title: ÐÐ°ÑÐ¸ÑÐ° ÐºÐ°Ð½Ð°Ð»Ð¾Ð² ÑÐ²ÑÐ·Ð¸ Ð¿Ð¾ÑÑÐµÐ´ÑÑÐ²Ð¾Ð¼ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Protection of communication channels through the use of nonlinear systems
Creators: name: Ð§ÐµÐ¼ÐµÑÐ¸ÑÐ¾Ð², ÐÐ³Ð¾ÑÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð¡Ð¸ÑÑÐµÐ¼Ð½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð·
ÐÐ¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐµ
ÐÐ½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ñ
Ñ Ð°Ð¾ÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ
ÑÐ¸Ð½Ñ ÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ñ
Ð¿Ð¾Ð»Ð½Ð°Ñ ÑÐ¸Ð½Ñ ÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ñ Ñ Ð°Ð¾ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ¾Ð²
Ñ Ð°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¿Ð¾ÐºÐ°Ð·Ð°ÑÐµÐ»Ð¸ ÐÑÐ¿ÑÐ½Ð¾Ð²Ð°
chaotic systems
synchronization
complete synchronization of chaotic generators
Lyapunov exponents

description: Ð¦ÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð¿Ð¾Ð²ÑÑÐµÐ½Ð¸Ðµ ÑÑÐ¾Ð²Ð½Ñ ÐºÐ¾Ð½ÑÐ¸Ð´ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾ÑÑÐ¸ Ð¸ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð² ÑÐµÐ»ÐµÐºÐ¾Ð¼Ð¼ÑÐ½Ð¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼Ð°Ñ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°ÑÑÑÑ Ð² ÑÐ°Ð±Ð¾ÑÐµ: 1) ÐÐ½Ð°Ð»Ð¸Ð· Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð¿Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð´ÐµÑÐµÑÐ¼Ð¸Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ ÑÐ°Ð¾ÑÐ° Ð´Ð»Ñ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸; 2) Ð°Ð½Ð°Ð»Ð¸Ð· Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¼Ð¾Ð³ÑÑ Ð³ÐµÐ½ÐµÑÐ¸ÑÐ¾Ð²Ð°ÑÑ ÑÐ°Ð¾Ñ; 3) Ð²ÑÐ±Ð¾Ñ ÑÑÐµÐ´ÑÑÐ² Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð´Ð»Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ°ÑÑÐµÑÐ° Ð¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼; 4) Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¸Ð½ÑÑÐ¾Ð½Ð½Ð¾ ÑÐ²ÑÐ·Ð°Ð½Ð½ÑÑ ÑÐ°Ð¾ÑÐ¸ÑÐ½ÑÑ ÑÐ¸ÑÑÐµÐ¼; 5) Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾ÑÐµÑÑÐ° Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ°Ð¾ÑÐ¸ÑÐ½ÑÑ ÑÐ¸ÑÑÐµÐ¼; 6) ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð°Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ ÑÐ¸ÑÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð°Ð½Ð½ÑÑ Ð´Ð¸ÑÐºÑÐµÑÐ½ÑÐ¼Ð¸ ÑÐ°Ð¾ÑÐ¸ÑÐ½ÑÐ¼Ð¸ Ð¿Ð¾ÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÐ½Ð¾ÑÑÑÐ¼Ð¸. ÐÐ±ÑÐµÐºÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ â Ð¿ÑÐ¾ÑÐµÑÑ ÐºÐ¾Ð½ÑÐ¸Ð´ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² Ð¿Ð¾ ÐºÐ°Ð½Ð°Ð»Ð°Ð¼ ÑÐ²ÑÐ·Ð¸ Ð² ÑÐµÐ»ÐµÐºÐ¾Ð¼Ð¼ÑÐ½Ð¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼Ð°Ñ. ÐÑÐµÐ´Ð¼ÐµÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ â Ð¼ÐµÑÐ¾Ð´Ñ Ð¸ ÑÑÐµÐ´ÑÑÐ²Ð° ÐºÐ¾Ð½ÑÐ¸Ð´ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÑÑÑÐ¾Ð¹ÑÑÐ² Ñ ÑÐ°Ð¾ÑÐ¸ÑÐ½Ð¾Ð¹ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¾Ð¹. ÐÐ°ÑÑÐ½Ð¾-Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ°Ñ Ð½Ð¾Ð²Ð¸Ð·Ð½Ð° ÑÐ°Ð±Ð¾ÑÑ: 1) ÐÐ¾Ð»ÑÑÐ¸Ð» ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ðµ Ð¼ÐµÑÐ¾Ð´ ÑÐ¸ÑÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð°Ð½Ð½ÑÑ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð´Ð¸ÑÐºÑÐµÑÐ½ÑÑ ÑÐ°Ð¾ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¿Ð¾ÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÐ½Ð¾ÑÑÐµÐ¹. ÐÐ° Ð±Ð°Ð·Ðµ Ð´Ð¸ÑÐºÑÐµÑÐ½Ð¾ â Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹ ÐÐ¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÐÐ¾ÑÐµÐ½ÑÐ° Ð±ÑÐ» ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐ¸ÑÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¸ÑÑÐ¾Ð´Ð½Ð¾Ð³Ð¾ Ð¼Ð°ÑÑÐ¸Ð²Ð° Ð±Ð°Ð¹ÑÐ¾Ð². 2) ÐÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½ ÑÑÐ´ Ð¼ÐµÑÐ¾Ð´Ð¾Ð², Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð½Ð° ÑÐµÐ¾ÑÐ¸Ð¸ Ð´ÐµÑÐµÑÐ¼Ð¸Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ ÑÐ°Ð¾ÑÐ°, Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ¾ÑÐ¾ÑÑÑ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ Ð¿Ð¾Ð²ÑÑÐ¸ÑÑ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÑ Ð¸ ÐºÐ¾Ð½ÑÐ¸Ð´ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾ÑÑÑ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð² ÑÐµÐ»ÐµÐºÐ¾Ð¼Ð¼ÑÐ½Ð¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼Ð°. ÐÐ° Ð±Ð°Ð·Ðµ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ ÐÐ¾ÑÐµÐ½ÑÐ° Ð±ÑÐ» ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ ÐºÐ¾Ð¼Ð¿Ð»ÐµÐºÑ Ð¸Ð¼Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÐ°Ð¾ÑÐ¸ÑÐ½ÑÑ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ¾Ð², ÑÐ¸ÑÑÐµÐ¼ ÑÐ¸Ð½ÑÑÐ¾Ð½Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¸ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð´Ð¸ÑÐºÑÐµÑÐ½ÑÑ Ð¸ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¾Ð²ÑÑ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ°Ð¾ÑÐ°.
description: The purpose of the work is to increase the level of confidentiality and efficiency of information transfer in telecommunication systems. The tasks that are solved in the work: 1) Analysis of methods and existing decisions on the use of deterministic chaos for information transfer; 2) analysis of mathematical models of dynamic systems that can generate chaos;3) selection of tools and algorithms for numerical calculation and modeling of nonlinear systems; 4) simulating synchronously connected chaotic systems; 5) modeling the process of signal transmission using chaotic systems; 6) algorithm development and software implementation of data encryption by discrete chaotic sequences. The object of the study is the process of confidential transmission of information signals through communication channels in telecommunication systems. The subject of research is the methods and means of confidential transmission of information signals using devices with chaotic dynamics. Scientific and practical novelty of the work: 1) The method of encrypting data based on discrete chaotic sequences has been developed. Based on the discrete-time Dynamic Lorentz model, an algorithm for encrypting the original byte array was developed. 2) A number of methods based on the theory of deterministic chaos are presented, with the help of which it is possible to increase the efficiency and confidentiality of information transfer to telecommunications systems. Based on the dynamic Lorentz system, a complex of simulation models of chaotic generators, synchronization and transmission systems of discrete and analog signals using chaos was developed.