Nonsingular Polynomials from Feedback Shift Registers

摘要

In this paper, we present nonsingular permutation polynomials from nonsingular feedback shift registers and examine nonlinearity and algebraic degree of nonsingular polynomials of certain forms. The upper bound on the nonlinearity of nonsingular Boolean functions is investigated. We also present n-variable nonsingular Boolean functions with algebraic degree n - 1 and highest possible nonlinearity for odd n.