For the implementation of error-correcting codes, cryptographic algorithms, and the construction of homomorphic methods for privacy-preserving, there is a need for methods of performing operations on elements GF(2m) that have low computational complexity. This paper analyzes the existing methods of performing operations on the elements GF(2m) and proposes a new method based on the use of a sparse table of elements of this field. The object of research is the processes of operations in information security systems. The subject of research is methods and algorithms for performing operations on elements GF(2m). The purpose of this research is to develop and improve methods and algorithms for performing operations on elements GF(2m) to reduce their computational complexity. Empirical methods and methods of mathematical and software modeling are used in the research. Existing and proposed algorithms are implemented using the C# programming language in the Visual Studio 2015 development environment. Experimental research of existing and developed algorithms was carried out according to the proposed method, which allows to level the influence of additional parameters on the results of the research. The conducted research on methods for performing operations on the elements GF(2m) shows the expediency of using a sparse table of field elements. This approach makes it possible to reduce the amount of RAM required for the software and hardware implementation of the developed method compared to the classical tabular method, which requires storage of a full table of correspondence of the polynomial and index representation of the field elements. In addition, the proposed method gives an increase in speed of more than 4 times for the operations of calculating the multiplicative inverse element and exponentiation. As a result, the proposed method allows to reduce the computational complexity of error-correcting codes, cryptographic algorithms, and the homomorphic methods for privacy-preserving.

One of the most important problems of modern cryptocurrency networks is the problem of scaling: advanced cryptocurrencies like Bitcoin can handle around 5 transactions per second. One of the most promising solutions to this problem are second layer payment protocols: payment networks implemented on top of base cryptocurrency network layer, based on the idea of delaying publication of intermediate transactions and using base network only as a finalization layer. Such networks consist of entities that interact with the cryptocurrency system via a payment channel protocol, and can send, receive and forward payments. This paper describes a formal actor-based model of payment channel network and uses it to formulate a modified payment protocol that can be executed in the network without requiring any information about its topology and thus can hide information about financial relations between nodes.

In this paper, the dynamic behavior of the damping system is analyzed with a two-mass pendulum absorber, the equations of motion of non-linear mechanical systems are built accordingly. AFC equation systems have been identified in the non-linear formulation. To obtain the frequency response, the Ritz averaging method is used. A new numerical method of determining the parameters of optimal tuning two-mass pendulum absorber in the non-linear formulation has been Proposed and implemented.

As elliptic curve cryptography is one of the popular ways of constructing an encoding and decoding processes, public-key algorithms as its basis provide people a comfortable way of exchanging pieces of encoded information. As the time goes by, a lot of algorithms have emerged, some of them are still in use today; some others are still being developed into new forms. The main point of algorithm innovation is to reduce the number of processed operations during every possible step to find maximum efficiency and highest speed while performing the calculations. This article describes an improved method of the López-Dahab-Montgomery (LD-Montgomery) scalar point multiplication in terms of working with binary elliptic curves. It is shown in the article that the possible improvement lies in reordering the set of operations which is used in LD-Montgomery scalar point multiplication algorithm. The algorithm is used to compute point multiplication results of the curves over binary Galois Fields featuring the following m values: . The article also presents the experimental results based on different scalars.