Method to Improve the Cryptographic Properties of S-Boxes

Abstract

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.

A graph theory approach to heuristic generation of cyclic permutations

“…However, this method does not fully guarantee the absence of fixed points. In this regard, authors of [20] show how is possible to construct an isomorphic AES, i.e., an equivalent encryption process, exploiting the linear properties of the round function with the affine equivalent S-box S ′ RD (x) = S RD (x) ⊕ q = L • x −1 for each x ∈ V 8 , which has 3 fixed points, 2 opposite fixed points and a lower value of nonlinearity of 96 [21]. This isomorphic block cipher conduct to further analysis that may lead to a weakening of the AES strength.…”

“…This isomorphic block cipher conduct to further analysis that may lead to a weakening of the AES strength. Other papers searching cryptographically good S-boxes are [21][22][23][24][25][26], however, most of them try to get rid of the fixed points be means of the affine equivalence.…”