On Inverses of Permutation Polynomials of Small Degree Over Finite Fields

作者：Zheng, Yanbin^*; Wang, Qiang; Wei, Wenhong

来源：IEEE Transactions on Information Theory, 2020, 66(2): 914-922.

DOI：10.1109/TIT.2019.2939113

• Ciphers
• Computer science
• Information theory
• Licenses
• Silicon
• Galois fields
• Finite fields
• permutation polynomials
• inverses
• binomial coefficients

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 $\mathbb {F}_{q}$ 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.

• 单位
  6; 1; 5; 桂林电子科技大学; 东莞理工学院