Devising methods to synthesize discrete complex signals with required properties for application in modern information and communication systems

Abstract

Information and communication systems (ICSs) must comply with increasingly stringent requirements to ensure the reliability and speed of information transmission, noise immunity, information security. This paper reports the methods to synthesize discrete complex cryptographic signals, underlying the construction of which are random (pseudo-random) processes; the methods for synthesizing characteristic discrete complex signals whose construction is based on using the nature of the multiplicative group of a finite field; the results of studying the properties of the specified signal systems. It is shown that the methods built provide a higher synthesis performance than known methods and make it possible to algorithmize the synthesis processes for the construction of software and hardware devices to form such signals. The win in the time when synthesizing nonlinear signals in finite fields using the devised method is, compared to the known method, for the period of 9,972 elements is 1,039.6 times. The proposed method for synthesizing the entire system of such signals, based on decimation operation, outperforms the known method of difference sets in performance. Thus, for a signal period of 2,380 elements, the win in time exceeds 28 times. It has also been shown that the application of such systems of complex signals could improve the efficiency indicators of modern ICSs. Thus, the imitation resistance of the system, when using complex discrete cryptographic signals with a signal period of 1,023 elements, is four orders of magnitude higher than when applying the linear signal classes (for example, M-sequences). For a signal period of 1,023 elements, the win (in terms of structural secrecy) when using the signal systems reported in this work exceeds 300 times at a period of 8,192, compared to the signals of the linear form (M-sequences)

Theoretical approaches to the synthesis of discrete signals with necessary properties

“…The section proposes a method for synthesis of discrete derivative signals based on the use of nonlinear discrete complex cryptographic signals as the signals generating orthogonal discrete signals (ODS) as initial ones. It is known [7,8] that ODSs have unsatisfactory ensemble, structural and correlation properties, therefore, the use of the ODS in the ICS, which have increased requirements for noise immunity, signal secrecy, information security is limited. Preservation of the advantages of the ODS, with simultaneous improvement of correlation, spectral, ensemble and structural properties, can be achieved based on formation of derivative signal systems.…”

“…It is shown in [2,3] that generating signals must have good autocorrelation properties (small values of lateral peaks of autocorrelation function) to ensure that derived signal systems meet the increased requirements for information security, noise immunity and secrecy of the ICS operation. Considering the above-said, it is advisable to use characteristic signals and cryptographic signals as generating signals [8,9].…”

“…Based on multiple calculations for signal lengths 64, 256, 1024, 2048, statistical and correlation character(istics of the CS and characteristic discrete signals (CDS) [8], as well as derived signals, formed on the basis of these signals, were calculated, and the Hadamard matrix rows of appropriate order were used as source.…”

“…Tables 7, 8 show the results of tests carried out on these tests. Numerous studies of the statistical properties of derivatives of nonlinear cryptographic sequences of symbols using NIST SP 800-22, FIPS-140 have shown that these sequences, formed using the proposed method [8], meet the requirements for random sequences.…”