Factorization is one of the most important problems in the theory of numbers and a modern asymmetric cryptography. Known methods of factorization are quite cumbersome; therefore, require significant computational resources for processing multi-bit numbers. The relevance of the factorization problem is dictated also by uncertainty regarding the theoretical foundation of stability for the disclosure of asymmetric cryptosystems. The advanced method of factorization of multi-bit numbers on the basis of Fermat's theorem with the help of the system of residual classes has been developed in this article. The operation of squaring is excluded from proposed method. Arithmetic operations are performed with numbers, which are smaller than the selected module. Last one allows to shifted zone of bit computing resources on several orders to deeper side and replaces the operation of finding the square root, which is caused of computational complexity of the Fermat's algorithm onto generating a binary key of factorization.

Direct spread spectrum technology is traditionally used in radio communication systems with multiple access, for example, in CDMA standards, in global satellite navigation systems, in Wi-Fi network wireless protocols, etc. It ensures high security and reliability of information transfer. In addition, spread spectrum technology provides the transmitted signals with a noise-like appearance, thus hiding the semantic content of the messages. We researched this technology for other implementations. The purpose of our study was to investigate new technologies for hiding data in multimedia files. In particular, we investigated the direct spread spectrum in the context of the development of methods for hiding data in audio containers. We considered various spreading sequences (chip codes) and also explored their use for hiding information in audio files. We conducted experimental studies and estimated the bit error rate (BER) in the recovered data. The article also evaluates the distortion of an audio container by the peak signal-to-noise ratio (PSNR). The results of our research enable us to find out which method of forming chip codes gives a lower BER with equal PSNR. We provide recommendations on the formation of spreading sequences to reliably and safely hide informational messages in audio files.

This paper proposes methods for the development of mathematical models and for the control of operation modes of technological objects in oil refinery in face of uncertainty based on fuzzy information. The mathematical formulation of the problem of decision-making on controlling modes, which are solved on the basis of mathematical modeling, is formalized and obtained. By using the example of the problem of decision-making on optimal operation modes of technological complex for the benzene production and based on the methods of fuzzy mathematics an algorithm of its solution is developed. The initial problem is formalized as a problem of decision-making in the fuzzy environment, since the investigated object is characterized by multicriteriality and frequently functions in a fuzzy environment. The mathematical formulation of the problem of object's mode selection in the fuzzy environment and the heuristic algorithm of its solution is obtained by modifying various optimality principles based on methods of the fuzzy sets theory.

In modern cryptosystems, there are many well-proven often used constructions, such as operations in binary fields. In this paper method of algorithm construction for modular reduction by fixed irreducible polynomial (trinomial or pentanomial) was proposed. This method applying allows to get a high performance algorithm of modular reduction for specified fixed polynomial and target platform while cryptosystems develop, for example elliptic curve cryptosystem.

The consortium of “The Future is in Applied Artificial Intelligence” Project designed the first competency-based applied artificial intelligence curriculum at the higher-education institution level. The development was based on advanced system research on existing artificial intelligence-related resources and surveying target groups of teachers, information technology students, and employers, which should enhance the performance of implementing artificial intelligence education. A review of applied artificial intelligence was prepared in the form of keyword clustering. The initial data were collected with the help of surveying by identifying job offers, existing artificial intelligence training courses, scientific projects, and real cases. A synthetic analysis of the textual information from the studies was conducted using the word clouds technique. A tensor-based approach was used for the presentation of the competency-based course. The specific numerical requirements for the course in the form of priorities followed from the solution to decision-making problems using the analytic hierarchy process technique. Based on a comprehensive study of surveys, educational experience, scientific projects, and business requirements, and a meta-analysis of the recent references, we specified the criteria for a training course in the form of a tensor-based representation of competencies in relation to content and educational modules.