almost enumeration of 8-variable bent functions

Qingshu Meng; Huanguo Zhang; Jingsong Cui; Min Yang

Paper 2005/100 Original: eprint.iacr.org/2005/100 ↗

almost enumeration of 8-variable bent functions

Qingshu Meng

Huanguo Zhang

Jingsong Cui

Min Yang

Abstract

Bent functions are important cryptographic Boolean functions. In order to enumerate eight-variable bent functions, we solve the following three key problems. Firstly, under the action of $AGL(7,2)$, we almost completely classify $R(4,7)/R(2,7)$. Secondly, we construct all seven-variable \emph{plateaued} functions from the orbits of $R(4,7)/R(2,7)$. Thirdly, we present a fast algorithm to expand \emph{plateaued} function into bent functions. Based on the results above, it is feasible to enumerate eight-variable bent functions in practice.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2007-01-27: last updated; 2005-04-05: published
Short URL: https://ia.cr/2005/100
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2005/100,
      author = {Qingshu Meng and Huanguo Zhang and Jingsong Cui and Min Yang},
      title = {almost enumeration of 8-variable bent functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/100},
      year = {2005},
      url = {https://eprint.iacr.org/2005/100}
}