Alexandr Kuznetsov - Academia.edu (original) (raw)

Papers by Alexandr Kuznetsov

Radiotekhnika

Cryptographic transformations with a secret key play an essential role in providing information a... more Cryptographic transformations with a secret key play an essential role in providing information and cyber security. Block and stream symmetric ciphers are used in various applications both as a separate cryptographic protection mechanism and as part of other applications (pseudo-random sequence generators, hashing algorithms, electronic signature protocols, etc.). Therefore, the design and study of individual components of symmetric ciphers is a relevant and important scientific task. In this paper we consider and investigates iterative algorithms for generating non-linear substitutions (substitutions, S-boxes), which are used in modern block and stream encryption algorithms with a symmetric key. Cryptographic resistance of symmetric ciphers to statistical, differential, linear and other methods of cryptanalysis is provided by the properties of substitutions. In addition, S-boxes must be random from the point of view of the possibility to use algebraic cryptanalysis. Therefore, the ...

Radiotekhnika

To ensure the security of information technology, cryptographic information protection tools are ... more To ensure the security of information technology, cryptographic information protection tools are used, in particular block and stream encryption algorithms with a symmetric key. Reliability and cryptographic strength of cryptoalgorithms is provided by the properties of the applied primitives. For example, non-linear substitutions (S-boxes) are used as the main component of modern symmetric ciphers. Therefore, generation of substitutions is an important scientific task directly related to the security of information technology and improvement of modern symmetric ciphers. The paper investigates the properties of iterative algorithms for generating non-linear substitutions and special cost functions, which play a decisive role in the heuristic search for S-boxes with the required properties. We consider the cost function of the WCF (Cost Function of the content of the Walsh-Hadamard spectrum) and optimize its parameters. The obtained optimization results in combination with the Hill Cl...

Computer Modeling and Intelligent Systems

In this article are discussed techniques of hiding information messages in cover image using dire... more In this article are discussed techniques of hiding information messages in cover image using direct spectrum spreading technology. This technology is based on the use of poorly correlated pseudorandom (noise) sequences. Modulating the information data with such signals, the message is presented as a noise-like form, which makes it very difficult to detect. Hiding means adding a modulated message to the cover image. If this image is interpreted as noise on the communication channel, then the task of hiding user's data is equivalent to transmitting a noise-like modulated message on the noise communication channel. At the same it is supposed that noise-like signals are poorly correlated both with each other and with the cover image (or its fragment). However, the latter assumption may not be fulfilled because a realistic image is not an implementation of a random process; its pixels have a strong correlation. Obviously, the selection of pseudo-random spreading signals must take this feature into account. We are investigating various ways of formation spreading sequences while assessing Bit Error Rate (BER) of information data as well as cover image distortion by mean squared error (MSE) and by Peak signal-to-noise ratio (PSNR). The purpose of our work is to justify the choice of extending sequences to reduce BER and MSE (increase PSNR).

Computer Modeling and Intelligent Systems

The methods of synthesis of discrete signals are analyzed with the special cross-correlation prop... more The methods of synthesis of discrete signals are analyzed with the special cross-correlation properties: m-sequences, signals of Legendre, Barker, Paley-Plotkin, Gold, small and large set of Kasami. Comparative researches of properties of the formed discrete signals are conducted. Separate direction develops in development of methods of forming of discrete signals, that is based on the use of algebraic and structural properties of circular shifts of group codes. It is shown that offered approach allows forming the great numbers of discrete sequences, ensemble and cross-correlation properties of that are set by the properties of the corresponding group controlled from distance, structural and cyclic.

Computer Modeling and Intelligent Systems

Electronic trust services are becoming an integral part of the information space. With the reliab... more Electronic trust services are becoming an integral part of the information space. With the reliable implementation of basic services as an electronic signature and electronic authentication, it is possible to build more complex systems that rely on them, particularly the electronic voting system. In the paper, the new concept for developing a decentralized electronic voting system using blockchain technology is proposed. The two-level architecture provides a secure voting process without redundancy of existing (not based on blockchain) systems. The presented blockchain-based voting protocol has six steps that ensure all requirements that are put forward to such types of protocols including voting transparency and anonymity.

