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Abstract

New methods to generate nonlinear substitutions with optimal properties that can be used in advanced symmetric cryptographic primitives are proposed in the thesis. These methods combine the heuristic approach and the theory of vectorial Boolean functions.

Based on the algebraic cryptanalysis of block ciphers submitted to the Ukrainian competition, the extended criterion of algebraic immunity and the criterion for multiple substitutions belonging to different equivalence classes were taken into account in the generation procedures.

The best among the proposed methods allows to increase the nonlinearity from 96 to 104 while the algebraic immunity and the δ-uniformity remain unchanged. The use of such substitutions in the block cipher «Kalyna», which was noted in the Ukrainian competition for selection of a prospective encryption algorithm, provides a high level of resistance against cryptographic attacks.

The efficiency of the new methods was confirmed by practical implementations for a cluster system. Using the developed programs, several specific substitutions for both existing and prospective symmetric cryptographic algorithms were proposed.