Strengthening Quality of Chaotic Bit Sequences

We discuss chaos and its quality as measured through the 0-1 test for chaos. When the 0-1 test indicates deteriorating quality of chaos, because of the finite precision representations of real numbers in digital implementations, then the process may eventually lead to a periodic sequence. A simple method for improving the quality of a chaotic signal is to mix the signal with another signal by using the XOR operation. In this paper, such mixing of weak chaotic signals is considered, yielding new signals with improved quality (with K values from the 0-1 test close to 1). In some sense, such a mixing of signals could be considered as a two-layer prevention strategy to maintain chaos. That fact may be important in those applications when the hardware resources are limited. The 0-1 test is used to show the improved chaotic behavior in the case when a continuous signal (for example, from the Chua, Rössler or Lorenz system) intermingles with a discrete signal (for example, from the logistic, Tinkerbell or Henon map). The analysis is presented for chaotic bit sequences. Our approach can further lead to hardware applications, and possibly, to improvements in the design of chaotic bit generators. Several illustrative examples are included.

SIGNAL PROCESSING AND CYBERSECURITY IN SOME CHAOTIC OPTICAL COMMUNICTAION SYSTEMS

A chaos –geometric approach to investigation of complex chaotic dynamical systems is applied to an analysis, modeling and processing the time series of emission intensities of chaotic transmitter/receiver systems (two unidirectionally coupled semiconductor laser systems in the all-optical scheme) suited for encoding at rates of GBit/s. the problem of a signal processing is directly connected with the corresponding cybersecurity in some optical chaos communictaion systems. The estimated values for the dynamic and topologic invariants such as the correlation and Kaplan-York dimensions, Lyapunov indicators, Kolmogorov entropy etc for investigated chaotic signal time series of two unidirectionally coupled semiconductor laser systems in the all-optical scheme.

Adaptive Control of Chaotic Signals: Investigated by Simulation Software and Real Electronic Circuits

Chaotic behavior is complicated, sensitive, and has the feature of great variety, which are the most potential signals to be applied in data encryption, secure communication, medical information protection, etc. As a consequence, in this paper, we try to propose three different ways to show our data generating results step by step, which means it can be proved effectively and used in practice: (1) Chaotic solutions simulated by MATLAB, (2) chaotic motion drawn via electronic circuits software Multisim, and (3) chaotic signal implemented on real electronic circuits with breadboard. In advance, following the same design principal, the adaptive chaotic signal is also designed and presented in the end of this article for further study, which provides a more flexible and variable chaotic signal to enhance the encryption effectiveness. The experimental results are extremely close to the two simulation results and can definitely be technically transferred to real encryption application.

Метод підвищення скритності систем передачі інформації на основі модуляції з ортогональним частотним розділенням і мультиплексуванням хаотичних піднесучих

The subject of the research is the processes of formation and processing of signals with orthogonal frequency divisionand multiplexing (OFDM) of chaotic sequences to ensure the stealthiness of data transmission. The research synthesizes the method for increasing the stealthiness of information transmission systems based on signals with OFDM-modulation on the basis of forming an analytical signal and chaotic mapping of Chebyshev polynomial. It would enable ensuring reliable information protection in radio transmission systems that use signals with OFDM-modulation, at the cost of the high level of structural and independent and Identically distributed (IID) (the degree of signal masking under noise) stealthiness of the signals. The tasks are to investigate the effectiveness of the developed method for increasing the stealthiness of information transmission systems by numerical assessment of the level of structural and IID-stealthiness and the quality of recovery of the masked information on the receiving side. The methods used are for the formation and processing of chaotic subcarriers in the signal with OFDM-modulation – methods of nonlinear dynamics, approaches to the formation of analytical chaotic signal and methods of the statistical theory of observation processing; to assess the level of structural and IID-stealthiness – steganography theory, a method of nonlinear time series analysis based on the use of BDS-statistics. The following results are obtained: the method for increasing the stealthiness of information transmission systems based on the use of signals with OFDM-modulation and chaotic subcarriers has been synthesized, has also evaluated the level of structural and IID-stealthiness of signals, that generated using the proposed method. It is established that compared with systems that use harmonic signals with OFDM-modulation, chaotic signals with OFDM-modulation can provide a higher level of IID-stealthiness. It was confirmed by the obtained results of visual, frequency, statistical and dynamic analysis. To assess the level of structural stealthiness, the expenditure of detecting the generated signals with a given probability has been estimated. The obtained results showed that the level of structural stealthiness increased by 2…2.5 times. It has shown that to ensure the required level of recovery of the generated signal, the signal-to-noise ratio at the input of the receiver must be greater than 4 dB. Conclusions. The scientific novelty of the obtained results lies in the following: for the first time, the method of subcarrier formation for signals with OFDM-modulation based on the use of analytical signal and Chebyshev polynomial of the first kind of tertiary is obtained. The proposed method provides the required level of structural and IID-stealthiness of information transmission systems, compared with conventional methods of signal generation with OFDM-modulation, due to the similarity of the generated signals with “white” noise.