Permutation polynomials and their differential properties over residue class rings

摘要

This paper mainly focuses on permutation polynomials over the residue class ring ~(ZN), where N>3 is composite. We have proved that for the polynomial f(x)=~(a1)x+~(a2x2)+?+ ~(akxk) with integral coefficients, f(x)modN permutes ~(ZN) if and only if f(x)modN permutes ~(Sμ) for all μ￡N, where ~(Sμ)={0