The article deals with the application of modern mathematical apparatus in information and cyber security namely fractal analysis. The choice of fractal modeling for the protection of information in the process of its digital processing is grounded. Based on scientific sources, the basic definitions of the research are analyzed: fractal, its dimension and basic properties used in the process of information protection. The basic types of fractals (geometric, algebraic, statistical) are presented and the most famous of them are described. The historical perspective of the development of fractal theory is conducted. Different approaches to the application of fractal theory in information and cyber security have been reviewed. Among them are: the use of fractal analysis in encryption algorithms; development of a method of protecting documents with latent elements based on fractals; modeling the security system of each automated workplace network using a set of properties that can be represented as fractals. The considered approaches to the application of fractal analysis in information and cyber security can be used in the preparation of specialists in the process of research work or diploma work.

This study focuses on the protection of information resources on the basis of risk-oriented approach for small and medium-sized businesses with an emphasis on risk assessment of information security (IS). The analysis of scientific sources allowed to characterize the essence of the risk-oriented approach and to formulate the main provisions for creating a model of information protection based on this technology. The content line of the model focuses on conducting qualitative and quantitative IS risk assessment, namely, SWOT-analysis, statistical method, expert assessment method and Monte Carlo method. The step-by-step procedure of carrying out the stages of analysis and implementation of these methods for IS risk assessment is described. In order to obtain a comprehensive map of IS risks at the initial stage, it is proposed to conduct a SWOT analysis, in particular to identify business weaknesses and external and internal threats. Use a statistical method to quantify IS risk if there are sufficient analytical reports. Otherwise, implement the method of expert assessments. The final step is to generate a script using the Monte Carlo method. To effectively describe the context of each information resource, use the technology of forming multiple pairs "threat - vulnerability". The relevance and possibilities of using this model as a methodology of information for small and medium businesses are substantiated.

The main problems of the network security at the moment are the difficulty of combining existing systems from different vendors and ensuring their stable interaction with each other. Intrusion detection is one of the main tasks of a proper level of network security, because it is they who notify about attacks and can block them when detected. Today, monitoring and analyzing the quality of traffic in the network, detecting and preventing intrusions is helped by IDS systems and IDS systems of the new generation IPS. However, they have been found to have certain drawbacks, such as the limitations of signature-based systems, as static attack signatures limit the flexibility of systems and pose the threat of missing detection of other attacks not entered into the database. This gives rise to the creation of more and more new hybrid systems, but the challenge is to ensure their efficiency and flexibility, which is helped by the use of artificial neural networks (ANNs). This paper considers ways to improve the use of the convolutional neural network model itself by means of modified processing, data analysis, the use of Softmax and FocalLoss functions to avoid the problem of uneven distribution of sample data by the ratio of positive and negative samples, based on training using the KDD99 dataset. The article provides practical examples of possible integration of IDS and ANN systems. Combinations of backpropagation neural networks and radiant-basis neural networks, which showed some of the best results and proved that the combination of networks helps to increase the efficiency of these systems and create a flexible network adjusted to the needs and requirements of the systems. Although the use of artificial neural networks is a popular tool, it has identified a number of disadvantages: critical dependence on the quality of the dataset, which pours both the quality of networking and the amount of data (the more data, the better and more accurate the network training). But if the data is excessive, there is a chance of missing such implicit, but also dangerous attacks as R2L and U2R.

The topic is relevant due to a detailed study of the factors determining the health level of nowadays students, and taking these factors into consideration for the development of programs to strengthen their health. Since the scientific literary data on the physical development of student youth is somewhat contradictory, namely the morphological and functional indicators of a person depends on the level of physical health and adaptive capacity, it has been decided to determine the freshmen’s anthropometric parameters. The aim of the study was to take anthropometric measurements of total and comprehensive body size of 105 students studying at Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, assess their compliance with anthropometric standards, determine the somatotype and foot shape in order to create a database for further monitoring of physical development and identify patterns of anthropometric indicators under conditions of modern learning technologies. Research methods. Anthropometric measurements were taken according to standard anthropometric methods suggested by V. V. Bunak [1]. Data estimation was performed by the method of centile intervals and indices. The foot shape was assessed by the plantogram based on the Chyzhyn index. The obtained data were statistically processed according to the STATISTICA 5.5 program. Research results. The peculiarities of anthropometric parameters and somatotype of Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University first-year students are established: height, body weight; girth sizes: chest, waist, hips; body mass index, Kettle mass-growth index, body harmony indices, foot shape

The article deals with the use of hashing algorithms for information security in training students of the specialty "125 Cybersecurity" at the Kiev Boris Grinchenko University. The modern hashing algorithms that are widely used in modern digital technologies, in particular, in the tasks of ensuring information security of modern information and communication systems has been analyzes in the article. The need for a thorough study of hashing as a means of ensuring information security has been identified and substantiated. The paper has present a thorough and detailed analysis of typical security tasks involving hashing algorithms such as implementing structures to efficiently store large data sets; searching and storing data in databases; password protection in the authentication process; formation of electronic digital signature; control of integrity and authenticity of important files; digital blockchain technologies and creation of cryptocurrencies. The special programs offered in the form of applications and online services for calculating hash codes of a file or text have been reviewed and compared. Among the tools used to provide students with practical hashing skills are the use of CryptoAPI, Cryptography Next Generation, and Security.Cryptography .NET Framework cryptographic services. Basic cryptographic functions that implement hashing algorithms have been considered. Prospective directions of hashing research for introduction into the educational process have been defined, namely: fuzzy hashing, quantum hashing. The study concluded that the need for a theoretical and practical study of hashing throughout the training of information security professionals.