Secure medical image encryption with hyperelliptic curve based S-boxes
Amal S. Alali, Rashad Ali, Muhammad Kamran Jamil, Javed Ali, Gulraiz
Abstract
Two fundamental prerequisites are needed for symmetric encryption techniques. Diffusion is the first of them. Confusion is the most significant and second factor. Substitution box (S-box) structure in these algorithms typically satisfies this condition. S-box architectures need to be robust as a result. The encryption procedure will therefore be hard to crack if the S-box is cryptographically sound. Getting a powerful S-box, however, is a challenging issue. Recent research has demonstrated that the security of a cryptosystem may be significantly improved by switching from static to dynamic S-boxes. Consequently, it is now essential to create new, secure S-boxes. In this paper, we proposed a practical method for generating dynamic S-boxes using a specific class of hyperelliptic curves defined over prime fields. The method involves selecting a large prime number and a random integer as parameters, iterating through candidate points on the curve, and applying a filtering condition to extract valid points. These points are then processed using a two-dimensional function and modular reduction to produce a list of unique values. If 256 unique values are obtained, they are reshaped into a [Formula: see text] S-box matrix. Computational results show that our approach can produce cryptographically robust S-boxes with a security level similar to certain existing S-boxes constructed using alternative mathematical structures. Compared to alternative solutions, our S-box exhibits exceptional non-linearity and resilience, effectively fending off both linear and differential assaults. The results of our investigation highlight how well this hyperelliptic curve-based S-box works to improve medical picture security.