Fibonacci Q-Matrix, Hyperchaos, and Galois Field (2⁸) for Augmented Medical Image Encryption

Abstract

This work introduces a novel image encryption algorithm specifically designed for the protection of color medical images, particularly crucial in the era of cloud storage, where security and privacy are paramount. The initial phase of the encryption process leverages a substantial array of Fibonacci Q-matrices to manipulate image data intricately. Following this, a unique Substitution box (S-box) transformation, developed in the Galois field (28), is applied to each of the RGB channels, further enhancing the security layers. The final phase employs an encryption key generated from a hyperchaotic system of differential equations that models a memristive coupled neural network, offering a high degree of unpredictability and resistance to attacks. Performance metrics show high security [Peak Signal-to-Noise Ratio (PSNR) of 8.21 dB, Mean Absolute Error (MAE) of 81.72, and ≈ 0 Pixel Cross-Correlation (PCC)], resistivity to occlusion and noise attacks, an enormous key space of 26112, and with savvy parallel processing techniques, a high encryption rate of 16.65 Mbps. The integration of this encryption algorithm into cloud storage systems is of significant importance, as it ensures secure and confidential handling of sensitive medical images, addressing the growing concerns about data breaches and unauthorized access in the healthcare sector. Compared to previous color image encryption techniques, this work provides a large key space of 26112 and a small encryption time per image of around 0.1 second for encrypting 16 images at once. Thus, this approach is suitable for medical imaging techniques, such as Computed Tomography (CT) scans that generate multiple images of the tissues for the diagnosis of the patient.