The c-boomerang uniformity of two classes of permutation polynomials over finite fields

Permutation polynomials over finite fields have been extensively studied not only for their applications in cryptography, but have also been applied to coding theory and combinatorial design theory. Recently, a new theoretical tool, the Boomerang Connectivity Table (BCT) and the corresponding boomerang uniformity were introduced to evaluate the resistance of a block cipher against boomerang attacks. Inspired by a multiplier differential, Stănică [Investigations on c-boomerang uniformity and perfect nonlinearity, Discret. Appl. Math., 2021] extended the concept of boomerang uniformity to c-boomerang uniformity. In this paper, we investigate two classes of permutation polynomials over \(\mathbb {F}_{p^{n}}\) ${\mathbb{F}}_{p^n}$ with respect to this new concept. We show that these permutations are 1-uniform c-BCT functions.