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Title:
Statistical and Algebraic Properties of DES
Authors: Stian Fauskanger, Igor Semaev
Abstract:D. Davies and S. Murphy found that there are at most 660 different probability distributions on the output from any three adjacent S-boxes after 16 rounds of DES [1]. In this paper it is shown that there are only 72 different distributions for S-boxes 4, 5 and 6. The distributions from S-box triplets are linearly dependent and the dependencies are described. E.g. there are only 13 linearly independent distributions for S-boxes 4, 5 and 6. A coset representation of DES S-boxes which reveals their hidden linearity is studied. That may be used in algebraic attacks. S-box 4 can be represented by significantly fewer cosets than the other S-boxes and therefore has more linearity. Open cryptanalytic problems are stated. [1] D. Davies and S. Murphy, “Pairs and Triplets of DES S-boxes”, Journal of Crypt. vol. 8(1995), pp. 1–25
ePrint: https://eprint.iacr.org/2015/803
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