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

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Cited by in corpus (18)

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• On Two Conjectures about Permutation Trinomials over ${\mathbb{F}}_{3^{2k}}$
• Determination of a Class of Permutation Trinomials in Characteristic Three
• Several Classes of Permutation Trinomials over ${\mathbb{F}}_{5^n}$ From Niho Exponents
• Constructions and necessities of some permutation polynomials
• On the constructions of $n$-cycle permutations
• A note on permutation polynomials over finite fields
• Some results about permutation properties of a kind of binomials over finite fields
• On a Class of Permutation Trinomials in Characteristic 2
• On many-to-one mappings over finite fields
• More constructions of $n$-cycle permutations
• Constructions of involutions over finite fields
• A new class of permutation trinomials constructed from Niho exponents
• Two-to-one mappings and involutions without fixed points over $\bF_{2^n}$
• Two types of permutation polynomials with special forms
• A conjecture on permutation trinomials over finite fields of characteristic two
• A family of permutation trinomials in ${\mathbb{F}}_{q^2}$