On Inverses of Permutation Polynomials of Small Degree over Finite Fields

Yanbin Zheng, Qiang Wang, Wenhong Wei

Published 2018-12-17Version 1

Permutation polynomials (PPs) and their inverses have applications in cryptography, coding theory and combinatorial design. In this paper, we make a brief summary of the inverses of PPs of finite fields,and list the inverses of all normalized PPs of degree at most 5. In this list, the explicit inverse of a class of fifth degree PPs is our main result,which is obtained by using some congruences of binomial coefficients, the Lucas' theorem, and a known formula for the inverses of PPs of finite fields.