On Inverses of Permutation Polynomials of Small Degree Over Finite Fields.

Permutation polynomials (PPs) and their inverses have applications in cryptography, coding theory and combinatorial design theory. In this paper, we make a brief summary of the inverses of PPs of finite fields, and give the inverses of all PPs of degree ≤ 6 over finite fields Fq for all q and the inverses of all PPs of degree 7 over F2(n). The explicit inverse of a class of fifth degree PPs is the...