Радиотехника, Sep 24, 2021

Radiotekhnika, 2021

Nonlinear substitutions (S-boxes) are used in most modern symmetric cryptoalgorithms. They are de... more Nonlinear substitutions (S-boxes) are used in most modern symmetric cryptoalgorithms. They are designed to mix input data and play a significant role in ensuring resistance against known cryptanalytic attacks (differential, linear, algebraic and other cryptanalysis methods). However, random generation of nonlinear substitutions with the desired indicators is an extremely difficult mathematical problem. This article explores the heuristic techniques for S-boxes informed search, in particular, discusses various cost functions used in most of the known algorithms (for example, local search, hill climbing, simulated annealing, genetic search, etc.). The aim of the study is to determine the specific parameters of heuristic functions, which, on the one hand, do not reduce the degree of awareness of the search nodes, and on the other hand, do not require significant computational costs. The article examines the influence of individual parameters on the value of the cost function and comple...

2020 IEEE International Conference on Problems of Infocommunications. Science and Technology (PIC S&T), 2020

This article is devoted to code-based cryptosystems. They provide high security level even in the... more This article is devoted to code-based cryptosystems. They provide high security level even in the conditions of quantum cryptographic analysis. A new improved code-based electronic signature scheme is proposed in this article. Due to the improved decoding scheme, we are able to significantly reduce the signature generation time. Also, quantitative estimates of the speed of the new cryptoalgorithm are provided. Practical studies have shown that the use of the proposed decoder can significantly reduce the number of attempts required to decode the syndrome, and, consequently, reduce the time required by the digital signature algorithm. Due to the fact that additional calculation of additional syndromes and re-decoding requires fewer calculations than increasing the value of the counter and performing all steps from hashing values to decoding again.

Radiotekhnika, 2021

Nonlinear substitutions (S-boxes) are an important component of modern symmetric cryptography alg... more Nonlinear substitutions (S-boxes) are an important component of modern symmetric cryptography algorithms. They complicate symmetric transformations and introduce nonlinearity into the input-output relationship, which ensures the stability of the algorithms against some cryptanalysis methods. Generation of S-boxes can be done in different ways. However, heuristic techniques are the most promising ones. On the one hand, the generated S-boxes are in the form of random substitutions, which complicates algebraic cryptanalysis. On the other hand, heuristic search allows one to achieve high rates of nonlinearity and δ-uniformity, which complicates linear and differential cryptanalysis. This article studies the simplest local search algorithm for generating S-boxes. To assess the efficiency of the algorithm, the concept of a track of a cost function is introduced in the article. Numerous experiments are carried out, in particular, the influence of the number of internal and external loops o...

Advances in Intelligent Systems and Computing, 2018

The article analyzes the most well-known practical methods of determining the alternative set (AS... more The article analyzes the most well-known practical methods of determining the alternative set (AS) of numbers in a residue numeral system (RNS). The AS determining is most frequently required to perform error verification, diagnosing and correction of data in RNS, that was introduced to a minimal information redundancy in the computational process dynamics. This suggests the occurrence of only a single error in a number. The main downside of the reviewed methods is a significant time needed to determine the AS. In order to reduce time for AS determining in RNS, one of the known methods has been improved in the article. The idea of method improvement supposes preliminary correspondence table compilation (first stage tables) for each correct number out of informational numeric range of a possible set of incorrect numbers, that are not included into the range. Based on the analysis of tables content, the second stage table is being compiled, which contains the correspondence of each incorrect number out of numeric range to a possible values of correct numbers. By applying introduced method, efficiency of data verification, diagnosing and correction is increased due to time reduction of the AS numbers determining in RNS.

The purpose of this article is to consider an algorithm for synthesizing the structure of the add... more The purpose of this article is to consider an algorithm for synthesizing the structure of the adder of two residuals i a and i b numbers 1 2 ( , ,..., ,..., ) i k A a a a a  and 1 2 ( , ,..., ,..., ) i k B b b b b  for an arbitrary value of the module i m of the residual class system (RCS), by organizing interbit connections between binary one-bit adders (BOA), the combination of which makes up the structure of modulo adder. The algorithm for the synthesis of adders by arbitrary modules is based on the usage of existing adders by module 2 1 n M   , which consists of a set of sequentially located BOA, by introducing and using additional inter-bit connections of the form i j    . Specific examples of the synthesis of structures of binary adders for various values of the RCS modules i m are given.

