Cryptology ePrint Archive: Report 2004/284
ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS
Qingshu Meng and Huanguo Zhang and Min Yang and Jingsong Cui
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.
Category / Keywords: secret-key cryptography / bent functions, Walsh transform, algebraic degree
Date: received 1 Nov 2004, last revised 1 Dec 2005
Contact author: mqseagle at sohu com
Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation
Note: a scholar told me one spelling error due to my unfamilarity to latex when i submitted this paper to eprint in 2004.
Version: 20051201:071440 (All versions of this report)
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