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Since the discovery of the Shor quantum algorithm, capable of solving factorization and discrete logarithm problems in polynomial time, post-quantum cryptographic algorithms have been actively developed. Although some of the post-quantum algorithms have already been standardized by NIST, an important problem remains their lower efficiency compared to the classical cryptographic algorithms. The purpose of this work is to accelerate operations on polynomials in lattice-based post-quantum signature schemes. The research is carried out by analyzing fast multiplucation and reduction algorithms. The paper considers the Number Theoretic Transform (NTT), K-RED and Montgomery reduction algorithms. The effectiveness of the K-RED algorithm in comparison with the algorithm Montgomery is substantiated. The question of the applicability of the NTT and fast reduction algorithms in the Russian signature scheme «Kryzhovnik» and NIST algorithms Falcon and CRYSTALS-Dilithium is considered. As a result of the research, recommendations for embedding the K-RED algorithm in the reference implementations of the Falcon and CRYSTALS-Dilithium signature schemes are given, as well as the implementation in C of accelerated multiplication using the NTT and the K-RED algorithm. The results of this research can be embedded in the NIST standards FIPS 204 and FIPS 206, as well as adapted for use in other lattice-based signature schemes.

The purpose of the paper is to study the sustainability of technological processes in the aspect of the security of critical information infrastructure (CII). Cybercrime today brings attackers an income (affecting critical information infrastructure objects) of about $1.5 trillion a year, which means that the security of critical information infrastructure is still requiring due attention. Currently, there is no generally accepted approach to conducting such an assessment and its definition remains an urgent problem. It is also important to understand that the stability of technological (including significant, critical) processes does not always ensure their safety (management safety), as well as ensuring safety does not ensure the execution of technological processes. The object of the study is the objects of the CII. The subject of the study is technological processes in the context of threats to information security. The technological process and its stability at CII facilities in the aspect of information security are studied. The analysis of regulatory legal acts (NPA) and scientific publications on the research topic is carried out. The analysis of the NPA of the CII showed that there are serious problems in this area. In order to formulate specific measures of sustainability of indicators, one can use the given sustainability matrix. The paper formulates the requirements for evaluation indicators. Based on the results of the study, it was found that the assessment of the stability of the functioning of objects can be implemented on real significant objects of the CII, while the stability coefficients of the elements can be detailed in more detail. Definitions and problems are considered, the main sources confirming the importance of the study are presented. The results of the study can be used when considering approaches to assessing the sustainability of technological processes in the context of CII safety.

The purpose of the paper is to consider the sustainability of the functioning of critical information infrastructure (CII) facilities. The states should ensure proper protection of their significant (if any) CII facilities. Significant negative consequences may arise for the subjects of the CII of Russia, critical sectors of the economy that have hundreds or even thousands of CII objects in their composition. As a result, this may lead to disruption of technological processes at a significant CII object. In order to ensure the stable operation of an object classified as a CII, it is required to perform an assessment of its (sustainable) functioning. Evaluation of the effectiveness of the applied measures to ensure the safety of significant objects (ZO) of the CII requires an assessment of the stability of their functioning, which is inherently determined by the stability of their critical processes. However, currently there is no generally accepted approach to conducting such an assessment and its definition is an urgent task. The objects of the research are the CII objects. The subject of the study is the sustainability of the functioning of data (CII) objects in the conditions of threats to information security (IS). The stability of CII objects are examined. The analysis of regulatory legal acts (NPA) and scientific publications on the research topic is carried out. This analysis of the NPA of the CII showed that there are problems in this area, therefore, the approach to ensuring the safety and stability of the functioning of both the CII and its individual objects should be based on certain principles. The main definitions and problems are discussed, the arguments confirming the importance of the study are provided. The results of the study can be used when considering approaches to assessing the functioning of CII facilities and improving the assessment of its stability.

The paper demonstrates a need to study the functional reliability of identification systems and the applicability of methods for ensuring the functional reliability of information systems for biometric identification systems. Methods of ensuring functional reliability of biometric identification systems via providing indicators of reliability of identification devices and introducing redundancy are considered. The applicability of the methods for biometric identification systems is investigated, its advantages and disadvantages are evaluated. Triple modular redundancy scheme has been developed for the program redundancy using N-version programming. An appropriate reliability scheme based on the principles of dual programming has been developed to implement the identification system with one additional redundant element. Based on the NIST statistics of face recognition algorithms for the developed reliability schemes the reliability indicators were evaluated and its advantages over a system consisting of a single non-redundant element have been shown. The proposed reliability schemes are consistent with the practice of ensuring the functional reliability of information systems and can be integrated into biometric identification systems that use biometric data as the main access identifier.

Currently, there is a tendency to use the hardware means of information protection in extreme operating conditions, in particular, in the presence of powerful radiation. In this regard, the problem of assessing the stability of the hardware means of information protection operation is being updated, which is determined by the radiation resistance of the large digital integrated circuits (LSI) that make up them. Methods for ensuring information security in the form of static and dynamic characteristics, which are based on the use of functional-logical modeling of large digital integrated circuits (LSI) under the influence of ionizing radiation, are considered. It is shown that in some cases, information security is characterized by deterministic and non-deterministic failures when exposed to ionizing radiation. Methods for predicting the information security of LSI under the influence of ionizing radiation are proposed, which are based on models of fuzzy digital and probabilistic reliability automata. In the first case, the behavior of complex devices is determined by the specific ratio of radiation-sensitive parameters of the elements, in the second case by the statistical spread of switching moments leading to changes in the logic of the same type of sample. Moreover, the nature of their changes during irradiation depends on many factors, including the type of radiation, its intensity and spectrum, the type of criterion parameter that characterizes the radiation resistance of the LSI, and the mode of operation of the microcircuits.Conducting such a comparison is a necessary step for an adequate assessment of the radiation resistance of the LSI, which allows us to develop a procedure for analyzing the resistance of digital devices.

