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Paper: ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS

Authors:
Qingshu Meng
Huanguo Zhang
Min Yang
Jingsong Cui
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URL: http://eprint.iacr.org/2004/284
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Abstract: It is well known that the degree of a $2m$-variable bent function is at most $m.$ However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree $m$ in $2m$ variables when $m>3;$ there is no homogenous bent function of degree $m-1$ in 2m variables when $m>4;$ Generally, for any nonnegative integer $k$, there exists a positive integer $N$ such that when $m>N$, there is no homogeneous bent functions of degree $m-k$ in $2m$ variables. In other words, we get a tighter upper bound on the degree of homogeneous bent functions. A conjecture is proposed that for any positive integer $k>1$, there exists a positive integer $N$ such that when $m>N$, there exists homogeneous bent function of degree $k$ in $2m$ variables.
BibTeX
@misc{eprint-2004-12250,
  title={ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / bent functions, Walsh transform, algebraic degree},
  url={http://eprint.iacr.org/2004/284},
  note={ mqseagle@sohu.com 13118 received 1 Nov 2004, last revised 1 Dec 2005},
  author={Qingshu Meng and Huanguo Zhang and Min Yang and Jingsong Cui},
  year=2004
}