Secure medical image encryption for healthcare applications: A fractional 4D chaotic system and symmetry-matrix-based approach

Abed Saif Ahmed Alghawli; Mohamed M. Darwish; Abed Saif Ahmed Alghawli; Mohamed M. Darwish

doi:10.3934/math.2026279

AIMS Mathematics

2026, Volume 11, Issue 3: 6744-6776. doi: 10.3934/math.2026279

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Secure medical image encryption for healthcare applications: A fractional 4D chaotic system and symmetry-matrix-based approach

Abed Saif Ahmed Alghawli ^{1
,
,},
Mohamed M. Darwish ^2,3

1.
Computer Science Department, Prince Sattam Bin Abdulaziz University, Aflaj, Kingdom of Saudi Arabia
2.
Department of Computer Science, University College of Al Wajh, University of Tabuk, Tabuk, Saudi Arabia
3.
Department of Computer Science, Faculty of Computers and Information, Assiut University, Assiut 71516

Received: 03 January 2026 Revised: 09 February 2026 Accepted: 09 March 2026 Published: 16 March 2026
MSC : 94A08

Safeguarding medical images against unauthorized access and alteration during storage and transmission is a critical challenge in modern telemedicine systems. This paper introduces a robust method to encrypt medical images in which the confusion stage is driven by a four-dimensional (4D) fractional-order chaotic system, and the diffusion process utilizes a symmetric matrix integrated with a one-dimensional (1D) chaotic map. The fractional 4D chaotic system reveals intricate dynamic behavior and is extremely sensitive to initial conditions, which enhances the confusion capability by thoroughly scrambling pixel positions. The symmetry matrix is combined with a generated chaotic sequence from a 1D chaotic map during the diffusion process that ensures strong pixel intensity diffusion and key dependence. Numerous experiments carried out on a variety of medical images confirm the outstanding performance of the suggested method. The suggested method features a key space exceeding 2¹⁰⁰, exhibiting significant robustness to brute-force attacks. It achieves unified average changing intensity (UACI) values above 33% and number of pixels change rate (NPCR) values exceeding 99.6%, confirms robustness to differential attacks, and successfully resists chosen-plaintext and known-plaintext attacks. Additionally, the low pixel correlation and uniform histograms, along with average values of information entropy of 7.9973 and 7.9993 for 256×256 and 512×512 images, respectively, demonstrate strong resilience to statistical attacks. Furthermore, robust evaluations against cropping and noise attacks demonstrate the scheme's practical security, highlighting its suitability for the safe storage and transmission of medical images in healthcare applications. Compared with related methods, the suggested method offers superior security performance.
- medical image encryption,
- confusion process,
- diffusion process,
- symmetry matrix,
- fractional order 4D chaotic system
Citation: Abed Saif Ahmed Alghawli, Mohamed M. Darwish. Secure medical image encryption for healthcare applications: A fractional 4D chaotic system and symmetry-matrix-based approach[J]. AIMS Mathematics, 2026, 11(3): 6744-6776. doi: 10.3934/math.2026279

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Abstract

Safeguarding medical images against unauthorized access and alteration during storage and transmission is a critical challenge in modern telemedicine systems. This paper introduces a robust method to encrypt medical images in which the confusion stage is driven by a four-dimensional (4D) fractional-order chaotic system, and the diffusion process utilizes a symmetric matrix integrated with a one-dimensional (1D) chaotic map. The fractional 4D chaotic system reveals intricate dynamic behavior and is extremely sensitive to initial conditions, which enhances the confusion capability by thoroughly scrambling pixel positions. The symmetry matrix is combined with a generated chaotic sequence from a 1D chaotic map during the diffusion process that ensures strong pixel intensity diffusion and key dependence. Numerous experiments carried out on a variety of medical images confirm the outstanding performance of the suggested method. The suggested method features a key space exceeding 2¹⁰⁰, exhibiting significant robustness to brute-force attacks. It achieves unified average changing intensity (UACI) values above 33% and number of pixels change rate (NPCR) values exceeding 99.6%, confirms robustness to differential attacks, and successfully resists chosen-plaintext and known-plaintext attacks. Additionally, the low pixel correlation and uniform histograms, along with average values of information entropy of 7.9973 and 7.9993 for 256×256 and 512×512 images, respectively, demonstrate strong resilience to statistical attacks. Furthermore, robust evaluations against cropping and noise attacks demonstrate the scheme's practical security, highlighting its suitability for the safe storage and transmission of medical images in healthcare applications. Compared with related methods, the suggested method offers superior security performance.

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