Development of a Pseudo-Random Sequence Generation Function Based on the “Kuznechik” Cryptographic Algorithm

Abstract

Purpose: increasing the cryptographic strength level of the pseudo-random sequence generation function based on the «Kuznechik» encryption algorithm. Research methods: methods for constructing pseudo-random sequence generators using a strong cryptographic algorithm as a generation function in accordance with the recommendations of NIST SP 800-90. Methods of probability theory and mathematical statistics (statistical hypothesis testing, Pearson’s criterion), methods for estimating the entropy of a random process. Results: а method for development of the main component of the deterministic generator – the function for generating pseudo-random sequences based on the «Kuznechik» encryption algorithm (Russian encryption standard GOST R 34.12-2015) due to a number of the original algorithm modifications is proposed. Features of the algorithm allow to use it in a mode that combines the advantages of the well-known encryption modes of block ciphers (OFB and CTR encryption modes). A procedure for generating round keys and other modifications of the algorithm that increase its security while maintaining its performance have been developed and implemented. The generator operation was evaluated on the basis of the statistical properties of the output sequences (NIST SP 800-22 tests), Pearson’s χ2 criterion, and min-entropy (NIST 800-90B tests). According to the characteristics mentioned above, the proposed generation function is comparable with the reference version based on GOST 34.12-2015 «Kuznechik», but exceeds it in terms of security.