Isaev S. Computational synthesis methods of nonlinear substitution blocks to improve the efficiency of symmetric crypto transformations

Object - the process of synthesis of nonlinear substitution boxes of symmetric crypto transformations. Purpose - improvement of the efficiency of symmetric crypto transformations based on the synthesis of nonlinear substitution boxes with improved properties. Methods - methods of mathematical modeling, information security theory, the mathematical apparatus of Boolean algebra, the theory of finite fields, the theory of probability and mathematical statistics. Theoretical and practical results - solved a number of relevant scientific and technical issues related to the development and improvement of mathematical model and computational methods of synthesis of substitution boxes with improved properties using a mathematical apparatus of non-binary cryptographic functions. A number of computing algorithms that form regular substitution blocks with improved cryptographic properties, and also evaluate the effectiveness of the reduced models of modern block ciphers are designed and impleneted. Scientific novelty - the mathematical model of regular nonlinear boxes of cryptotransformations using symmetric non-binary cryptographic functions in arithmetic of finite fields is developed, method for the synthesis of nonlinear substitution boxes (the method of simulated annealing) through the development of search criterions using spectral and correlation properties of non-binary cryptographic functions and dynamic weights is improved; computational method for forecasting efficiency evaluations of symmetric cryptotransformations based on the study of differential and linear properties of the reduced cipher models with accounting of nonlinearity and autocorrelation properties of used nonlinear substitution boxes is developed, computational methods for evaluating the computational effectiveness of probabilistic (bit-to-bit) synthesis of regular nonlinear substitution boxes with given cryptographic properties are developed. The acts of the realization of the research results in the production of JSC "Microcrypt Technologies", and in the educational process of Kharkiv National University named after V.N. Karazin are received. The results of the thesis are recommended to use when carrying out scientific-research and research-constructional works on development of new cryptographic means of protection information, in higher educational institutions of the Ministry of Education and Science of Ukraine in the study of subjects on information protection theory.