Effective Construction of a Class of Bent Quadratic Boolean Functions

In this paper, we consider the characterization of the bentness of quadratic Boolean functions of the form $f(x)=\sum_{i=1}^{\frac{m}{2}-1} Tr^n_1(c_ix^{1+2^{ei}})+ Tr_1^{n/2}(c_{m/2}x^{1+2^{n/2}}) ,$where$n=me$,$m$isevenand$c_i\in GF(2^e)$\mathrm{.}Forageneral$m$, it is difficult to determine the bentness of these functions. We present the bentness of quadratic Boolean function for two cases: $m=2^v{p}^r$ and $m=2^{v}pq$, where $p$ and $q$ are two distinct primes. Further, we give the enumeration of quadratic bent functions for the case $m=2^{v}pq$.