# Three classes of balanced vectorial semi-bent functions

### Abstract

Semi-bent functions play an important role in symmetric ciphers and sequence designs. So far, there are few studies related to the construction of vectorial semi-bent functions even though lots of work has been done on single-output semi-bent functions. In this paper, three classes of balanced vectorial semi-bent functions are presented with varying cryptographic properties. The classes denoted $\mathcal{DC}$ and $\mathcal{DS}$ are constructed using disjoint codes and disjoint spectra functions, respectively. The former class has a useful provable property that its component functions do not admit linear structures. It is shown that the number of output bits of the constructed $n$-variable $\mathcal{DC}$ and $\mathcal{DS}$ vectorial functions can respectively reach $(n+1)/2$ and $n/3$. In addition, a construction method of semi-bent functions from $\mathbb{F}_2^{3n}\to\mathbb{F}_2^n$ by using almost bent (AB) functions on $\mathbb{F}_2^n$ is given.

Publication
Designs, Codes and Cryptography