A highly nonlinear S-box based on a fractional linear transformation

We study the structure of an S-box based on a fractional linear transformation applied on the Galois field [Formula: see text]. The algorithm followed is very simple and yields an S-box with a very high ability to create confusion in the data. The cryptographic strength of the new S-box is critically analyzed by studying the properties of S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability and differential approximation probability. We also apply majority logic criterion to determine the effectiveness of our proposed S-box in image encryption applications.