Communication systems based on chaotic synchronization are gaining interest in the area of secure and covert data transmission. In this paper, a novel digital communication technique based on a coherent chaotic data transmission approach is proposed. In general, this technique resembles the well-known approach based on the modulation of nonlinearity parameters. The key idea of this study is to modulate a signal by varying not the system parameter but the symmetry coefficient in discrete chaotic models obtained by the special numerical integration method. For this purpose, the self-adjoint semi-implicit integration method of order 2 is used to obtain discrete master and slave models of the considered chaotic oscillator. The experimental results explicitly show that, like during parameter modulation, transmitting and receiving oscillators may completely synchronize only if the symmetry coefficients are equal in both systems. The architecture of the communication system based on the proposed modulation is presented. The practical applicability of the approach is confirmed by transmitting a test binary sequence between the transmitter and receiver models and preliminary benchmarking of the obtained communication system. Since the symmetry coefficient modulation does not significantly impact the chaotic behavior of the transmitting digital system, its better suitability for covert messaging was experimentally confirmed by comparing it with the parameter modulation technique.

Chaos-based communications are a promising application of chaos theory and nonlinear dynamics. Their key features include concealed transmission, high security, and native broadband signals. Many studies have recently been published devoted to this technology. However, the practical implementations of chaos-based communications are rare due to multiple shortcomings: high hardware requirements, complex signal processing algorithms, and a lack of efficient modulation techniques for chaotic signals. In this study, we consider a simple hardware prototype of a coherent chaos-based communication system based on a novel type of modulation: adaptive symmetry of the finite-difference scheme used in a chaos generator. We explicitly demonstrate the possibility of covertly transmitting data using a chaotic transmitter and receiver implemented in a general-purpose microcontroller unit. A comparison between traditional parameter and symmetry modulation is given through a return map analysis and bit error rate estimation. The communication secrecy is analyzed using quantified return map analysis. The obtained results confirm the possibility of creating chaos-based communication systems based on symmetry modulation.

Synchronization of nonlinear systems is a crucial problem in many applications, including system identification, data forecasting, compressive sensing, coupled oscillator topologies, and neuromorphic systems. Despite many efficient synchronization techniques being developed, there are some unresolved issues such as fast and reliable synchronization using short or noisy fragments of available data. In this paper, we use time-reversible integration to obtain a synchronization technique as a generalization of the well-known Pecora-Carroll method. The proposed time-symmetric synchronization technique employs the time reversibility of a discrete system obtained by the symmetric integration method. This approach allows the complete synchronization of two chaotic systems using minimal, sparse, or noisy sync data from one state variable without any controller. An example of rapid unidirectional time-symmetric synchronization of several test chaotic systems is shown to verify the performance of the proposed technique. We show that the time-reversible approach works for both conservative and dissipative systems, but highly depends on initial conditions. To increase the overall performance of the time-symmetric synchronization scheme, we suggest using a computationally simple and easy-to-implement time-reversible semi-implicit numerical integration method. Several possible applications include chaos-based communications, chaotic signal filtering, and systems based on coupled oscillators.