TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Chaos-based image encryption using discrete maps

, * , , , ,

* Corresponding author · click or hover a name for details

pp. 4097–4107Vol. 29Issue 10-BOctober 2026DOI: 10.47974/JDMSC-3035 Crossmark XML
Received:
01 Apr 2026
Published Online:
31 Oct 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-3035
Pages:
4097–4107

Abstract

Image encryption using chaos has become an effective method of protecting digital visual information because of its high sensitivity, randomness and nonlinear nature. The current paper outlines a discrete map-based encryption model which uses chaotic sequences to provide strong protection to images. The model proposed combines both permutation and diffusion processes based on discrete chaotic maps to attain good confusion and diffusion properties. The encryption algorithm is a stepwise algorithm that is meant to encode pixel positions and intensities and the decryption algorithm, when the correct keys are used, would guarantee proper decoding of the algorithm. It can be shown using key sensitivity analysis that any small change in the initial parameters will lead to a large difference in the output, which will make it more resistant to brute-force and differential attacks. The effectiveness of the proposed chaos-based encryption scheme is confirmed by the experimental results showing a high level of entropy, low level of correlation, and enhanced security performance over traditional techniques.

Keywords

Subject Classifications

68P2568M2537D45

References

[1] B. Zhang and L. Liu, “Chaos-based image encryption: Review, application, and challenges,” Mathematics, vol. 11, no. 11, Art. no. 2585 (2023), doi: 10.3390/math11112585.

[2] A Dinu and M. Frunzete, “Image encryption using chaotic maps: Development, application, and analysis,” Mathematics, vol. 13, no. 16, Art. no. 2588 (2025), doi: 10.3390/math13162588.

[3] R. Amutha, “Chaotic image encryption using circular shift and modular arithmetic,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 1, pp. 215–228 (2026), doi: 10.47974/JDMSC-2411.

[4] M. Lawnik, L. Moysis, and C. Volos, “Chaos-based cryptography: Text encryption using image algorithms,” Electronics, vol. 11, no. 19, Art. no. 3156 (2022), doi: 10.3390/electronics11193156.

[5] R. Premkumar, M. Mahdal, and M. Elangovan, “An efficient chaos-based image encryption technique using bitplane decay and genetic operators,” Sensors, vol. 22, no. 20, Art. no. 8044 (2022), doi: 10.3390/s22208044.

[6] H. Fan, C. Zhang, H. Lu, M. Li, and Y. Liu, “Cryptanalysis of a new chaotic image encryption technique based on multiple discrete dynamical maps,” Entropy, vol. 23, no. 12, Art. no. 1581 (2021), doi: 10.3390/e23121581.

[7] M. J. Jaber, Z. J. Jaber, and A. J. Obaid, “An efficient hybrid chaotic map-based encryption technique for multiple image security systems,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 5, pp. 1507–1522 (2024), doi: 10.47974/JDMSC-1934.

[8] H. Zhang, X. Feng, J. Sun, and P. Yan, “Chaotic image security techniques and developments: A review,” Mathematics, vol. 13, no. 12, Art. no. 1976 (2025), doi: 10.3390/math13121976.

[9] J. A. Vargas Valencia, M. A. Londoño-Arboleda, H. D. Salinas Jiménez, C. A. Marín Arango, and L. F. Duque Gómez, “Image encryption using chaotic box partition–permutation and modular diffusion with PBKDF2 key derivation,” Journal of Cybersecurity and Privacy, vol. 6, no. 1, Art. no. 21 (2026), doi: 10.3390/jcp6010021.

[10] L. Liu, “Preface to the special issue ‘Chaos-based secure communication and cryptography’,” Mathematics, vol. 14, no. 7, Art. no. 1089, 2026, doi: 10.3390/math14071089.

[11] M. T. Anderson, F. Müller, and L. Kovács, “A comprehensive review of spectral graph methods for multi-domain routing protocols: Security models, optimization techniques, and emerging computing applications,” International Journal of Recent Advances in Engineering and Technology, vol. 14, no. 2, pp. 175–181 (2025). [Online], doi: 10.65521/intjournalrecadvengtech.v14i2.2034.

[12] N. Chaudhary, T. B. Shahi, and A. Neupane, “Secure image encryption using chaotic, hybrid chaotic and block cipher approach,” Journal of Imaging, vol. 8, no. 6, Art. no. 167 (2022), doi: 10.3390/jimaging8060167.

[13] P. Sahane, M. Gulhane, N. Rakesh, S. M. M. Naidu, M. Grover, and V. Mahajan, “Evaluating lightweight encryption schemes for resource-constrained devices in wireless sensor networks,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 5-A, pp. 1803–1812 (2025).

Views: 6Downloads: 2Citations: 0