A Semi-Linear Relation between Inputs and Outputs of DES S-Boxes

The Data Encryption Standard (DES) is the most widely used cryptosystem developed by a team of cryptographers working at IBM. DES has been cryptanalyzed intensively by resear-chers, but no efficient attack has been found on DES so far. This is mainly due to the lack of an obvious algebraic relation in the structure of S-boxes, which makes it impossible to use known methods to attack DES. S-boxes are the nonlinear part of DES with strong properties. This paper presents a semi-linear relation between input and output of S-boxes that could be used to cryptanalyze DES. This is based on Differential Cryptanalysis method proposed by Biham and Shamir.