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 DESis precoded separately intoaproperly constructed copy of the inherent even-weight code of length 4. The study is focused on finding multi-round linear characteristics for thus modified DESciphers 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 DESwith the same number of rounds. The latter means that the complexity of successful linear cryptanalysis against these ciphers will mainly increase comparing to the DESitself. The present research extends inanatural way our previous work[Linear Cryptanalysis and Modified DESwith Parity Check in the S-boxes, LNCS 9540 (2016), pp. 60-78].
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