Secure medical image encryption with hyperelliptic curve based S-boxes

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.