Improvement of the construction technique of substitution blocks for symmetric encryption algorithms

As it is known, block symmetric encryption algorithms are widely used to ensure information confidentiality. The re- sistance of encryption algorithms to the most common types of cryptanalysis is determined the quality of the blocks of substitutions. In the present work, the development of a methodology for constructing substitution blocks is being continued. In the first approach, Boolean functions with given cryptographic properties are used as component functions of substitution blocks. Previously, one of the authors proposed a reasonable methodology for the phased selection of Boolean functions for construction block. In this paper, in addition to such cryptographic properties of Boolean functions, such as: balance, possessing a strict avalanche effect, possessing correlation immunity, for the first time the nonlinearity distances of the first and second orders of Boolean functions are considered simultaneously. A study of the full set of Boolean functions of four variables was conducted. The result of it is the optimal set of Boolean functions for building substitution blocks when encrypted with the GOST 28147-89 algorithm. In the second approach, the substitution block are determined by an irreducible polynomial over the Galois field, such a scheme, used in the Rijndael encryption algorithm, is considered to be strong. The growth of calculating power of the computer necessitates an increase of the cryptographic strength of encryp- tion algorithms. The authors have proposed substitution blocks for each round of the Rijndael scheme, based on different irreducible polynomials. A study of compositions representing a different combination of specially selected irreducible polynomials for ten rounds was carried out and the optimal set of polynomials with the best values of the encryption quality indica- tors by the Rijndael scheme was obtained.