A medical image encryption scheme based on Mobius transformation and Galois field

Data security and privacy are considered to be the biggest problems faced by service providers who have worked with public data for a long time. A key element of modern encryption that is utilized to increase textual confusion is the Substitution box (S-box) and the algebraic strength of the S-box has a significant impact on how secure the encryption method is. In this article, we present a unique method that uses a linear fractional transformation on a finite field to produce cryptographically robust S-boxes. Firstly, we choose a specific irreducible polynomial of degree 8 in DOUBLE-STRUCK CAPITAL Z2[x] to construct GF (28). Later, we used the action of PGL(2, GF (28)) on GF (28) to generate a robust S-box. The effectiveness of the built-in S-box was evaluated using several criteria including non-linearity, differential uniformity, strict avalanche criteria, linear approximation probability, and bit independence criterion. The proposed S-box's characteristics are compared to those of most recent S-boxes to confirm the higher performance. Additionally, the S box was used to encrypt images to show its usefulness for multimedia security applications. We performed several tests, including contrast, correlation, homogeneity, entropy, and energy, to evaluate the success of the encryption technique. The proposed method for ciphering an image is very effective, as proven by its comparison with several S boxes.