## IACR paper details

Title | ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS |
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Booktitle | IACR Eprint archive |
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Pages | |
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Year | 2004 |
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URL | http://eprint.iacr.org/2004/284 |
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Author | Qingshu Meng |
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Author | Huanguo Zhang |
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Author | Min Yang |
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Author | Jingsong Cui |
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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. |
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Search for the paper

@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
}

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