Two double-spend attack strategies on a proof-of-stake consensus are considered. For each strategy, the probability of its success is obtained, which depends on the network parameters and the number of confirmation blocks. These results can be used to define how many confirmation blocks a vendor should wait after a correspondent transaction before sending goods or services.

The paper is devoted to the investigation of the distributed proof generation process, which makes use of recursive zk-SNARKs. Such distributed proof generation, where recursive zk-SNARK-proofs are organized in perfect Mercle trees, was for the first time proposed in Latus consensus protocol for zk-SNARKs-based sidechains. We consider two models of a such proof generation process: the simplified one, where all proofs are independent (like one level of tree), and its natural generation, where proofs are organized in partially ordered set (poset), according to tree structure. Using discrete Markov chains for modeling of corresponding proof generation process, we obtained the recurrent formulas for the expectation and variance of the number of steps needed to generate a certain number of independent proofs by a given number of provers. We asymptotically represent the expectation as a function of the one variable n/m, where n is the number of provers m is the number of proofs (leaves of tree). Using results obtained, we give numerical recommendation about the number of transactions, which should be included in the current block, idepending on the network parameters, such as time slot duration, number of provers, time needed for proof generation, etc.

An exact value of round functions collision probability for 3-round Feistel network is derived. The upper bound of algorithm execution complexity for distinguishing Feistel network from a random permutation is given.

Five symmetric block ciphers were proposed to Ukrainian national public cryptographic competition. Developers used different methods for achiev- ing security and performance of the algorithms. An overview of proposed sym- metric block ciphers and results of their security analysis is given in this paper.