The paper presents the results of solving the urgent problem of improving the performance indicators of information and communication systems (ICS), in particular, information security, noise immunity, secrecy, the speed of formation and processing of information. The use of the distributed spectrum technology (broadband noise-like signals) is a promising direction for ensuring the security of information resources. The methods used for data formation and processing, as well as the classes of broadband signals used as physical data carriers, do not allow providing the necessary (especially for critical infrastructure facilities) indicators of information security and noise immunity. In this case, as discrete sequences (DS) that expand the spectrum (manipulate the carrier frequency), should be used DS based on nonlinear construction rules and having improved correlation, ensemble and structural properties. Methods for the synthesis and formation of nonlinear discrete complex signals, namely, the so-called cryptographic signals, are proposed. The first method, presented in the article, uses random (pseudo-random) processes. Another method is based on the implementation of the operation of decimation of the original discrete sequence of symbols obtained from the results of the implementation of the first method; it provides the synthesis of an ensemble of signals for a certain signal duration. Analytical expressions are obtained for determining the synthesis time of an ensemble of signals using the proposed methods. It is shown that the speed of the signal generation method based on the decimation operation for a certain signal duration is more than three orders of magnitude higher than the speed of the method based on the random (pseudo-random) processes used. At the same time, based on the carried out computer simulation, it is shown that the signals obtained using the proposed methods have identical correlation, ensemble, and structural properties.
Наведений аналіз актуальних досліджень щодо криптографії на решітках. Аналіз відбувається відповідно до найбільш актуальних алгоритмів, що пройшли до другого етапу конкурсу NIST США. Деякі з них комбіновані-включають в себе декілька схожих алгоритмів з минулого етапу. Для детального їх розгляду приведено ряд актуальних тем дослідження для пост-квантових алгоритмів, що дозволяє описувати та класифікувати їх більш суттєво.
The article shows that the solution to the problem of increasing the noise immunity (noise immunity and secrecy of functioning) of the ICS can be achieved using systems of nonlinear signals with improved ensemble, structural and correlation properties. Two classes of nonlinear complex discrete signals are considered: characteristic discrete signals (CDS) and cryptographic signals (CS). Methods for the synthesis of these signals are presented. The paper gives a statistical simulation model for studying the noise immunity of various classes of signals in the Gaussian channel. Using this model, estimates of the dependence of the error probability on the signal-to-noise ratio were obtained for various classes of signals, namely: CDS, KS and standard BPSK AFM-16 signals. It is shown that for the signal-to-noise ratio – 10 the error probability for the CDR is 4.6875e-06, for the CS is 3.515625e-06, and for the AFM-16 is 0.002025. Thus, the use of nonlinear complex discrete signals, in particular, CDS and KS, can significantly increase the noise immunity of signal reception in modern ICS. At the same time, taking into account the improved ensemble and structural properties of these nonlinear signals, it is possible to improve significantly the indicators of crypto- and imitation security of the systems functioning.
The search for effective methods of synthesis of discrete signals (sequences) that correspond to the potentially possible limiting characteristics of correlation functions and possess the necessary correlation, structural, ensemble properties remains an urgent problem. The authors have proposed a method for the synthesis of derivatives of signal systems, for which orthogonal signals are used as the initial ones, and nonlinear discrete complex cryptographic signals (CS) are used as generating signals. The synthesis of the latter ones is based on the use of random (pseudo-random) processes, including algorithms for cryptographic information transformation. Derivative signals synthesized in this way have improved (in comparison with linear signal classes) ensemble and correlation properties, while the statistical properties of such signal systems remain unexplored. The paper presents the results of testing derived signal systems using the tests defined in FIPS PUB 140 and NIST 800-22. Analysis of the results obtained allows us to assert that the statistical properties of this class of derived signals satisfy the requirements for pseudo-random sequences: unpredictability, irreversibility, randomness, independence of symbols, etc. In essence, such signals do not differ from random sequences. The use of the proposed class of derived signals will improve the performance of signal reception noise immunity, information security and secrecy of the ICS functioning.
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