In this work, a new direction of technical steganography related to the concealment of informatio... more In this work, a new direction of technical steganography related to the concealment of information in the process of layer-by-layer creation (cultivation) of a solid-state object using various 3D-printing technologies was investigated. Information data is converted into a digital 3D-model of elementary physical objects that are placed inside this 3D-model of the container product. After printing, a solid object physically contains the hidden information that cannot be deleted or distorted without damaging the container product. In addition, the applied methods do not reduce the operational, aesthetic and any other properties of the finished product. The proposed complex is invariant to the method of layer-by-layer growing, that is, it can be equipped with any peripheral devices of 3D-printing of various manufacturers with any materials and principles of layer-by-layer creation.

The results of studies of the properties of random permutations carried out with the participatio... more The results of studies of the properties of random permutations carried out with the participation of the authors are generalized. It is shown that random substitutions overwhelmingly have good cryptographic, and in particular, algebraic properties. The prospects of using random S-blocks to build block symmetric ciphers with improved dynamic rates of arrival to random substitution are substantiated. A refined model of random substitution and the corresponding criteria are proposed, with the help of which one can verify the suitability of substitutions generated randomly for use in modern cipher designs. It is a check, since with a very high probability the checked substitutions will be suitable.

The theoretical questions of derivative orthogonal discrete signa©ls large ensemble synthesis is ... more The theoretical questions of derivative orthogonal discrete signa©ls large ensemble synthesis is examined in this article. These signals possess the advanced correlation ensemble and structural properties. The practical application of the synthesized signals allows decreasing the probability of error in the communication and management network, and promoting their carrying capacity. It is shown, that the forming consequences possess the advanced ensemble and correlation properties among the well-known ones that allow increasing the quality of the data transfer in the space communication and management network.

International Journal of Computing, 2019

This paper presents the results of the comparative analysis of safety statistics and performance ... more This paper presents the results of the comparative analysis of safety statistics and performance of encryption, the Strumok stream symmetric cipher (proposed for the national encryption standard of Ukraine) with other known cryptographic transformation algorithms, such as SALSA20, SNOW2.0, HC, AES with usages in stream mode, etc. They are accepted as national, international standards or are presented by the New European Schemes for Signatures, Integrity, and Encryptions (NESSI), Cryptography Research and Evaluation Committees (CRYPTREC) and others. The result of safety statistics is an analysis of the cryptographic properties of the output sequences using statistical test sets developed by the National Institute of Standards and Technology (NIST STS) and the DIEHARD tests. The result of the study of performance is the evaluation of the use of central processing unit (CPU) time to convert one octet of data to 64-bit computing platforms, following the test profile used in the eSTREAM ...

SN Computer Science, 2021

This paper presents the research results of mixed base number systems using binomial representati... more This paper presents the research results of mixed base number systems using binomial representation of numbers. It also shows the investigated non-linear coding techniques with full constant-weight codes, which are based on the binomial numeration. These codes can be used in a variety of computer applications: in code-based cryptosystems; to detect errors in asymmetric communication channels, etc. We propose a new numeral system. It combines the features of positional and binomial numeration. We suggest a technique of full non-binary constant-weight coding based on a generalized binomialpositional representation. It allows us to generalize the known approach to the non-binary case and practically implement computational algorithms for generating full set of non-binary constant-weight sequences. There are the analytical relations that relate the positional and binomial representations of numbers. The article provides several examples, which clear up the usefulness and the constructiveness of the proposed approach, and simplify the perception and understanding of results. We also consider some aspects of the potential use of the proposed numeral system. In particular, the article discusses asymmetric communication channels (the model of a binary Z-channel and its generalization to the non-binary model), and shows the advantage of constant-weight codes for error detection.

