Cryptanalysis of the system based on word problems using logarithmic signatures

Rapid development and advances of quantum computers are contributing to the development of public key cryptosystems based on mathematically complex or difficult problems, as the threat of using quantum algorithms to hack modern traditional cryptosystems is becoming much more real every day. It should be noted that the classical mathematically complex problems of factorization of integers and discrete logarithms are no longer considered complex for quantum calculations. Dozens of cryptosystems were considered and proposed on various complex problems of group theory in the 2000s. One of such complex problems is the problem of the word. One of the first implementations of the cryptosystem based on the word problem was proposed by Magliveras using logarithmic signatures for finite permutation groups and further proposed by Lempken et al. for asymmetric cryptography with random covers. The innovation of this idea is to extend the difficult problem of the word to a large number of groups. The article summarizes the known results of cryptanalysis of the basic structures of the cryptosystem and defines recommendations for ways to improve the cryptographic properties of structures and the use of non-commutative groups as basic structures.

Method for dealing with non-stationary natural and simulating interference in intellectual surveillance radars

The article discusses a method for dealing with non-stationary natural and simulating interference in intelligent surveillance radars. When creating simulating marks, the introduction of amplitude modulation into the relayed radar sounding signal is used. As a result of the analysis, it was possible to find out that in the imitating noise, in this case, the so-called "intelligent" fluctuations of the burst structure of false marks appear, which differ from the fluctuations of the packs of real marks and can be easily detected by a human operator. The method is based on the definition of semantic components at the stage of formation and analysis of a symbolic model of amplitude fluctuations of a burst of signals from non-stationary natural and simulating interference and from real moving objects. In this case, the semantic features of amplitude fluctuations are determined by solving predicate equations for transforming these fluctuations into symbolic images of noise marks and real mobile aircraft. As a result of semantic analysis of the amplitude fluctuations of the burst in the time domain, classification distinctive features of fluctuations in the burst of signals from natural imitating noise and air objects were obtained. The semantic components of the decision-making algorithm are investigated, which are similar to the decision-making algorithms by a human operator. Process knowledge of transforming radar signals into symbolic images of amplitude fluctuations of a burst in the time domain is formalized. The formalization of the processing of symbolic images includes a system of predicate equations, by solving which the types of amplitude fluctuations of the burst are identified. Based on the results of experimental data, the transformations of real radar signals into symbolic images of burst fluctuations were carried out on the basis of the algebra of finite predicates. The authors also managed to propose these transformations to be used as the basis of an effective toolkit for obtaining classification distinctive features of packet fluctuations from interference and from aircraft.

Measurement of software quality based on international standards

Quality is one of the factors that ensure the commercial success and safety of using the software. Quality is understood as conformity the explicit and implicit requirements of various stakeholders. It is necessary to ensure a joint understanding between developers and users, engineers need to understand the meaning of the concept of quality, characteristics and importance of quality for the developed or maintained software. Measurements are the basis for quality assurance. They are the main tool for managing the life cycle of software products, assessing the implementation of plans and monitoring. To quantify quality, it is necessary to measure the characteristics of the software. Standardization provides unification of requirements for quality, its measurement and assessment. The use of standards has many potential benefits for any organization, especially in key areas such as measuring the quality of software products, information and measurement systems. Recognized international standards organizations have published the ISO/IEC 25000 series of standards for systems and software quality requirements and evaluation (SQuaRE), which is gaining widespread practical application. The paper discusses a series of the SQuaRE international standards, analyzes the relationship between the quality model, quality characteristics, quality measures and a new concept, i.e., a quality measure element of the software, presents the measurement of quality based on these standards.

Investigation of the computational complexity of methods for hiding information in cluster steganosystems

Several methods of technical steganography are currently known. Hiding information in a model in 3D printing, this industry of hiding information has certain advantages and disadvantages, namely: the relatively high cost of creating a hidden message and the difficulty in reading the information. The second area of technical steganography is related to network traffic. In this method, information can be hidden, for example, in the header fields of protocols, or, for example, the transmission of a hidden message by sending packets in a certain sequence. There are also methods of hiding information in the structure of the file system, but the known methods are either capable of hiding a small amount of information, or have an insufficient level of resistance to detection. Thus, an urgent task is to develop a method for hiding information, which is able to hide more information and has a higher level of resistance to detection, with a satisfactory level of computational complexity. This paper presents methods of technical steganography based on the structural features of file systems in storage media, in particular, hiding information in the FAT file system by mixing clusters of certain key files (cover files). Methods of hiding information in the structure of a clustered file system by mixing clusters of cover files require significant computational resources. In this paper, research has been carried out on methods to increase computational efficiency in terms of the amount of required RAM, and the number of the required number of basic operations to hide a message.

