Properties of the cost function in the iterative algorithm for generating nonlinear substitution

Abstract

To ensure the security of information technology, cryptographic information protection tools are used, in particular block and stream encryption algorithms with a symmetric key. Reliability and cryptographic strength of cryptoalgorithms is provided by the properties of the applied primitives. For example, non-linear substitutions (S-boxes) are used as the main component of modern symmetric ciphers. Therefore, generation of substitutions is an important scientific task directly related to the security of information technology and improvement of modern symmetric ciphers. The paper investigates the properties of iterative algorithms for generating non-linear substitutions and special cost functions, which play a decisive role in the heuristic search for S-boxes with the required properties. We consider the cost function of the WCF (Cost Function of the content of the Walsh-Hadamard spectrum) and optimize its parameters. The obtained optimization results in combination with the Hill Climbing iterative search algorithm can reduce significantly the number of iterations. In particular, we show that for a substitution search with a non-linearity of 104, on average, we reduce the computational complexity of generation by more than 20%. In addition, it is possible to increase the success rate of the heuristic search. In particular, for the selected settings, in 100% of cases, a beaktive S-box with a non-linearity of 104 was found.