On some properties of Chebyshev polynomial sequences modulo 2^k

Abstract

In this paper, we give a characterization of permutation polynomials modulo 2^k: the period of sequences generated by iterating such polynomials is a power of two. Chebyshev polynomials are examples of such polynomials. Based on these findings, we also evaluate the factual key space of a recently proposed key exchange protocol based on Chebyshev polynomials modulo 2^k.