Theoretical approaches to the synthesis of discrete signals with necessary properties

Methods for information exchange, formation and processing of data used in information and communication systems (ICS), as well as classes of broadband signals used as a physical data carrier, do not provide the necessary (for individual ICS applications) indicators of cyber and information security, noise immunity of reception signals and secrecy of IKS functioning. Most of the existing systems use signals, the construction of which is based on linear laws, which allows an attacker, based on the establishment of the parameters of the signals used in the system, to carry out deliberate interference in the operation of the ICS with minimal energy consumption. The article presents conceptual approaches to the construction of secure ICS, which determine the need to cover the entire spectrum of information transformations in the complex, and based on the synthesis of signal systems with improved ensemble, correlation, structural properties. A method is proposed for synthesizing discrete derivatives of signals based on nonlinear discrete complex cryptographic signals (CS) and orthogonal signals formed on the basis of the rows of the Hadamard matrix (initial signals),. Based on computer modeling and the performed calculations, it is shown that the derivative signals formed on the basis of cryptographic sequences and rows of the Hadamard matrix have improved properties compared to orthogonal and linear classes of signals. Approaches to the construction are stated and a general characteristic of the hardware-software complex for synthesis, analysis, study of properties, generation, processing of a number of studied signal classes is given. It is shown that the use of such signals will improve such indicators of the system functioning as information security, noise immunity of signal reception and secrecy of functioning.

Optimization of local search algorithm parameters for generating nonlinear substitutions

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 of local search on the complexity of generating the target S-box is investigated. The optimal (from the point of view of minimum time consumption) parameters of the local search algorithm for generating S-blocks with a target nonlinearity of 104 and the number of parallel computing threads 30 are substantiated. It is shown that with the selected (optimal) parameters it is possible to reliably form S-blocks with a nonlinearity of 104.

Investigation of the expediency of using AVX512 for the implementation of modern algorithms for electronic signatures

Development and investigation of electronic signatures on algebraic lattices is one of the promising directions in post-quantum cryptography. Cryptosystems CRYSTALS-Dilithium and Falcon represent lattice cryptography in the category of electronic signatures in the NIST PQC open competition among the finalists. Most operations in these cryptosystems are reduced to addition and multiplication of polynomials in a finite field with a generating cyclotomic polynomial xN + 1. Using such a field allows the use of a number-theoretic transformation (NTT) to create fast and reliable software implementations. In practice, vectorized set (SIMD) instructions are used to achieve good performance. AVX2 instructions are most often used among existing implementations. At the same time, the possibility of using AVX512 instructions remains little explored. The purpose of this work is to investigate the feasibility of applying AVX512 instructions to optimization of the NTT, used in modern EPs on algebraic lattices. In particular, the paper presents a method for implementing a number-theoretic transformation using AVX512 for CRYSTALS-Dilithium and Falcon. An increase in performance is shown in comparison with the reference optimized author's implementations.

Feature of statistical data processing by computer mathematics systems tools

Processes of error accumulation were analysed during arithmetic operations on statistical data obtained in the course of research on oscillations in cross-field electron vacuum devices. The features of statistical data processing obtained as a result of experimental research were investigated using the most widespread computer mathematical packages. The features of statistical data processing were investigated by processing a sample of 80 values of the magnetron generation frequency using popular mathematical packages Excel, Maple, Matlab and MathCad and comparing the results obtained with calculations using theoretical formulas. Calculation results for all packages give the same results for mean, variance and standard deviation. As for the coefficients of skewness and kurtosis, most of the results do not coincide. Analysis of the calculation results showed that the difference in the obtained values ​​of the skewness and kurtosis is due to different definitions of these indicators in mathematical packages Excel, Maple, Matlab and MathCad. It is proved that in Microsoft Excel we cannot correctly construct a histogram without using additional operations, because the interval limits are calculated with errors. It leads to an incorrect determination of the number of elements into these intervals. To build correctly a histogram using the Excel package, it is necessary to calculate the interval limits in advance. It is concluded that before using computer mathematical packages for processing statistical data, it is necessary to analyze first by what formulas the required parameters are calculated and take appropriate measures to eliminate possible discrepancies with the parameters calculated using theoretical formulas.

Analysis of methods for assessing and managing cyber risks and information security

Global trends to increase the threats to information and cybersecurity, increasing the level of vulnerability of information and telecommunications systems (ITS) necessitate the development and implementation of new standards and regulations on information security, the introduction of new technologies and best practices in information security. The main approach to information and cybersecurity in ITS is the Risk-Based Protection Strategy. The main task of information risk management (IR) is to identify and assess objectively the most significant risks for the company's business, as well as the need to use risk controls to increase the efficiency and profitability of the company's economic activities. It is believed that quality risk management allows you to use the optimal efficiency and cost of risk control and information protection measures, adequate to the current goals and objectives of the company's business. The paper presents results of solving the current problem of finding optimal methods for assessing the risks of information and cybersecurity. Criteria for selecting the best methods of risk assessment are proposed. The analysis of known methods of risk assessment for compliance with these criteria is performed. Proposals have been formulated to create promising methods for risk assessment, their application to modern information security management systems, especially those designed for critical infrastructure, will most effectively address the problems of information and cybersecurity, as well as privacy.

Investigation of heuristic search functions for nonlinear substitutions for symmetric cryptography

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 complexity of its calculation. It also provides specific recommendations for the formation of parameters for heuristic search for S-boxes, which significantly affect the efficiency of generating nonlinear substitutions for symmetric cryptography.