The boomerang uniformity of three classes of permutation polynomials over 𝔽2n

Abstract

Permutation polynomials with low boomerang uniformity have wide applications in cryptography. In this paper, by utilizing the Weil sums technique and solving some certain equations over [Formula: see text], we determine the boomerang uniformity of these permutation polynomials: (1) [Formula: see text], where [Formula: see text], [Formula: see text] with [Formula: see text]; (2) [Formula: see text], where [Formula: see text], [Formula: see text] with [Formula: see text]; (3) [Formula: see text], where [Formula: see text], [Formula: see text] with [Formula: see text]. The results show that the boomerang uniformity of [Formula: see text], [Formula: see text] and [Formula: see text] can attain [Formula: see text].