In this article, heuristic methods of hill climbing for cryptographic Boolean functions satisfying the required properties of balance, nonlinearity, autocorrelation, and other stability indicators are considered. A technique for estimating the computational efficiency of gradient search methods, based on the construction of selective (empirical) distribution functions characterizing the probability of the formation of Boolean functions with indices of stability not lower than required, is proposed. As an indicator of computational efficiency, an average number of attempts is proposed to be performed using a heuristic method to form a cryptographic Boolean function with the required properties. Comparative assessments of the effectiveness of the heuristic methods are considered. The results of investigations of the cryptographic properties of the formed Boolean functions in comparison with the best known assessments are given. On the basis of the conducted research, it can be concluded that the functions constructed in accordance with the developed method have high persistence indexes and exceed the known functions by these indicators.
Heuristic methods of gradient search of 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 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.
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