Radiotekhnika, 2021

This article discusses noise-like discrete signals (pseudo-random sequences) for asynchronous cod... more This article discusses noise-like discrete signals (pseudo-random sequences) for asynchronous code division systems for radio channels. Asynchrony implies the use of sequences that are statistically uncorrelated for an arbitrary cyclically shifted copy of the signals, i.e. their cross-correlation coefficient for arbitrarily chosen starting points is close to zero. The fundamental theoretical limit for this characteristic is the well-known Welch boundary. In this paper, we compare the correlation properties of various sets (Gold codes, Kasami sequences, etc.) with this fundamental limit. The parameters of different codes are estimated, the corresponding bound is shown and compared with the real correlation characteristics of the codes. For the approximation, the Laurent series expansion and the Puiseau series were used. The asymptotic properties were also estimated. The paper also considers new ensembles of noise-like discrete signals for asynchronous systems. These codes are statist...

Acta Polytechnica, 2020

This article explores a mathematical model of a data transmission channel with errors grouping. W... more This article explores a mathematical model of a data transmission channel with errors grouping. We propose an estimating method for energy gain from coding and energy efficiency of binary codes in channels with grouped errors. The proposed method uses a simplified Bennet and Froelich's model and allows leading the research of the energy gain from coding for a wide class of data channels without restricting the way of the length distributing the error bursts. The reliability of the obtained results is confirmed by the information of the known results in the theory of error-correcting coding in the simplified variant.

2009 Sixth International Conference on Information Technology: New Generations, 2009

With cryptographic investigations, the design of Boolean functions is a wide area. The Boolean fu... more With cryptographic investigations, the design of Boolean functions is a wide area. The Boolean functions play important role in the construction of a symmetric cryptosystem. In this paper the modified hill climbing method is considered. The method allows using hill climbing techniques to modify bent functions used to design balanced, highly nonlinear Boolean functions with high algebraic degree and low autocorrelation. The experimental results of constructing the cryptographically strong Boolean functions are presented.

This paper describes the system parameters and software implementation of a HECDSA cryptosystem b... more This paper describes the system parameters and software implementation of a HECDSA cryptosystem based on genus-2 hyperelliptic curves over prime fields. We show how to reduce the computational complexity for special cases and compare the given cryptosystem with the well-known ECDSA cryptosystem based on elliptic curves.

Radiotekhnika

Cryptographic transformations with a secret key play an essential role in providing information a... more Cryptographic transformations with a secret key play an essential role in providing information and cyber security. Block and stream symmetric ciphers are used in various applications both as a separate cryptographic protection mechanism and as part of other applications (pseudo-random sequence generators, hashing algorithms, electronic signature protocols, etc.). Therefore, the design and study of individual components of symmetric ciphers is a relevant and important scientific task. In this paper we consider and investigates iterative algorithms for generating non-linear substitutions (substitutions, S-boxes), which are used in modern block and stream encryption algorithms with a symmetric key. Cryptographic resistance of symmetric ciphers to statistical, differential, linear and other methods of cryptanalysis is provided by the properties of substitutions. In addition, S-boxes must be random from the point of view of the possibility to use algebraic cryptanalysis. Therefore, the ...

Radiotekhnika

To ensure the security of information technology, cryptographic information protection tools are ... more To ensure the security of information technology, cryptographic information protection tools are used, in particular block and stream encryption algorithms with a symmetric key. Reliability and cryptographic strength of cryptoalgorithms is provided by the properties of the applied primitives. For example, non-linear substitutions (S-boxes) are used as the main component of modern symmetric ciphers. Therefore, generation of substitutions is an important scientific task directly related to the security of information technology and improvement of modern symmetric ciphers. The paper investigates the properties of iterative algorithms for generating non-linear substitutions and special cost functions, which play a decisive role in the heuristic search for S-boxes with the required properties. We consider the cost function of the WCF (Cost Function of the content of the Walsh-Hadamard spectrum) and optimize its parameters. The obtained optimization results in combination with the Hill Cl...

