On a Linear Cryptanalysis of a Family of Modified DES Ciphers with Even Weight S-Boxes

We investigate the effect of inserting extra linearity in the Data Encryption Standard (DES) through appropriate nonsingular linear encodings of the output of the individual S-boxes. More specifically, we examine the general situation when the output of each S-box of the DES is precoded separately into a properly constructed copy of the inherent even-weight code of length 4. The study is focused on finding multi-round linear characteristics for thus modified DES ciphers having maximal effectiveness. Depending on the particular encodings, it turns out that the effectiveness of interest may be larger but in most cases is smaller than that one for the original DES with the same number of rounds. The latter means that the complexity of successful linear cryptanalysis against these ciphers will mainly increase comparing to the DES itself. The present research extends in a natural way our previous work [Linear Cryptanalysis and Modified DES with Parity Check in the S-boxes, LNCS 9540 (2016), pp. 60-78].