On inverse of permutation polynomials of small degree over finite fields, II

Abstract

It is known that x(x s − a) (q m −1)/s with a ∈ F * q n is a permutation polynomial of F q n if and only if a is not a s-th power of an element of F * q n . In this paper, the inverse of f (x) on F q n is presented. In particular, explicit expressions of inverses of x(x 2 − a) 2 , x(x 3 − a) 2 and x(x 2 − a) 3 are given.

Compositional Inverses of AGW-PPs

“…It is difficult to obtain the explicit compositional inverse of a random PP, except for several well-known classes. Compositional inverses of different classes of PPs of special forms have been obtained in explicit or implicit forms; see [2,5,6,9,13,14,16,17,18,19,22,23,24] for more details. Recently, Niu, Li, Qu and Wang [9] obtained a general method to finding compositional inverses of AGW-PPs.…”

Compositional inverses of AGW-PPs –dedicated to professor cunsheng ding for his 60th birthday

“…It is difficult to obtain the explicit compositional inverse of a random PP, except for several well-known classes. Compositional inverses of different classes of PPs of special forms have been obtained in explicit or implicit forms; see [2,4,5,9,10,13,17,18,21,22,23,24,27,28,29,30] for more details. Recently, Niu, Li, Qu and Wang [13] obtained a general method to find compositional inverses of AGW-PPs.…”