Computer Modeling and Intelligent Systems

In this article are discussed techniques of hiding information messages in cover image using dire... more In this article are discussed techniques of hiding information messages in cover image using direct spectrum spreading technology. This technology is based on the use of poorly correlated pseudorandom (noise) sequences. Modulating the information data with such signals, the message is presented as a noise-like form, which makes it very difficult to detect. Hiding means adding a modulated message to the cover image. If this image is interpreted as noise on the communication channel, then the task of hiding user's data is equivalent to transmitting a noise-like modulated message on the noise communication channel. At the same it is supposed that noise-like signals are poorly correlated both with each other and with the cover image (or its fragment). However, the latter assumption may not be fulfilled because a realistic image is not an implementation of a random process; its pixels have a strong correlation. Obviously, the selection of pseudo-random spreading signals must take this feature into account. We are investigating various ways of formation spreading sequences while assessing Bit Error Rate (BER) of information data as well as cover image distortion by mean squared error (MSE) and by Peak signal-to-noise ratio (PSNR). The purpose of our work is to justify the choice of extending sequences to reduce BER and MSE (increase PSNR).

Computer Modeling and Intelligent Systems

The methods of synthesis of discrete signals are analyzed with the special cross-correlation prop... more The methods of synthesis of discrete signals are analyzed with the special cross-correlation properties: m-sequences, signals of Legendre, Barker, Paley-Plotkin, Gold, small and large set of Kasami. Comparative researches of properties of the formed discrete signals are conducted. Separate direction develops in development of methods of forming of discrete signals, that is based on the use of algebraic and structural properties of circular shifts of group codes. It is shown that offered approach allows forming the great numbers of discrete sequences, ensemble and cross-correlation properties of that are set by the properties of the corresponding group controlled from distance, structural and cyclic.

Computer Modeling and Intelligent Systems

Electronic trust services are becoming an integral part of the information space. With the reliab... more Electronic trust services are becoming an integral part of the information space. With the reliable implementation of basic services as an electronic signature and electronic authentication, it is possible to build more complex systems that rely on them, particularly the electronic voting system. In the paper, the new concept for developing a decentralized electronic voting system using blockchain technology is proposed. The two-level architecture provides a secure voting process without redundancy of existing (not based on blockchain) systems. The presented blockchain-based voting protocol has six steps that ensure all requirements that are put forward to such types of protocols including voting transparency and anonymity.

Радиотехника, Sep 24, 2021

Radiotekhnika, 2021

Nonlinear substitutions (S-boxes) are used in most modern symmetric cryptoalgorithms. They are de... more Nonlinear substitutions (S-boxes) are used in most modern symmetric cryptoalgorithms. They are designed to mix input data and play a significant role in ensuring resistance against known cryptanalytic attacks (differential, linear, algebraic and other cryptanalysis methods). However, random generation of nonlinear substitutions with the desired indicators is an extremely difficult mathematical problem. This article explores the heuristic techniques for S-boxes informed search, in particular, discusses various cost functions used in most of the known algorithms (for example, local search, hill climbing, simulated annealing, genetic search, etc.). The aim of the study is to determine the specific parameters of heuristic functions, which, on the one hand, do not reduce the degree of awareness of the search nodes, and on the other hand, do not require significant computational costs. The article examines the influence of individual parameters on the value of the cost function and comple...

2020 IEEE International Conference on Problems of Infocommunications. Science and Technology (PIC S&T), 2020

This article is devoted to code-based cryptosystems. They provide high security level even in the... more This article is devoted to code-based cryptosystems. They provide high security level even in the conditions of quantum cryptographic analysis. A new improved code-based electronic signature scheme is proposed in this article. Due to the improved decoding scheme, we are able to significantly reduce the signature generation time. Also, quantitative estimates of the speed of the new cryptoalgorithm are provided. Practical studies have shown that the use of the proposed decoder can significantly reduce the number of attempts required to decode the syndrome, and, consequently, reduce the time required by the digital signature algorithm. Due to the fact that additional calculation of additional syndromes and re-decoding requires fewer calculations than increasing the value of the counter and performing all steps from hashing values to decoding again.

