Several Classes of Permutation Trinomials From Niho Exponents

TL;DR

This paper constructs new classes of permutation trinomials over finite fields of characteristic two using Niho exponents, expanding the known families of such polynomials with potential applications in cryptography and coding theory.

Contribution

It introduces several novel classes of permutation trinomials over _{2^n} derived from Niho exponents, based on solving low-degree equations.

Findings

Multiple new permutation trinomial classes are constructed.

The methods involve subtle manipulations of equations over finite fields.

Results contribute to the understanding of permutation polynomials in characteristic two.

Abstract

Motivated by recent results on the constructions of permutation polynomials with few terms over the finite field $\mathbb{F}_{2^n}$, where $n$ is a positive even integer, we focus on the construction of permutation trinomials over $\mathbb{F}_{2^n}$ from Niho exponents. As a consequence, several new classes of permutation trinomials over $\mathbb{F}_{2^n}$ are constructed from Niho exponents based on some subtle manipulation of solving equations with low degrees over finite fields.