an immune algorithm based on the Hidden Markov Model (HMM) to investigate its performance. The implemented HMM has low computational complexity and allows to evaluate performance and correctness of the modeled algorithm when different hypermutation functions with different parameters are used. The simulation model is tested with the suggested in this work immune algorithm for generation of \((8\times 8)\) bijective S-boxes whose aim is to reduce the number of spectral Walsh coefficients of maximum magnitude.