On Inverses of Permutation Polynomials of Small Degree Over Finite Fields
Yanbin Zheng, Qiang Wang, Wenhong Wei · IEEE Transactions on Information Theory · 2019
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 main result, which is obtained by using Lucas' theorem, some congruences of binomial coefficients, and a known formula for the inverses of PPs of finite fields.