Method to Improve the Cryptographic Properties of S-Boxes

This study presents a method based on elementary logic and arithmetic operations to enhance the cryptographic properties of Substitution Boxes (S-Boxes). S-Boxes are a crucial component of cryptosystems, as they apply the confusion principle to information before it is encrypted, making them vital for ensuring the security of sensitive information transmitted through insecure channels. The proposed method employs bitwise XOR, Modular Addition, and Circular Shift operations, which are applied to selected S-Boxes, resulting in numerous S-Box variants that have no fixed points or reverse fixed points. We found that some of these variants can increase nonlinearity when using modular addition or circular shift operations and are therefore more suitable for use in cryptosystems. Our study contributes to the understanding of how S-Boxes can be enhanced by elementary logic and arithmetic operations. We recommend using the proposed method with the bitwise XOR operation when the S-Box has high nonlinearity (112) but requires removing fixed points and reverse fixed points. Otherwise, first use modular addition or circular shift operations to increase nonlinearity.