A Robust Golden Matrix Based T-Dna Rules for Securing Medical Images

Abstract

This paper presents a novel hybrid image encryption technique that integrates the Logistic Map, Golden Matrix transformation, and Reversible T-DNA rules to ensure enhanced security and efficiency in medical image protection. The proposed method leverages the chaotic behavior of the Logistic Map for generating sensitive key streams, while the Golden Matrix, based on the golden ratio and Lucas balancing numbers, introduces complex pixel transformations. Additionally, the T-DNA transformation, inspired by DNA computing, enables robust and reversible encryption at the nucleotide level. Our approach achieves strong cryptographic properties including high entropy values (~7.99), reduced pixel correlation, and significant resistance to statistical and differential attacks. Comparative experiments demonstrate that the proposed method outperforms traditional Fibonacci-based ciphers in both security strength and execution time, reducing computational time by over 50% for 255×255 images. Furthermore, the framework is adaptable to various image sizes and formats. These results establish the proposed method as a secure, efficient, and bio-inspired solution for safeguarding sensitive medical images in modern cryptographic applications.