We study the compositional inverses of some general classes of permutation polynomials over finite fields. We show that we can write these inverses in terms of the inverses of two other polynomials bijecting subspaces of the finite field, where one of these is a linearized polynomial. In some cases we are able to explicitly obtain these inverses, thus obtaining the compositional inverse of the permutation in question. In addition we show how to compute a linearized polynomial inducing the inverse map over subspaces on which a prescribed linearized polynomial induces a bijection. We also obtain the explicit compositional inverses of two classes of permutation polynomials generalizing those whose compositional inverses were recently obtained in [22] and [24], respectively.

Additional Metadata
Keywords Compositional inverse, Dickson matrix, Finite fields, Linearized polynomials, Permutation polynomials
Persistent URL dx.doi.org/10.1016/j.ffa.2014.02.006
Journal Finite Fields and their Applications
Citation
Tuxanidy, A. (Aleksandr), & Wang, Q. (2014). On the inverses of some classes of permutations of finite fields. Finite Fields and their Applications, 28, 244–281. doi:10.1016/j.ffa.2014.02.006