INVESTIGATION OF PROPERTIES OF CHAOTIC GENERATORS OF PSEUDO-RANDOM SEQUENCES CONSTRUCTED USING FUZZY LOGIC
Ключові слова:
generator, chaos, one-dimensional map, pseudo-random sequence, statistical test.Анотація
Telecommunication systems with a broadband signal spectrum have improved immunity to interference. However, such systems also need to be protected from information interception. Specially designed pseudo-random bit sequence generators are used for this purpose. The use of known pseudo-random equations does not ensure their high confidentiality due to the possibility of their disclosure upon receipt of the signal. A significant increase in system confidentiality can be achieved by using pseudo-random
sequences based on the use of chaotic mappings.
Chaotic signals are essentially pseudo-random, but they are generated by deterministic systems. All computer models of chaos are only an approximation to mathematical chaos. Any analysis of these sequences does not allow them to be reproduced, so they have significant advantages when used to expand the signal spectrum and create a pseudo-noise broadband signal.
The aim of the article is to develop a method of creating pseudo-random sequences based on the rules of fuzzy logic and one-dimensional chaotic systems, as well as to analyze the statistical characteristics of pseudo-random sequences formed in this way. The study used the three most well-known one-dimensional mappings, namely logistic, square and cubic, and presented the results of statistical verification of sequences formed using the rules of fuzzy logic. As a result, a pseudo-random bit generator was proposed and implemented using fuzzy logic rules and two one-dimensional chaotic systems, and the statistical characteristics of the sequences generated by such a generator were verified. The results show that the obtained sequences satisfy most of the tests from the NIST set.
The use of fuzzy logic-based pseudo-random sequences based on the rules of fuzzy logic and deterministic chaos is effective for building broadband telecommunication systems, which will allow them to ensure a high degree of confidentiality in the transmission of information.
