Cryptographic Uncertainness: Some Experiments on Finite Semifield Based Substitution Boxes

Abstract

Substitution boxes (S-boxes) are an important part of the design of block ciphers. They provide nonlinearity and so the security of the cipher depends strongly on them. Some block ciphers use S-boxes given by lookup tables (e.g., DES) where as others use S-boxes obtained from finite field operations (e.g., AES). As a generalization of the latter, finite semifields (i.e., finite nonassociative division rings) have been suggested as algebraic structures from which S-boxes with good cryptographic properties might be obtained. In this paper we present the results of experiments on the construction of S-boxes from finite semifields of orders 256 and 64, using the left and right inverses of these rings.