Univariate Niho Bent Functions From o-Polynomials
Lilya Budaghyan, Alexander Kholosha, Claude Carlet, Tor Helleseth · IEEE Transactions on Information Theory · 2016
In this paper, we discover that univariate form of a Niho bent function is a sum of functions having the form of a Leander-Kholosha bent function taken with particular coefficients from F*(2n) for every term. We know that the Niho bent functions are related to o-polynomials. The power terms in the univariate Niho bent function can be derived by working, in a first step, on each monomial of the corresponding o-polynomial separately, and in a second step, adding them to obtain the global expression. This allows, knowing the monomials in an o-polynomial, to obtain the power terms of the polynomial representing corresponding bent function. However, the coefficients are not calculated explicitly. 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.