A new color image encryption algorithm based on orthogonal Lagrange-Fourier moments and a 6D chaotic system of fractional-order

Faisal S. Alsubaei; Mohamed Meselhy Eltoukhy; Mohamed M. Darwish; Khalid M. Hosny; Faisal S. Alsubaei; Mohamed Meselhy Eltoukhy; Mohamed M. Darwish; Khalid M. Hosny

doi:10.3934/math.2026704

AIMS Mathematics

2026, Volume 11, Issue 6: 17166-17190. doi: 10.3934/math.2026704

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A new color image encryption algorithm based on orthogonal Lagrange-Fourier moments and a 6D chaotic system of fractional-order

1.
Department of Cybersecurity, College of Computer Science and Engineering, University of Jeddah, Jeddah, Saudi Arabia
2.
Department of Information Technology, College of Computing and Information Technology at Khulais, University of Jeddah, Jeddah, Saudi Arabia
3.
Department of Computer Science, University College of Al Wajh, University of Tabuk, Tabuk, Saudi Arabia
4.
Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig 44519, Egypt

Received: 19 March 2026 Revised: 25 April 2026 Accepted: 01 June 2026 Published: 15 June 2026
MSC : 94A08

To enhance image security in transmission and storage, we proposed a new color image encryption approach based on orthogonal Lagrange-Fourier moments (OLFMs) and a 6D fractional-order chaotic system (6D-FCS), in which the complex dynamic behavior of 6D-FCS is leveraged to generate highly unpredictable key streams, thereby ensuring strong confusion and diffusion properties. The proposed encryption algorithm comprised two stages: First, the 6D-FCS was employed to generate chaotic sequences that shuffle pixel positions, establishing the confusion stage and ensuring a high level of pixel scrambling. Second, OLFMs were used to modify pixel values, thereby achieving the diffusion stage. The numerical simulations and security analysis showed that the proposed encryption algorithm provides a key space greater than 2⁶⁴⁷, indicating strong security and outstanding encryption performance, as evidenced by key space, correlation coefficient, information entropy, histogram, UACI, and NPCR, thereby resisting statistical, differential, noise, and cropping attacks, highlighting its efficacy for image encryption. Moreover, the proposed encryption algorithm exhibits significant security and superiority to the related algorithms.
- 6D fractional-order chaotic system,
- confusion and diffusion stages,
- orthogonal Lagrange-Fourier moments,
- color image encryption
Citation: Faisal S. Alsubaei, Mohamed Meselhy Eltoukhy, Mohamed M. Darwish, Khalid M. Hosny. A new color image encryption algorithm based on orthogonal Lagrange-Fourier moments and a 6D chaotic system of fractional-order[J]. AIMS Mathematics, 2026, 11(6): 17166-17190. doi: 10.3934/math.2026704

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Abstract

To enhance image security in transmission and storage, we proposed a new color image encryption approach based on orthogonal Lagrange-Fourier moments (OLFMs) and a 6D fractional-order chaotic system (6D-FCS), in which the complex dynamic behavior of 6D-FCS is leveraged to generate highly unpredictable key streams, thereby ensuring strong confusion and diffusion properties. The proposed encryption algorithm comprised two stages: First, the 6D-FCS was employed to generate chaotic sequences that shuffle pixel positions, establishing the confusion stage and ensuring a high level of pixel scrambling. Second, OLFMs were used to modify pixel values, thereby achieving the diffusion stage. The numerical simulations and security analysis showed that the proposed encryption algorithm provides a key space greater than 2⁶⁴⁷, indicating strong security and outstanding encryption performance, as evidenced by key space, correlation coefficient, information entropy, histogram, UACI, and NPCR, thereby resisting statistical, differential, noise, and cropping attacks, highlighting its efficacy for image encryption. Moreover, the proposed encryption algorithm exhibits significant security and superiority to the related algorithms.

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