ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS

Qingshu Meng; Huanguo Zhang; Min Yang; Jingsong Cui

Paper 2004/284

ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS

Qingshu Meng, Huanguo Zhang, Min Yang, and Jingsong Cui

Abstract

It is well known that the degree of a $2 m$ -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 $2 m$ variables when $m > 3;$ there is no homogenous bent function of degree $m - 1$ in 2m variables when Generally, for any nonnegative integer , there exists a positive integer such that when , there is no homogeneous bent functions of degree in 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 , there exists a positive integer such that when , there exists homogeneous bent function of degree in variables.

Note: a scholar told me one spelling error due to my unfamilarity to latex when i submitted this paper to eprint in 2004.

Metadata

Available format(s): PDF PS
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: bent functions Walsh transform algebraic degree
Contact author(s): mqseagle @ sohu com
History: 2005-12-01: revised; 2004-11-03: received; See all versions
Short URL: https://ia.cr/2004/284
License: CC BY

BibTeX

@misc{cryptoeprint:2004/284,
      author = {Qingshu Meng and Huanguo Zhang and Min Yang and Jingsong Cui},
      title = {{ON} {THE} {DEGREE} {OF} {HOMOGENEOUS} {BENT} {FUNCTIONS}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2004/284},
      year = {2004},
      url = {https://eprint.iacr.org/2004/284}
}