Mykola Onai

Work place: Faculty of Applied Mathematics, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Ukraine



Research Interests: Network Security


Mykola Onai was born on December 06, 1986. He received his Bachelor’s Degree in Computer Engineering (June 2008) and his Master of Science Degree in Computer Systems and Networks (June 2010), both from the Department of Special Purpose Computer Systems at National Technical University of Ukraine "Kyiv Polytechnic Institute", Kyiv, Ukraine and the PhD degree in Computer Systems and Components in February 2018 from the Computer Systems Software Department at the National Technical University "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine. He is currently an Associate Professor in the Computer Systems Software Department at National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

His main research interests are Finite Field Arithmetic, Public Key Cryptography, Elliptic Curve Cryptography, Computer Security, Network Security and Hardware Algorithms for Cryptography. Mykola Onai has authored and co-authored more than 55 scientific publications, 8 copyright certificates and is inventor of 4 patents.

Author Articles
Method of Performing Operations on the Elements of GF(2m) Using a Sparse Table

By Ivan Dychka Mykola Onai Andrii Severin Cennuo Hu

DOI:, Pub. Date: 8 Feb. 2024

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.

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Blind Payment Protocol for Payment Channel Networks

By Zhengbing Hu I.A. Dychka Mykola Onai Yuri Zhykin

DOI:, Pub. Date: 8 Jun. 2019

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.

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Non-Linear Model of the Damping Process in a System with a two-mass Pendulum Absorber

By Zhengbing Hu Viktor Legeza Ivan Dychka Mykola Onai

DOI:, Pub. Date: 8 Jan. 2019

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.

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Improved Method of López-Dahab-Montgomery Scalar Point Multiplication in Binary Elliptic Curve Cryptography

By Zhengbing Hu Ivan Dychka Mykola Onai Mykhailo Ivashchenko Su Jun

DOI:, Pub. Date: 8 Dec. 2018

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.

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