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Paper: A NOVEL ALGORITHM ENUMERATING BENT FUNCTIONS

Authors:
Meng Qing-shu
Yang min
Zhang huan-guo
Cui jing-song
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URL: http://eprint.iacr.org/2004/274
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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
BibTeX
@misc{eprint-2004-12240,
  title={A NOVEL ALGORITHM ENUMERATING BENT FUNCTIONS},
  booktitle={IACR Eprint archive},
  keywords={foundations / homogeneous bent functions, Walsh transformation,},
  url={http://eprint.iacr.org/2004/274},
  note={ mqseagle@sohu.com 12712 received 16 Oct 2004, last revised 21 Oct 2004},
  author={Meng Qing-shu and Yang min and Zhang huan-guo and Cui jing-song},
  year=2004
}