Possible options to improve cryptographic reliability of algorithms based on Nyberg construction

Nowadays one of the most used tools to protect data from unauthorized access is block symmetric-key cryptographic algorithms. The rapid growth of computer processing power and significant development of linear cryptanalysis actual- ize the task to continue increasing reliability of the existing algorithms, as well as developing new ones. An important component in determining the stability of a block symmetric-key cryptographic algorithm to the most common types of cryptanalysis is the quality of S-box substitution. This work was aimed at calculating and achieving all possible S-box substitutions, based on irreducible polynomials over the Galois field and their compositions. For this purpose a set of programs to obtain S-box substitutions which have different cryptographic characteristics with its help was developed. Calculation of the quantitative values of these characteristics was performed by presenting S-box substitutions in the form of sets of Boolean functions. Particular attention was paid to such characteristics as nonlinearity of Boolean func- tions, the maximum modulus of the correlation coefficients and the numbers of zeros of the correlation matrix of S-box substitutions, as those are the most important characteristics. These blocks substitutions can be the basis for further study of possible options to improve Rijndael algorithm’s cryptographic reliability.