International Association
for Cryptologic Research

Recently, obtaining vectorial Boolean bent functions of the form $Tr^{n}_{m}(P(x))$, where $P(x)\\in \\mathbb{F}_{2^{n}}[x]$, from Boolean bent functions of the form $Tr^{n}_{1}(P(x))$ has attracted several attentions and some open problems about this issue were proposed. This paper first provides three constructions of vectorial Boolean bent functions in the form $Tr^{n}_{m}(P(x))$, where two of them imply answers to two open problems proposed by E.Pasalic et al. and A.Muratovi\\\'{c}-Ribi\\\'{c} et al. respectively. And by analyzing known types of Boolean bent functions of the form $Tr^{n}_{1}(P(x))$, the existence and constructions of several types of vectorial Boolean bent functions in the form $Tr^{n}_{m}(P(x))$ are obtained.