Paper 2005/100

almost enumeration of 8-variable bent functions

Qingshu Meng, Huanguo Zhang, Jingsong Cui, and 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.

Note: one reference is added and several spelling mistakes are corrected

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Reed-Muller codegroup actionbent functions
Contact author(s)
mqseagle @ sohu com
History
2007-01-27: last of 2 revisions
2005-04-05: received
See all versions
Short URL
https://ia.cr/2005/100
License
Creative Commons Attribution
CC BY

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},
      note = {\url{https://eprint.iacr.org/2005/100}},
      url = {https://eprint.iacr.org/2005/100}
}
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