The Boomerang Uniformity of Power Permutations x2k−1 over F2n*

Abstract

The boomerang uniformity is a safety index of S-boxes, which measures the resistance of block ciphers to the boomerang attack. In this paper, we investigate the boomerang uniformity of power permutations of the form x^2k−1 over $\mathbb{F}_{2^n}$. As a result, the relationship between the differential uniformity and the boomerang uniformity of x^2k−1 is given. Especially, for even n, the boomerang uniformity of power permutation x⁷ is completely determined.