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 DC and 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 DC and DS vectorial functions can respectively reach (n + 1)/2 and n/3. In addition, a construction method of semi-bent functions from F 3n 2 → F n 2 by using almost bent (AB) functions on F n 2 is given.