Welcome to the resource topic for
**2004/284**

**Title:**

ON THE DEGREE OF HOMOGENEOUS BENT FUNCTIONS

**Authors:**
Qingshu Meng, Huanguo Zhang, Min Yang, 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.

**ePrint:**
https://eprint.iacr.org/2004/284

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

**Example resources include:**
implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .