Kazymyrov O. Methods and techniques of generation of nonlinear substitutions for symmetric encryption algorithms

New methods of constructing nonlinear substitutions, which are used in symmetric cryptographic primitives, with optimal properties are presented in the thesis. Several methods of substitutions' generation for both existing and prospective symmetric cryptographic algorithms are proposed. These methods are based on the criteria approach using the theory of vectorial Boolean functions. Based on the algebraic cryptanalysis of ciphers submitted to the Ukrainian competition, the extended algebraic immunity criterion and the criterion for multiple substitutions belonging to different equivalence classes were taken into account in the search procedure. Proposed methods allow to increase the non-linearity from 96 to 104. The usage of such substitutions in the block cipher "Kalyna", which was noted in the national competition for selection of prospective encryption algorithm, gives a high level resistance to all known attacks. Efficiency of the new methods confirmed by practical search using a cluster system, which allows to find specific substitution constructions for symmetric cryptoalgorithms.