Abstract
Coherent chaos-based communication is a developing technique for secure data transmission based on synchronization of chaotic oscillators at the transmitter and receiver sides, which is treated as a more secure method than non-coherent communication, chaotic symbolic dynamics, and other approaches. Nowadays, digital implementation of such systems allows high precision in parameter matching and sophisticated message recovery algorithms, though challenges remain: first, in adapting chaotic signals for non-ideal physical media, e.g., acoustic channels with frequency-dependent attenuation and noise, while, second, still providing the high level of security. The current study provides the implementation of a coherent chaotic communication system based on the Sprott Case S chaotic oscillator that meets these challenges. We utilize the modulation technique, minimizing changes in chaotic dynamics that may be captured by an intruder, propose an optimization of chaotic oscillator parameters to match channel characteristics and establish a signal normalization procedure to neutralize attenuation at the receiver side. Applying spectral and return map attacks, we show that the measures taken to counteract distortion in the path do not reduce the security of the transmission. In an experiment with a physical acoustic path, we demonstrate the practical operability of our approach.
References
Anishchenko, V., T. Vadivasova, D. Postnov, and M. Safonova, 1992. Synchronization of chaos. International Journal of Bifurcation and Chaos, 2: 633–644.
Babajans, R., D. Cirjulina, and D. Kolosovs, 2025. Field-programmable gate array-based chaos oscillator implementation for analog–discrete and discrete–analog chaotic synchronization applications. Entropy, 27: 334.
Babajans, R., D. Cirjulina, D. Kolosovs, and A. Litvinenko, 2022. Quadrature chaos phase shift keying communication system based on Vilnius chaos oscillator. In 2022 Workshop on Microwave Theory and Techniques in Wireless Communications (MTTW), pp. 5–8, IEEE.
Babkin, I., V. Rybin, V. Andreev, T. Karimov, and D. Butusov, 2024. Coherent chaotic communication using generalized Runge–Kutta method. Mathematics, 12: 994.
Bai, C., H.-P. Ren, M. S. Baptista, and C. Grebogi, 2019. Digital underwater communication with chaos. Communications in Nonlinear Science and Numerical Simulation, 73: 14–24.
Baptista, M. S., 2021. Chaos for communication. Nonlinear Dynamics, 105: 1821–1841.
Bonny, T. and W. Al Nassan, 2024. Optimizing security and cost efficiency in n-level cascaded chaotic-based secure communication system. Applied System Innovation, 7: 107.
Bonny, T., W. Al Nassan, and A. Sambas, 2024. Comparative analysis and FPGA realization of different control synchronization approaches for chaos-based secured communication systems. PLOS ONE, 19: 1–33.
Bonny, T., W. A. Nassan, S. Vaidyanathan, and A. Sambas, 2023. Highly-secured chaos-based communication system using cascaded masking technique and adaptive synchronization. Multimedia Tools and Applications, 82: 34229–34258.
Butusov, D., T. Karimov, A. Voznesenskiy, D. Kaplun, V. Andreev, et al., 2018. Filtering techniques for chaotic signal processing. Electronics, 7: 450.
Butusov, D., V. Rybin, and A. Karimov, 2025. Fast time-reversible synchronization of chaotic systems. Physical Review E, 111: 014213.
Butusov, D. N., V. Y. Ostrovskii, A. I. Karimov, and V. S. Andreev, 2019. Semi-explicit composition methods in memcapacitor circuit simulation. International Journal of Embedded and Real-Time Communication Systems (IJERTCS), 10: 37–52.
Cuomo, K. M., A. V. Oppenheim, and S. H. Strogatz, 1993. Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 40: 626–633.
Eisencraft, M., R. Fanganiello, J. Grzybowski, D. Soriano, R. Attux, et al., 2012. Chaos-based communication systems in non-ideal channels. Communications in Nonlinear Science and Numerical Simulation, 17: 4707–4718.
Kaddoum, G., 2016. Wireless chaos-based communication systems: A comprehensive survey. IEEE Access, 4: 2621–2648.
Kolumbán, G., G. Kis, Z. JaKo, and M. P. Kennedy, 1998. FM-DCSK: A robust modulation scheme for chaotic communications. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 81: 1798–1802.
Mushenko, A., J. Dzuba, A. Nekrasov, and C. Fidge, 2020. A data secured communication system design procedure with a chaotic carrier and synergetic observer. Electronics, 9: 497.
Oppenheim, A., K. Cuomo, S. Isabelle, and G. Wornell, 1992. Signal processing in the context of chaotic signals. In Acoustics, Speech, and Signal Processing, IEEE International Conference on, Volume 4, pp. 117–120, Los Alamitos, CA, USA, IEEE Computer Society.
Parlitz, U., L. Chua, L. Kocarev, K. Halle, and A. Shang, 1992. Transmission of digital signals by chaotic synchronization. International Journal of Bifurcation and Chaos, 2: 973–977.
Pecora, L. M. and T. L. Carroll, 1990. Synchronization in chaotic systems. Physical Review Letters, 64: 821–824.
Pérez, G. and H. A. Cerdeira, 1995. Extracting messages masked by chaos. Physical Review Letters, 74: 1970–1973.
Pisarchik, A., R. Jaimes-Reategui, and J. Garcia-Lopez, 2008. Synchronization of multistable systems. International Journal of Bifurcation and Chaos, 18: 1801–1819.
Rybin, V., I. Babkin, Y. Bobrova, M. Galchenko, A. Mikhailov, et al., 2025. Variable-step semi-implicit solver with adjustable symmetry and its application for chaos-based communication. Mathematics, 13.
Rybin, V., D. Butusov, E. Rodionova, T. Karimov, V. Ostrovskii, et al., 2022. Discovering chaos-based communications by recurrence quantification and quantified return map analyses. International Journal of Bifurcation and Chaos, 32: 2250136.
Rybin, V., T. Karimov, O. Bayazitov, D. Kvitko, I. Babkin, et al., 2023. Prototyping the symmetry-based chaotic communication system using microcontroller unit. Applied Sciences, 13.
Sprott, J. C., 1994. Some simple chaotic flows. Physical Review E, 50: R647–R650.
Trickey, J. S., G. Cárdenas-Hinojosa, L. Rojas-Bracho, G. S. Schorr, B. K. Rone, et al., 2022. Ultrasonic antifouling devices negatively impact Cuvier’s beaked whales near Guadalupe Island, México. Communications Biology, 5: 1005.
Voznesensky, A., D. Butusov, V. Rybin, D. Kaplun, T. Karimov, et al., 2022. Denoising chaotic signals using ensemble intrinsic time-scale decomposition. IEEE Access, 10: 115767–115775.
Wang, H., Z. Zhi Han, and Z. Mo, 2010. Synchronization of hyperchaotic systems via linear control. Communications in Nonlinear Science and Numerical Simulation, 15: 1910–1920.
Wang, S., 2018. Dynamical analysis of memristive unified chaotic system and its application in secure communication. IEEE Access, 6: 66055–66061.

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