Cryptographic Analysis of All 4 x 4 - Bit S-Boxes

Markku-Juhani O.  Saarinen

Paper 2011/218

Cryptographic Analysis of All 4 x 4 - Bit S-Boxes

Markku-Juhani O. Saarinen

Abstract

We present cryptanalytic results of an exhaustive search of all $16!$ bijective 4-bit S-Boxes. Previously affine equivalence classes have been exhaustively analyzed in 2007 work by Leander and Poschmann. We extend on this work by giving further properties of the optimal S-Box linear equivalence classes. In our main analysis we consider two S-Boxes to be cryptanalytically equivalent if they are isomorphic up to the permutation of input and output bits and a XOR of a constant in the input and output. We have enumerated all such equivalence classes with respect to their differential and linear properties. These equivalence classes are equivalent not only in their differential and linear bounds but also have equivalent algebraic properties, branch number and circuit complexity. We describe a ``golden'' set of S-boxes that have ideal cryptographic properties. We also present a comparison table of S-Boxes from a dozen published cryptographic algorithms.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Accepted to Selected Areas in Cryptography (SAC) 2011, August 11-12, 2011 Toronto, Ontario, Canada.
Keywords: S-Box Differential cryptanalysis Linear cryptanalysis Exhaustive permutation search.
Contact author(s): mjos @ iki fi
History: 2011-07-12: last of 9 revisions; 2011-05-07: received; See all versions
Short URL: https://ia.cr/2011/218
License: CC BY

BibTeX

@misc{cryptoeprint:2011/218,
      author = {Markku-Juhani O.  Saarinen},
      title = {Cryptographic Analysis of All 4 x 4 - Bit S-Boxes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/218},
      year = {2011},
      url = {https://eprint.iacr.org/2011/218}
}