Optimization of the PCF Cost Function for the Generation of Highly Nonlinear S-boxes

Abstract

Creation of reliable telecommunication communication channels providing confidential data, it is currently impossible to have reliable encryption algorithms. The most popular services that provide encryption algorithms include confidentiality, integrity, and authenticity services. Most modern symmetric encryption algorithms use nonlinear substitutions or abbreviated S-boxes. Their properties have a direct impact on the cryptographic strength of symmetric encryption. So, generating S-boxes with the right properties is certainly an important task for creating S-boxes. In this paper, we consider heuristic methods for generating nonlinear substitutions that use special cost functions (heuristics). During generation, the search algorithm changes the randomly generated substitution at each iteration and tries to reduce the value of the cost function. Search attempts are stopped either after finding the S-box with the desired properties, or after performing a certain number of iterations. Doubtless, the search efficiency depends on the chosen heuristic, namely, on the parameters of the cost function. In this paper, we consider the PCF cost function and optimize its parameters. We managed to optimize the parameters of this heuristic and achieve the least number of search iterations.