Several Classes of Permutation Trinomials From Niho Exponents

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.

Cryptography and Communications

References in corpus (2)

• A Class of Permutation Trinomials over Finite Fields
• Determination of a Type of Permutation Trinomials over Finite Fields, II

Cited by in corpus (4)

• On Two Conjectures about Permutation Trinomials over ${\mathbb{F}}_{3^{2k}}$
• Several Classes of Permutation Trinomials over ${\mathbb{F}}_{5^n}$ From Niho Exponents
• A note on permutation polynomials over finite fields
• A new class of permutation trinomials constructed from Niho exponents