Several Classes of Permutation Trinomials From Niho Exponents

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.