With the surge of digital advancements, securing medical images has become increasingly vital due to the confidential nature of healthcare information. This research introduces an innovative image encryption method that combines Elliptic Curve Cryptography (ECC) and the Blum-Goldwasser Cryptosystem (BGC) within a public-key infrastructure, further enhanced by chaotic sequence generation to boost randomness. The encryption workflow initiates with a secure key exchange that leverages the computational efficiency of ECC alongside the probabilistic security features of BGC, which are grounded in the discrete logarithm and quadratic residuosity problems. To enhance data obscurity, a chaotic map is utilized for pixel randomization, ensuring high levels of unpredictability and resistance to pattern-based attacks. The integration of ECC and BGC provides multiple security layers, making the system robust against brute-force attempts and differential cryptanalysis. Comprehensive performance evaluations through extensive simulations demonstrate the proposed method's superiority over existing encryption techniques. Key performance indicators achieved include an information entropy of 7.9998, indicating near-maximum randomness; an average correlation coefficient of 0.0010, signifying negligible pixel dependency; a Number of Pixels Change Rate (NPCR) of 99.6901%, and a Unified Average Changing Intensity (UACI) of 33.5260%, both highlighting strong resistance to differential attacks. Additionally, the encryption process is highly efficient, completing in merely 0.142 seconds, underscoring its feasibility for real-time applications. These findings validate the proposed hybrid chaotic image encryption approach as a robust solution for protecting medical data and other sensitive imagery against evolving cyber threats.

Keywords: Blum-Gold wasser Cryptosystem, Chaotic Encryption, Cryptanalysis, Elliptic Curve Cryptography, Image Encryption, Public Key Encryption.