Enhancing the Security and Efficiency of Biomedical Image Encryption through a Novel Hyper-Chaotic Logistic Map

In the field of medicine, the preservation of medical confidentiality stands as paramount, for it directly influences the secure treatment and dissemination of medical data.Safeguarding against falsification or unauthorized access to patients' medical data, including medical images, is crucial.Conventional methods of image encryption, alongside chaos-based encryption techniques, prove insufficient in addressing the wide-ranging demands for security and expediency.Consequently in this paper, we propose a pioneering hyper-chaotic logistic map characterized by a high Lyapunov dimension D L = 2.1886 and its rapid synchronization, which are used in biomedical image encryption, for the first time.This novel encryption method satisfies the most stringent security criteria, demonstrating remarkable resilience against various types of attacks, well in particular resilience against Statistical, Differential, Cipher-text, Noise, and Brute force attacks, as validated by compelling numerical values, we note a correlation coefficient spanning -1.8319 10 -4 to 6.6977 10 -4 and a vast key space of more than 2 298 .This well-established encryption duration ensures the shortest feasible encryption time, approximately 0.3 seconds for images of size 512x512.Finlay, in a comprehensive assessment, we showcase that our proposal satisfies strict security standards and surpasses the encryption techniques suggested by other researchers in terms of security and velocity.