More permutation polynomials with differential uniformity six

Fractional differential equations with Legendre polynomials

More Classes of Complete Permutation Polynomials over $\F_q$

In this paper, by using a powerful criterion for permutation polynomials given by Zieve, we give several classes of complete permutation monomials over Fqr . In addition, we present a class of complete permutation multinomials, which is a generalization of recent work. Index Terms Finite field, Complete permutation polynomials, Walsh transform, Niho exponents.

Permutation polynomials and their differential properties over residue class rings

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) = a1x 1 + · · · + akx with integral coefficients, f(x) mod N permutes ZN if and only if f(x) mod N permutes Sμ for all μ | N , where Sμ = {0 < t < N : gcd(N, t) = μ} and SN = S0 = {0}. Based on it, we give a lower bound of the differential u...

Permutation Polynomials modulo m

This paper mainly studies problems about so called “permutation polynomials modulo m”, polynomials with integer coefficients that can induce bijections over Zm = {0, · · · , m−1}. The necessary and sufficient conditions of permutation polynomials are given, and the number of all permutation polynomials of given degree and the number induced bijections are estimated. A method is proposed to dete...

On inverse permutation polynomials

We give an explicit formula of the inverse polynomial of a permutation polynomial of the form xrf(xs) over a finite field Fq where s | q − 1. This generalizes results in [6] where s = 1 or f = g q−1 s were considered respectively. We also apply our result to several interesting classes of permutation polynomials.