On semi-bent functions with Niho exponents

Semi-bent functions are a kind of Boolean functions with high nonlinearity. They have important applications in cryptography and communications. In this paper, two classes of semi-bent functions with Niho exponents are proposed. It is shown that all semi-bent functions of the first class attain the maximum algebraic degree, and there exists one subclass of semi-bent functions with maximum algebraic degree in the second class. Furthermore, two examples of semi-bent functions in a small field are given by using the zeros of some Kloosterman sums. Based on the result given by Kim et al., two examples of infinite families of semi-bent functions are also obtained. These results provide more available Boolean functions with high nonlinearity and high algebraic degrees for designing the filter generators of stream ciphers.