Statistical and Algebraic Properties of DES

Stian Fauskanger; Igor Semaev

Paper 2015/803

Statistical and Algebraic Properties of DES

Stian Fauskanger and 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

Note: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-38898-4_6

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Springer International Publishing
DOI: 10.1007/978-3-319-38898-4_6
Keywords: DES S-box output distributions linear dependencies coset representation
Contact author(s): stian @ fauskanger me
History: 2016-05-10: last of 2 revisions; 2015-08-11: received; See all versions
Short URL: https://ia.cr/2015/803
License: CC BY

BibTeX

@misc{cryptoeprint:2015/803,
      author = {Stian Fauskanger and Igor Semaev},
      title = {Statistical and Algebraic Properties of {DES}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/803},
      year = {2015},
      doi = {10.1007/978-3-319-38898-4_6},
      url = {https://eprint.iacr.org/2015/803}
}