On the Diffusion Property of Iterated Functions

Jian Liu; Sihem Mesnager; Lusheng Chen

Paper 2015/873

On the Diffusion Property of Iterated Functions

Jian Liu, Sihem Mesnager, and Lusheng Chen

Abstract

For vectorial Boolean functions, the behavior of iteration has consequence in the diffusion property of the system. We present a study on the diffusion property of iterated vectorial Boolean functions. The measure that will be of main interest here is the notion of the degree of completeness, which has been suggested by the NESSIE project. We provide the first (to the best of our knowledge) two constructions of $(n,n)$-functions having perfect diffusion property and optimal algebraic degree. We also obtain the complete enumeration results for the constructed functions.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. IMACC CONFERENCE 2015
Keywords: Boolean functions degree of completeness perfect diffusion property algebraic degree balancedness.
Contact author(s): smesnager @ univ-paris8 fr
History: 2015-09-14: revised; 2015-09-13: received; See all versions
Short URL: https://ia.cr/2015/873
License: CC BY

BibTeX

@misc{cryptoeprint:2015/873,
      author = {Jian Liu and Sihem Mesnager and Lusheng Chen},
      title = {On the Diffusion Property of Iterated Functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/873},
      year = {2015},
      url = {https://eprint.iacr.org/2015/873}
}