Radiotekhnika, 2021

Nonlinear substitutions (S-boxes) are an important component of modern symmetric cryptography alg... more Nonlinear substitutions (S-boxes) are an important component of modern symmetric cryptography algorithms. They complicate symmetric transformations and introduce nonlinearity into the input-output relationship, which ensures the stability of the algorithms against some cryptanalysis methods. Generation of S-boxes can be done in different ways. However, heuristic techniques are the most promising ones. On the one hand, the generated S-boxes are in the form of random substitutions, which complicates algebraic cryptanalysis. On the other hand, heuristic search allows one to achieve high rates of nonlinearity and δ-uniformity, which complicates linear and differential cryptanalysis. This article studies the simplest local search algorithm for generating S-boxes. To assess the efficiency of the algorithm, the concept of a track of a cost function is introduced in the article. Numerous experiments are carried out, in particular, the influence of the number of internal and external loops o...

Advances in Intelligent Systems and Computing, 2018

The article analyzes the most well-known practical methods of determining the alternative set (AS... more The article analyzes the most well-known practical methods of determining the alternative set (AS) of numbers in a residue numeral system (RNS). The AS determining is most frequently required to perform error verification, diagnosing and correction of data in RNS, that was introduced to a minimal information redundancy in the computational process dynamics. This suggests the occurrence of only a single error in a number. The main downside of the reviewed methods is a significant time needed to determine the AS. In order to reduce time for AS determining in RNS, one of the known methods has been improved in the article. The idea of method improvement supposes preliminary correspondence table compilation (first stage tables) for each correct number out of informational numeric range of a possible set of incorrect numbers, that are not included into the range. Based on the analysis of tables content, the second stage table is being compiled, which contains the correspondence of each incorrect number out of numeric range to a possible values of correct numbers. By applying introduced method, efficiency of data verification, diagnosing and correction is increased due to time reduction of the AS numbers determining in RNS.

The purpose of this article is to consider an algorithm for synthesizing the structure of the add... more The purpose of this article is to consider an algorithm for synthesizing the structure of the adder of two residuals i a and i b numbers 1 2 ( , ,..., ,..., ) i k A a a a a  and 1 2 ( , ,..., ,..., ) i k B b b b b  for an arbitrary value of the module i m of the residual class system (RCS), by organizing interbit connections between binary one-bit adders (BOA), the combination of which makes up the structure of modulo adder. The algorithm for the synthesis of adders by arbitrary modules is based on the usage of existing adders by module 2 1 n M   , which consists of a set of sequentially located BOA, by introducing and using additional inter-bit connections of the form i j    . Specific examples of the synthesis of structures of binary adders for various values of the RCS modules i m are given.

In this work, a new direction of technical steganography related to the concealment of informatio... more In this work, a new direction of technical steganography related to the concealment of information in the process of layer-by-layer creation (cultivation) of a solid-state object using various 3D-printing technologies was investigated. Information data is converted into a digital 3D-model of elementary physical objects that are placed inside this 3D-model of the container product. After printing, a solid object physically contains the hidden information that cannot be deleted or distorted without damaging the container product. In addition, the applied methods do not reduce the operational, aesthetic and any other properties of the finished product. The proposed complex is invariant to the method of layer-by-layer growing, that is, it can be equipped with any peripheral devices of 3D-printing of various manufacturers with any materials and principles of layer-by-layer creation.

The results of studies of the properties of random permutations carried out with the participatio... more The results of studies of the properties of random permutations carried out with the participation of the authors are generalized. It is shown that random substitutions overwhelmingly have good cryptographic, and in particular, algebraic properties. The prospects of using random S-blocks to build block symmetric ciphers with improved dynamic rates of arrival to random substitution are substantiated. A refined model of random substitution and the corresponding criteria are proposed, with the help of which one can verify the suitability of substitutions generated randomly for use in modern cipher designs. It is a check, since with a very high probability the checked substitutions will be suitable.

The theoretical questions of derivative orthogonal discrete signa©ls large ensemble synthesis is ... more The theoretical questions of derivative orthogonal discrete signa©ls large ensemble synthesis is examined in this article. These signals possess the advanced correlation ensemble and structural properties. The practical application of the synthesized signals allows decreasing the probability of error in the communication and management network, and promoting their carrying capacity. It is shown, that the forming consequences possess the advanced ensemble and correlation properties among the well-known ones that allow increasing the quality of the data transfer in the space communication and management network.

