Sequences of numbers via permutation polynomials over some finite rings

Abstract

A polynomial can represent every function from a finite field to itself. The functions which are also permutations of the field give rise to permutation polynomials, which have potential applications in cryptology and coding theory. Permutation polynomials over finite rings are studied with respect to the sequences they generate. The sequences obtained through some permutation polynomials are tested for randomness by carrying out known statistical tests. Random number generation plays a major role in cryptography and hence permutation polynomials may be used as random number generators. © 2020. All rights reserved.