Rodinko M. Methods of construction and research of properties of lightweight block ciphers and their components

The dissertation is devoted to the development and improvement of methods on cryptographic properties analysis of block ciphers components and construction of perspective cryptographic transformations. The aim of the dissertation is to increase performance of symmetric cryptographic transformations and improve methods of analysis of their strength. In the dissertation it is improved the gradient descent method for generating nonlinear substitution tables, which significantly reduces the complexity of optimal S-boxes generation. It is further developed the mathematical method of estimating the collision properties of non-injective key schedules of block ciphers, which differs in the application of an improved mathematical model and more efficient mathematical apparatus and allows to obtain an accurate estimate of the collision probability of two round key sequences. In the dissertation for the first time two methods of searching for one-round differential characteristics for a certain class of ARX-ciphers are proposed, which allow to obtain estimates of the strength of the round function of a block cipher of the certain class to differential cryptanalysis with low computational complexity. Moreover, methods of searching for multi-round differential characteristics for a certain class of ARX-ciphers have been further developed, which differ by an improved mechanism for selecting input differences and forming an initial set of one-round differential characteristics, which allows to estimate the strength of a full-scale block cipher of the certain class to differential cryptanalysis. A perspective post-quantum lightweight block cipher Cypress is developed, which provides high and ultra-high levels of security and exceeds the performance of known lightweight block ciphers on general-purpose processors and mobile platforms, and also the strength of the block cipher Cypress-256 to the differential cryptanalysis in accordance with the requirements of the practical criterion is proven.