Optimizing Security of Medical Images Against Statistical Cryptanalysis Using Isomorphic Elliptic Curves

With the growing exchange of digital images in the Internet of Things (IoT), securing sensitive data, particularly medical images, has become critical. These images are essential for diagnosis but vulnerable to cyberattacks due to predictable anatomical patterns. Traditional encryption methods typically ignore these patterns, making them vulnerable to statistical attacks. We propose a novel image encryption scheme that incorporates both local and global image information using isomorphic elliptic curves (ECs) for optimal security. At the local level, central pixels and their neighboring are identified and independently encrypted using points on isomorphic ECs, selected through a carefully designed random walk algorithm. This process ensures robust disruption of spatial dependencies while maintaining computational efficiency. At the global level, a plain-image-sensitive shuffling generator is designed for a second confusion layer. The proposed scheme demonstrates high security against statistical cryptanalysis when evaluated using a benchmark medical image database MedPix and standard evaluation criteria. Additionally, comparisons with state-of-the-art methods reveal up to an 8-fold reduction in pixel correlation and significant computational efficiency, with encryption speeds up to 60 times faster than existing approaches. These findings highlight the potential of our scheme for real-world applications, particularly in securing sensitive medical data while balancing security and performance.