№ 1 (47)

Paper presents our standpoint on the main stages of the cellular automata theory formation, based on our many years of research in this eld. Along with English-speaking authors, the results of Soviet and Russian authors are presented, who made a fairly signi cant contribution to the theory of cellular automata, emphasizing a rather essential contribution of domestic researchers in this direction. Finally, our standpoint is presented on the place of the problematics of cellular automata in the system of modern natural science.
Keywords: cellular automata, homogeneous structures, modelling, parallel processing, reversibility, automata theory, computing models.

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Purpose of work is the development of a new approach to designing post-quantum digital signature algorithms that are free from the shortcomings of known analogs - large sizes of the signature and public key.Research method is the use of power vector equations with multiple occurrences of the signature S as a signature veri cation equation. The computational dif culty of solving equations of the said type relatively the unknown value of S ensures the resistance of the signature scheme to attacks using S as a tting parameter. The possibility of calculating the value of S by the secret key is provided by using the public key in the form of a set of secret elements of the hidden group, masked by performing left and right multiplications by matched invertible vectors.Results of the study include a new proposed concept for the development of post-quantum digital signature algorithms on non-commutative algebras, which use a hidden commutative group. One of its main differences is the use of a secret key in the form of a set of vectors, the knowledge of which makes it possible to calculate the correct signature value for the random powers present in the veri cation equation. The form of the latter de nes a system of quadratic vector equations connecting the public key with the secret, which is reduced to a system of many quadratic equations with many unknowns, given over a nite eld. The computational dif culty of nding a solution to the latter system determines the security of the algorithms developed within the framework of the proposed concept. A quantum computer is ineffective for solving this problem, therefore, the said algorithms are post-quantum. As analogs in construction, digital signature algorithms based on the computational dif culty of the hidden discrete logarithm problem are considered, however, the use of a hidden group and exponentiation operations represent only a general technique for ensuring the correctness of the signature schemes developed within the framework of the concept, and not for specifying a basic computationally dif cult problem. To improve the performance of the signature generation and veri cations procedures, the four-dimensional algebras de ned by sparse basis vector multiplication tables are used as an algebraic support. The proposed concept is con rmed by the development of a speci c post-quantum algorithm that provides a signi cant reduction in the size of the public key and signature in comparison with the nalists of the NIST global competition in the nomination of post-quantum digital signature algorithms.Practical relevance: The developed new concept for constructing post-quantum digital signature algorithms expands the areas of their application in conditions of limited computing resources.
Keywords: finite non-commutative algebra; associative algebra; computationally difficult problem; discrete logarithm; hidden commutative group; digital signature; multivariate cryptography; post-quantum cryptography.

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Keywords: digital information, Information space, Cyberspace, Digital technology, Cyber threats, Cyber-Physical Systems (CPS).

The purpose of the article is an analytical review of the application of cellular automata and their generalizations in cryptography.Research method: an analysis of scienti c publications on the topic of the article.Results: The review article analyzes the literature devoted to the use of cellular automata and their generalizations for the construction of cryptographic algorithms. The article consists of two parts.The rst part was devoted to classical cellular automata and symmetric cryptographic algorithms based on them. It brie y discussed the history of the theory of cellular automata and its application in various scienti c elds. A review of the works of a number of authors who proposed symmetric cryptographic algorithms and pseudorandom sequence generators based on one-dimensional cellular automata was presented. The security of such cryptographic algorithms turned out to be insuf cient. The following was a review of articles devoted to the use of two-dimensional cellular automata for constructing ciphers (this approach gave the best results). Multidimensional cellular automata were also mentioned.This second part of the article is devoted to a review of works devoted to the use of generalized cellular automata in cryptography - on the basis of such automata, it is possible to create symmetric encryption algorithms and cryptographic hash functions that provide a high level of security and high performance in hardware implementation (for example, on FPGA), as well as having fairly low requirements for hardware resources. In addition, an attention is paid to interesting connections of generalized cellular automata, in the context of their use in cryptography, with the theory of expander graphs. Attention is also paid to the security of cryptographic algorithms based on generalized cellular automata. The works devoted to the implementation of various cryptographic algorithms based on generalized cellular automata on FPGA and GPU are mentioned. In addition, an overview of asymmetric cryptoalgorithms based on cellular automata is given. The questions about the belonging of some problems on cellular automata and their generalizations to the class of NP-complete problems, as well as to some other complexity classes, are also considered.
Keywords: cellular automation, generalized cellular automation, stream cipher, block cipher, hash function, Ramanujan graph, public-key cryptography.

