Paper 2004/274

A NOVEL ALGORITHM ENUMERATING BENT FUNCTIONS

Meng Qing-shu, Yang min, Zhang huan-guo, and Cui jing-song

Abstract

By the relationship between the Walsh spectra at partial points and the Walsh spectra of its sub-functions, by the action of general linear group on the set of Boolean functions, and by the Reed-Muller transform, a novel method is developed, which can theoretically construct all bent functions. With this method, we enumerate all bent functions in 6 variables; in 8-variable case, our method is more efficient than the method presented by Clark though we still can not enumerate all bent functions; enumeration of all homogeneous bent functions of degree 3 in eight variables can be done in one minute by a P4 1.7G HZ computer; construction of homogenous bent function of degree 3 in 10 variables is efficient too; the nonexistence of homogeneous bent functions in 10 variables of degree 4 is proved

Note: this paper presents an algorithm enumerating bent functions.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
homogeneous bent functionsWalsh transformation
Contact author(s)
mqseagle @ sohu com
History
2004-10-30: received
Short URL
https://ia.cr/2004/274
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2004/274,
      author = {Meng Qing-shu and Yang min and Zhang huan-guo and Cui jing-song},
      title = {A NOVEL ALGORITHM ENUMERATING BENT FUNCTIONS},
      howpublished = {Cryptology ePrint Archive, Paper 2004/274},
      year = {2004},
      note = {\url{https://eprint.iacr.org/2004/274}},
      url = {https://eprint.iacr.org/2004/274}
}
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