Piecewise constructions of inverses of cyclotomic mapping permutation polynomials

TL;DR

This paper introduces a piecewise interpolation method to explicitly construct inverses of cyclotomic mapping permutation polynomials over finite fields, simplifying the inversion process for these complex functions.

Contribution

It provides a novel piecewise interpolation approach to explicitly invert cyclotomic mapping permutation polynomials over arbitrary finite fields.

Findings

Explicit inverse formulas for cyclotomic permutation polynomials

Applicable to arbitrary finite fields

Simplifies the inversion process for these polynomials

Abstract

Given a permutation polynomial of a large finite field, finding its inverse is usually a hard problem. Based on a piecewise interpolation formula, we construct the inverses of cyclotomic mapping permutation polynomials of arbitrary finite fields.