Abstract
In this chapter the authors propose to use fractional-order chaotic system s for data encryption, the encryption is a hybrid cipher, that takes elements of stream ciphers and block ciphers, to allow to handle large messages without compromising the security of the message or severely increasing the need of computational power to process the encryption algorithm. The cipher relies on the synchronization of chaotic systems by using state observers, the observer is capable of accurately recovering states and uncertainties within the fractional-order chaotic system. To test the algorithm and observer, the messages in this chapter are color images.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Laskin, N. (2000). Fractional market dynamics. Physica A: Statistical Mechanics and its Applications, 287(3–4), 482–492.
Hilfer, R. (2000). Applications of fractional calculus in physics. Singapore: World Scientific.
Zhou, X. J., Gao, Q., Abdullah, O., & Magin, R. L. (2010). Studies of anomalous diffusion in the human brain using fractional order calculus. Magnetic Resonance in Medicine, 63(3), 562–569.
Montesinos-Garcia, J. J., & Martinez-Guerra, R. (2019). A numerical estimation of the fractional-order Liouvillian systems and its application to secure communications. International Journal of Systems Science, 50(4), 791–806.
Montesinos-Garcia, J. J., & Martinez-Guerra, R. (2018). Colour image encryption via fractional chaotic state estimation. IET Image Processing, 12(10), 1913–1920.
Martinez-Guerra, R., Perez-Pinacho, C. A., & Gomez-Cortes, G. C. (2015). Synchronization of integral and fractional order chaotic systems. In A differential algebraic and differential geometric approach. Berlin: Springer.
Owolabi, K. M., Gomez-Aguilar, J. F., & Karaagac, B. (2019). Modelling, analysis and simulations of some chaotic systems using derivative with Mittag–Leffler kernel. Chaos, Solitons & Fractals, 125, 54-63.
Goufo, E. F. D., & Atangana, A. (2019). Modulating chaotic oscillations in autocatalytic reaction networks using atangana–baleanu operator. In Fractional derivatives with Mittag-Leffler kernel (pp. 135–158). Cham: Springer.
Li, Y., Chen, Y., & Podlubny, I. (2009). Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica, 45(8), 1965–1969.
Toufik, M., & Atangana, A. (2017). New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models. The European Physical Journal Plus, 132(10), 444.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Martínez-Guerra, R., Montesinos-García, J.J., Flores-Flores, J.P. (2023). Secure Communications by Using Atangana-Baleanu Fractional Derivative. In: Encryption and Decryption Algorithms for Plain Text and Images using Fractional Calculus . Synthesis Lectures on Engineering, Science, and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-20698-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-20698-6_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-20697-9
Online ISBN: 978-3-031-20698-6
eBook Packages: Synthesis Collection of Technology (R0)eBColl Synthesis Collection 12