Plain convolution encryption as an alternative to overcoming the limitations of synchronization-based methods

Authors

DOI:

https://doi.org/10.31349/RevMexFis.71.040602

Keywords:

Lorenz system; Fourier spectrum analysis

Abstract

This paper revisits the send/retrieve message process using synchronization of the Lorenz system with a monochromatic message. We analyze how the fidelity of the retrieved signal depends on the message frequency and demonstrate message hacking through Fourier spectrum analysis. Various parameters affecting fidelity and noise in the hacked signal are also examined. Additionally, we transmit text messages recovered through synchronization and investigate their vulnerability to hacking. As a countermeasure, we propose a method to send both types of messages using the convolution as the encryption function to hide the message in the chaotic signal. This approach enhances retrieval fidelity and significantly increases resistance to hacking compared to synchronization-based methods.

References

U. Parlitz, L.O. Chua, Lj. Kocarev, K.S. Halle, and A. Shang, Transmission of digital signals by chaotic synchronization, International Journal of Bifurcation and Chaos 02 (1992) 973, https://doi.org/10.1142/S0218127492000562

O. M. Al-Hazaimeh, M. F. Al-Jamal, N. Alhindawi, and A. Omari, Image encryption algorithm based on lorenz chaotic map with dynamic secret keys, Neural Computing and Applications 31 (2019) 1, https://doi.org/10.1007/s00521-017-3195-1

D. A. Q. Shakir, A. Salim, S. Q. A. Al-Rahman, and A. M. Sagheer, Image encryption using lorenz chaotic system, Journal of Techniques 5 (2023) 122, https://doi.org/10.51173/jt.v5i1.840

T. Haridas, Upasana S.D., Vyshnavi G., M. S. Krishnan, and S. Shankar Muni, Chaos-based audio encryption: Efficacy of 2d and 3d hyperchaotic systems, Franklin Open 8 (2024) 100158, https://doi.org/10.1016/j.fraope.2024.100158

B. Fraser, P. Yu, and T. Lookman, Steps towards improving the security of chaotic encryption, Phys. Rev. E 66 (2002) 017202, https://doi.org/10.1103/PhysRevE.66.017202

S. Wang, J. Kuang, J. Li, Y. Luo, H. Lu, and G. Hu, Chaosbased secure communications in a large community, Phys. Rev. E 66 (2002) 065202, https://doi.org/10.1103/PhysRevE.66.065202

E. Klein, R. Mislovaty, I. Kanter, and W. Kinzel, Publicchannel cryptography using chaos synchronization, Phys. Rev. E 72 (2005) 016214, https://doi.org/10.1103/PhysRevE.72.016214

D. Rontani, M. Sciamanna, A. Locquet, and D. S. Citrin, Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks, Phys. Rev. E 80 (2009) 066209, https://doi.org/10.1103/PhysRevE.80.066209

S. Li, G. Alvarez, G. Chen, and X. Mou, Breaking a chaosnoise-based secure communication scheme, Chaos: An Interdisciplinary Journal of Nonlinear Science 15 (2005), https://doi.org/10.1063/1.1856711

S. Bu and B.-H. Wang, Improving the security of chaotic encryption by using a simple modulating method, Chaos, Solitons and Fractals 19 (2004) 919, https://doi.org/10.1016/S0960-0779(03)00260-1

G. Alvarez and S. Li, Cryptanalyzing a nonlinear chaotic algorithm (nca) for image encryption, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 3743, https://doi.org/10.1016/j.cnsns.2009.02.033

J. S. Teh, M. Alawida, and Y. C. Sii, Implementation and practical problems of chaos-based cryptography revisited, Journal of Information Security and Applications 50 (2020) 102421, https://doi.org/10.1016/j.jisa.2019.102421

M. Alawida, Enhancing logistic chaotic map for improved cryptographic security in random number generation, Journal of Information Security and Applications 80 (2024) 103685, https://doi.org/10.1016/j.jisa.2023.103685

B. Norouzi and S. Mirzakuchaki, Breaking an image encryption algorithm based on the new substitution stage with chaotic functions, Optik 127 (2016) 5695, https://doi.org/10.1016/j.ijleo.2016.03.076

S. Noshadian, A. Ebrahimzade, and S.Javad Kazemitabar, Breaking a chaotic image encryption algorithm, Multimedia Tools and Applications 79 (2020) 25635, https://doi.org/10.1007/s11042-020-09233-6

R. Zhou and S. Yu, Break an enhanced plaintextrelated chaotic image encryption algorithm, Chaos, Solitons and Fractals 181 (2024) 114623, https://doi.org/10.1016/j.chaos.2024.114623

K. M. Cuomo and A. V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications, Phys. Rev. Lett. 71 (1993) 65, https://doi.org/10.1103/PhysRevLett.71.65

The Unicode Consortium, Unicode character code charts, (2024)

Downloads

Published

2025-07-01

How to Cite

[1]
F. Rosales-Infante, M. L. Romero-Amezcua, I. Álvarez-Rios, and F. S. Guzman, “Plain convolution encryption as an alternative to overcoming the limitations of synchronization-based methods”, Rev. Mex. Fís., vol. 71, no. 4 Jul-Aug, pp. 040602 1–, Jul. 2025.