On the domination polynomial of a digraph: a generation function approach

Let G be a directed graph on n vertices. The domination polynomial of G is the polynomial D(G, x) =∑ni=0 d(G, i)xi, where d(G, i) is the number of dominating sets of G with i vertices. In this paper, we prove that the domination polynomial of G can be obtained by using an ordinary generating function. Besides, we show that our method is useful to obtain the minimum-weighted dominating set of a graph.

Reliability analysis method for redundancy systems based on GO methodology and the universal generation function

In this study, Goal-Oriented (GO) methodology, as an important technique for reliability analysis, is used in multi-state redundancy systems. However, traditional GO operation is usually not sufficiently effective for such multi-state redundancy systems because of the complex computational problem. To solve this problem, an efficient UGF-based GO operation that combines the advantages of GO methodology and the universal generation function (UGF) is proposed. The algorithm can avoid the complex calculation process caused by the algorithm-based GO operation of traditional probability formulas, and can simplify the correction of the shared signal by regarding it as the system’s conditional probability. In addition, the further correction problem in which some dependent shared signals with a common failure are caused by other shared signals is also considered. Some application examples are presented to illustrate the proposed UGF-based GO methodology, as well as its effectiveness and practicability.

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

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.