A Hybrid Chaotic and Number Theoretic Approach for Securing DICOM Images

Abstract

The advancements in telecommunication and networking technologies have led to the increased popularity and widespread usage of telemedicine. Telemedicine involves storage and exchange of large volume of medical records for remote diagnosis and improved health care services. Images in medical records are characterized by huge volume, high redundancy, and strong correlation among adjacent pixels. This research work proposes a novel idea of integrating number theoretic approach with Henon map for secure and efficient encryption. Modular exponentiation of the primitive roots of the chosen prime in the range of its residual set is employed in the generation of two-dimensional array of keys. The key matrix is permuted and chaotically controlled by Henon map to decide the encryption keys for every pixel of DICOM image. The proposed system is highly secure because of the randomness introduced due to the application of modular exponentiation key generation and application of Henon maps for permutation of keys. Experiments have been conducted to analyze key space, key sensitivity, avalanche effect, correlation distribution, entropy, and histograms. The corresponding results confirm the strength of the proposed design towards statistical and differential crypt analysis. The computational requirements for encryption/decryption have been reduced significantly owing to the reduced number of computations in the process of encryption/decryption.