The boomerang uniformity of three classes of permutation polynomials over 픽2n.

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 픽2n, we determine the boomerang uniformity of these permutation polynomials: (1) f1(x) = (x2m + x + δ)22m+1 + x, where n = 3m, δ ∈ 픽2n with Trmn(δ) = 1; (2) f2(x) = (x2m + x + δ)22m−1+2m−1 + x, where n = 3m, δ ∈ 픽2n with Trmn(δ) = 0; (3) f3(x) = (x2m + x + δ)23m−1+2m−1 + x, where n = 3m, δ ∈ 픽2n with Trmn(δ) = 0. The results show that the boomerang uniformity of f1(x), f2(x) and f3(x) can attain 2n. [ABSTRACT FROM AUTHOR]