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The purpose of the study: to identify the main systems that control cyberspace and the key elements whose management will allow controlling a given segment of cyberspace.Research method: theory of complex systems; synergetic.Result: The paper considers the main control systems that play a key role in the management of cyberspace, highlights the structural elements of cyberspace and their interrelations with each other. Regional and local Internet registrars are considered, their coherence graph is presented, as well as the coherence graph by country. Based on the study, the author's vision of the organizational structure of the cyberspace management system (in relation to domain names and IP addresses). Autonomous systems and traf c exchange points are considered, the structure of external connectivity of autonomous systems and its change over time are given on examples. The largest telecommunication alliances are presented, which have an impact on the activities of telecom operators (directly or indirectly) and, as a result, on the set of resources and services (as well as their cost) received by end users provided by telecommunication operators.Scienti c novelty: the considered structure of the cyberspace management system made it possible to identify the main systems that control cyberspace and the key elements whose management will allow controlling a given segment of cyberspace.
Keywords: cyberspace, autonomous system, management, Internet registrars, traffic exchange point, telecommunication alliances, connectivity graph, ICANN.

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Purpose of the article: to increase fault tolerance, security level and simplify the process of updating systems using a micro service architecture using virtualization tools.Method: Using microkernel virtualization tools called Unikernel images. Unikernel are virtual machine images containing a single application. Each micro service of the system runs in the Unikernel image, the processes and services used are not contained in the image.The result: a de nition of Unikernel is given; a comparison is made with existing virtualization systems. The mechanisms that implement the Unikernel technology are listed. The de nitions of the library operating system and microkernel are given. The de nition of Unikernel is given as a technology that combines library operating systems and microkernels. The main advantages of using Unikernel are listed: ensuring the security of information systems and ease of updates. A developed software tool for testing Unikernel images for the possibility of penetrating an information system in the event of a vulnerability of the “remote execution of arbitrary code” type in the software tool. The image was tested. In conclusion, the assessment of the effectiveness of the use of Unikernel technology for building systems with a micro service architecture, in particular for building SIEM systems.
Keywords: Unikernel, virtualization, operating systems, cloud computing, security, vulnerability, SIEM.

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Purpose of the article: to increase fault tolerance, security level and simplify the process of updating systems using a micro service architecture using virtualization tools.Method: Using microkernel virtualization tools called Unikernel images. Unikernel are virtual machine images containing a single application. Each micro service of the system runs in the Unikernel image, the processes and services used are not contained in the image.The result: a de nition of Unikernel is given; a comparison is made with existing virtualization systems. The mechanisms that implement the Unikernel technology are listed. The de nitions of the library operating system and microkernel are given. The de nition of Unikernel is given as a technology that combines library operating systems and microkernels. The main advantages of using Unikernel are listed: ensuring the security of information systems and ease of updates. A developed software tool for testing Unikernel images for the possibility of penetrating an information system in the event of a vulnerability of the “remote execution of arbitrary code” type in the software tool. The image was tested. In conclusion, the assessment of the effectiveness of the use of Unikernel technology for building systems with a micro service architecture, in particular for building SIEM systems.
Keywords: Unikernel, virtualization, operating systems, cloud computing, security, vulnerability, SIEM.

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