One-stroke polynomials over a ring of modulo $2^w$

TL;DR

This paper characterizes one-stroke permutation polynomials over rings modulo 2^w, identifying conditions for maximal period, which are useful for cryptography and pseudo-random number generation.

Contribution

It provides the necessary and sufficient conditions for one-stroke polynomials to be permutation polynomials with maximal periods over rings modulo 2^w.

Findings

Derived conditions for one-stroke permutation polynomials

Identified criteria for maximal period polynomials

Applicable to cryptography and pseudo-random number generators

Abstract

Permutation polynomials over a ring of modulo $2^w$ are compatible with digital computers and digital signal processors, and so they are in particular expected to be useful for cryptography and pseudo random number generator. In general, the period of the polynomial should be long in such fields. In this paper, we derive the necessary and sufficient condition which specify one-stroke polynomials which are permutation polynomials whose periods are maximized.