Improving Chaotic Image Encryption Using Maps with Small Lyapunov Exponents
Abstract
Chaos-based encryption is one of the promising cryptography techniques that can be used. Although chaos-based encryption provides excellent security, the finite precision of number representation in computers affects decryption accuracy negatively. In this paper, a way to mitigate some problems regarding finite precision is analyzed. We show that the use of maps with small Lyapunov exponents can improve the performance of chaotic encryption scheme, making it suitable for image encryption.
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An image-encryption scheme based on a chaotic system with a small LE can reduce decryption error by using a chaotic system with low numerical solution error, and experiments on an XOR encryption scheme proved its positive effect.
“However, an image-encryption scheme based on chaotic systems with a small LE was proposed in [53].The authors utilized a chaotic system with a low numerical solution error to reduce the decryption error and proved its positive effect by conducting experiments on an XOR encryption scheme.”
From Chaos-Based Image Encryption: Review, Application, and Challenges (2023) · cites this paper as [53]
The Lyapunov exponent control strategy is suitable for arbitrary chaotic interval maps.
“This strategy is suitable for the Lyapunov exponent control method of an arbitrary chaotic interval map.”
From Chaos-Based Image Encryption: Review, Application, and Challenges (2023) · cites this paper as [53]
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Research works printed but not linked: 8
- [1][1] A.V. Tutueva, D.N. Butusov, D.O. Pesterev, D.A. Belkin, N.G. Ryzhov, 'Novel normalization technique for chaotic pseudo-random number generators based on semi-implicit ODE solvers,' 2017 International Conference on Quality Management, Transport and Information Security, Information Technologies (IT&QM&IS), Saint Petersburg, Russia, pp. 284-287, Sept. 2017. -
- [3][3] L.G. Nardo, E.G. Nepomuceno, J. Arias-Garcia, D. N. Butusov, 'Image encryption using finite-precision error,' Chaos, Solitons and Fractals, vol. 123, pp. 69-78, Jun. 2019. -
- [4][4] E.G. Nepomuceno, L. G. Nardo, J. Arias-Garcia, D. N. Butusov, A. Tutueva, 'Image encryption based on the pseudo-orbits from 1D chaotic map,' Chaos, vol. 29, no. 6, Jun. 2019. -
- [5][5] A.M. Mendes, E.G. Nepomuceno, 'A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions,' Int. J. Bifurc. Chaos, vol. 26, no. 13, p. 1650226, Dec. 2016. -
- [6][6] E.G. Nepomuceno, S.A.M. Martins, 'A lower bound error for freerun simulation of the polynomial NARMAX,' Syst. Sci. Control Eng., vol. 4, no. 1, pp. 50-58, Jan. 2016. -
- [7][7] H. Kantz, 'A robust method to estimate the maximal Lyapunov exponent of a time series,' Phys. Lett. A, vol. 185, no. 1, pp. 77-87, Jan. 1994. -
- [8][8] I.V. Bogach, D.D. Lupiak, Yu.Yu. Ivanov, O.V. Stukach, "Analysis and Experimental Research of Modifications of the Image Segmentation Method Using Graph Theory". 2019 International Siberian Conference on Control and Communications (SIBCON). 1820 April 2019, Russia. DOI: 10.1109/SIBCON.2019.8729659. - · DOI
- [9][9] T.D. Rogers, D.C. Whitley, 'Chaos in the cubic mapping,' Mathematical Modelling,Vol. 4, Issue 1, pp. 9-25, 1983.
Cited by
Sorted by citations
Chaos-Based Image Encryption: Review, Application, and Challenges
Zhang, B., & Liu, L. (2023) · Mathematics · doi:10.3390/math11112585 · Cited by 328 · see citing works
“However, an image-encryption scheme based on chaotic systems with a small LE was proposed in [53].”
Method
- Authors
- Santos, T. A., Magalhaes, E. P., Basilio, N. P., Nepomuceno, E. G., Karimov, T. I., & Butusov, D. N.
- Affiliations
- Federal University of São João del-Rei (BR)
- Venue
- 2020 Moscow Workshop on Electronic and Networking Technologies (MWENT)
- Publisher
- IEEE
- Published
- 2020-03
- Pages
- 1-4
- OpenAlex
- W3016445469
- Cited by
- 7
- References
- 0
- Citations by year
- 2025: 2 · 2024: 2 · 2023: 1 · 2021: 1 · 2020: 1
- FWCI
- 0.23
- Type
- conference paper
- Language
- en
- Open access
- closed
- Licence
- Locations
- Moscow Workshop on Electronic and Networking Technologies (MWENT) (publishedVersion)
- Maynooth University ePrints and eTheses Archive (Maynooth University) (acceptedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Keywords
- chaotic image encryption, Lyapunov exponents, chaotic maps, finite precision effects, chaos-based cryptography
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