International Journal of Computing, 2019

This paper presents the results of the comparative analysis of safety statistics and performance ... more This paper presents the results of the comparative analysis of safety statistics and performance of encryption, the Strumok stream symmetric cipher (proposed for the national encryption standard of Ukraine) with other known cryptographic transformation algorithms, such as SALSA20, SNOW2.0, HC, AES with usages in stream mode, etc. They are accepted as national, international standards or are presented by the New European Schemes for Signatures, Integrity, and Encryptions (NESSI), Cryptography Research and Evaluation Committees (CRYPTREC) and others. The result of safety statistics is an analysis of the cryptographic properties of the output sequences using statistical test sets developed by the National Institute of Standards and Technology (NIST STS) and the DIEHARD tests. The result of the study of performance is the evaluation of the use of central processing unit (CPU) time to convert one octet of data to 64-bit computing platforms, following the test profile used in the eSTREAM ...

SN Computer Science, 2021

This paper presents the research results of mixed base number systems using binomial representati... more This paper presents the research results of mixed base number systems using binomial representation of numbers. It also shows the investigated non-linear coding techniques with full constant-weight codes, which are based on the binomial numeration. These codes can be used in a variety of computer applications: in code-based cryptosystems; to detect errors in asymmetric communication channels, etc. We propose a new numeral system. It combines the features of positional and binomial numeration. We suggest a technique of full non-binary constant-weight coding based on a generalized binomialpositional representation. It allows us to generalize the known approach to the non-binary case and practically implement computational algorithms for generating full set of non-binary constant-weight sequences. There are the analytical relations that relate the positional and binomial representations of numbers. The article provides several examples, which clear up the usefulness and the constructiveness of the proposed approach, and simplify the perception and understanding of results. We also consider some aspects of the potential use of the proposed numeral system. In particular, the article discusses asymmetric communication channels (the model of a binary Z-channel and its generalization to the non-binary model), and shows the advantage of constant-weight codes for error detection.

Radiotekhnika, 2021

This article discusses noise-like discrete signals (pseudo-random sequences) for asynchronous cod... more This article discusses noise-like discrete signals (pseudo-random sequences) for asynchronous code division systems for radio channels. Asynchrony implies the use of sequences that are statistically uncorrelated for an arbitrary cyclically shifted copy of the signals, i.e. their cross-correlation coefficient for arbitrarily chosen starting points is close to zero. The fundamental theoretical limit for this characteristic is the well-known Welch boundary. In this paper, we compare the correlation properties of various sets (Gold codes, Kasami sequences, etc.) with this fundamental limit. The parameters of different codes are estimated, the corresponding bound is shown and compared with the real correlation characteristics of the codes. For the approximation, the Laurent series expansion and the Puiseau series were used. The asymptotic properties were also estimated. The paper also considers new ensembles of noise-like discrete signals for asynchronous systems. These codes are statist...

Acta Polytechnica, 2020

This article explores a mathematical model of a data transmission channel with errors grouping. W... more This article explores a mathematical model of a data transmission channel with errors grouping. We propose an estimating method for energy gain from coding and energy efficiency of binary codes in channels with grouped errors. The proposed method uses a simplified Bennet and Froelich's model and allows leading the research of the energy gain from coding for a wide class of data channels without restricting the way of the length distributing the error bursts. The reliability of the obtained results is confirmed by the information of the known results in the theory of error-correcting coding in the simplified variant.

2009 Sixth International Conference on Information Technology: New Generations, 2009

With cryptographic investigations, the design of Boolean functions is a wide area. The Boolean fu... more With cryptographic investigations, the design of Boolean functions is a wide area. The Boolean functions play important role in the construction of a symmetric cryptosystem. In this paper the modified hill climbing method is considered. The method allows using hill climbing techniques to modify bent functions used to design balanced, highly nonlinear Boolean functions with high algebraic degree and low autocorrelation. The experimental results of constructing the cryptographically strong Boolean functions are presented.

This paper describes the system parameters and software implementation of a HECDSA cryptosystem b... more This paper describes the system parameters and software implementation of a HECDSA cryptosystem based on genus-2 hyperelliptic curves over prime fields. We show how to reduce the computational complexity for special cases and compare the given cryptosystem with the well-known ECDSA cryptosystem based on elliptic curves.