Univariate Niho Bent Functions from o-Polynomials

Abstract

In this paper, we discover that any univariate Niho bent function is a sum of functions having the form of Leander-Kholosha bent functions with extra coefficients of the power terms. This allows immediately, knowing the terms of an o-polynomial, to obtain the powers of the additive terms in the polynomial representing corresponding bent function. However, the coefficients are calculated ambiguously. The explicit form is given for the bent functions obtained from quadratic and cubic o-polynomials. We also calculate the algebraic degree of any bent function in the Leander-Kholosha class.