Linear cryptanalysis and modified DES with embedded parity check in the S-boxes

Abstract

It is a common belief that the presence of linear relations in the S-boxes of some block cipher algorithm facilitates its linear cryptanalysis and related attacks towards. In the present work, we clarify that claim in respect to a linear cryptanalysis (in the very spirit of Matsui’s classic one) applied to modified DES algorithm with S-boxes having parity check bits. The results of our investigations show that embedding parity checks in the outputs of these S-boxes does not generally guarantee more suitable for that kind of cryptanalysis best multi-round linear characteristics. Their structure, the corresponding bias and the number of effective bits depend crucially on the parity position chosen, and may lead not only to reduction but as well to growth in complexity of successful linear cryptanalysis compared to that towards the original DES.