The study is devoted to the accuracy of information security risk assessment. The paper substantiates the relevance of risk assessment, based on the consequences of their implementation for business and the probability of their occurrence. The method of qualitative assessment of information security risks (the method of expert assessment) is analysed on a specific example. The application of cluster analysis methods is justified. In detail, the examples show the use of cluster analysis methods: the nearest neighbor method; the remote neighbor method; the k-means method. The principal disadvantages of the first two methods are: the appearance of large clusters that do not have similarities; the lack of the ability of experts to set the desired number of clusters in advance. The application of the k-means method is justified - the ability of experts to set the desired number of clusters in advance by setting the initial centers. The results obtained with the usual qualitative assessment are compared with the results obtained by the methods of cluster analysis. The expediency of using cluster analysis methods to improve the accuracy of information security risk assessment is justified.

In order to formalize the mathematical formulation of the research problem on the justification of programs for the modernization of automated security systems, their composition, structure, and main tactical and technical characteristics were analyzed. Modern security systems for stationary remote objects of increased security are complex automated systems that include several subsystems functionally completed and integrated into a single complex and security forces on duty. Analysis of the structural diagram of typical automated security systems for stationary remote objects of increased security showed that in the general case applied to the considered task of existing security systems, it is advisable to use a decomposition into subsystems as a method of the system analysis. By using the subsystems of automated security systems, perimeter and local security zones are formed. Each of the subsystems and its constituent parts in the process of functioning perform one or more functions assigned to the security system as a whole. The results of the analysis show that the existing automated security systems do not fully comply with the requirements of the guidance documents, thus indicating possible directions for their modernization, including the use of technical detection equipment operating on different physical principles of operation, television surveillance equipment and means of transport (transportation) prohibited materials. Moreover, partial modernization is possible in the form of replacing one of the two technical means of detection with more advanced ones. The results of the study showed that the main characteristics of automated security systems that determine their quality are integral indicators: efficiency; reliability; stability of functioning; the cost of creating and operating automated security systems. The combination of several integral indicators into one complex indicator was carried out using the procedures for their special logical-weight processing foreseen by the prioritization method. Taking into account the analysis of the composition, structure of construction and the main tactical and technical characteristics of automated security systems, a mathematical formulation of the research problem can be formulated in further studies.

The issues related to the security of significant objects of critical information infrastructure are considered. The relevance of these problems is primarily due to the fact that the number of cyberattacks on various sectors of the Russian economy and primarily on significant objects of critical information infrastructure (state, defense, oil and gas industry, etc.) is increasing. Unfortunately, the limited access to the available information in this area does not allow today the researchers in the field of information security to conduct a proper analysis. In addition the corresponding media and Internet resources are incomplete. The tasks of ensuring the security of significant objects of critical information infrastructure in order to ensure their sustainable functioning under the destructive impact of computer attacks are regulated by a number of fundamental normative legal acts, primarily the Federal law No. 187-FZ "on security of critical information infrastructure of the Russian Federation" (2017) and the Doctrine of information security of the Russian Federation (2016). Currently at the stage of formation of the digital economy the creation of national information resources and the protection of significant objects of critical information infrastructure is one of the major sources of economic, political, social and military power of the state, the basis of socio-economic and socio-political development of the Russian Federation. The subject of the study is significant objects of critical information infrastructure as the basis of stability and existence of the state, the Russian Federation. The work pays considerable attention to the requirements for structural units to ensure the security of significant objects of critical information infrastructure. Thus, the risk of computer attacks for the subjects of critical information infrastructure has serious consequences, ranging from damage to the reputation and to the paralyzation of enterprise with the subsequent disruption of defense orders for the army and Navy. The requirements to structural units of security of significant objects of critical information infrastructure as well as to their staffing are considered.

With the rapid growth of the multimedia technology, copyright protection has become a very important issue, especially for images. The advantages of easy photo distribution are discarded by their possible theft and unauthorized usage on different websites. Therefore, there is a need in securing information with technical methods, for example digital watermarks. This paper reviews digital watermark embedding methods for image copyright protection, advantages and disadvantages of digital watermark usage are produced. Different watermarking algorithms are analyzed. Based on analysis results most effective algorithm is chosen – differential energy watermarking. It is noticed that the method excels at providing image integrity. Digital watermark embedding system should prevent illegal access to the digital watermark and its container. Requirements for digital watermark are produced. Possible image attacks are reviewed. Modern modifications of embedding algorithms are studied. Robustness of the differential energy watermark is investigated. Robustness is a special value, which formulae is given further in the article. DEW method modification is proposed, it’s advantages over original algorithm are described. Digital watermark serves as an additional layer of defense which is in most cases unknown to the violator. Scope of studied image attacks includes compression, filtration, scaling. In conclusion, it’s possible to use DEW watermarking in copyright protection, violator can easily be detected if images with embedded information are exchanged.