Heuristic methods of gradient search for the cryptographic boolean functions

Heuristic methods of gradient search of the cryptographic Boolean functions that satisfy the required properties of balance, nonlinearity, autocorrelation, and other stability indicators are considered. The proposed method of gradient descent is investigated, in particular, estimates of nonlinearity and correlation immunity of the synthesized Boolean functions are given. A method for evaluating the computational efficiency of gradient search methods is proposed, based on the construction of sample (empirical) distribution functions, which characterize the probability of the formation of the Boolean functions with persistence indicators not lower than those required. As an indicator of computational efficiency, we propose the average number of attempts that need to be performed using the heuristic method to form a cryptographic Boolean function with the required properties. It is shown that the proposed gradient descent method allows the formation of cryptographic functions with the required durability indicators in fewer steps. The results of investigations of the cryptographic properties of the formed Boolean functions in comparison with the best known assessments are given.