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arXiv · 1812.06768

On Inverses of Permutation Polynomials of Small Degree over Finite Fields

Yanbin Zheng·Qiang Wang·Wenhong Wei
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Abstract

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 $\leq 6$ over finite fields $\mathbb{F}_{q}$ for all $q$ and the inverses of all PPs of degree $7$ over $\mathbb{F}_{2^n}$. 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.

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Yanbin Zheng, Qiang Wang, Wenhong Wei. 2018-12-17. On Inverses of Permutation Polynomials of Small Degree over Finite Fields. https://doi.org/10.1109/tit.2019.2939113

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