The Boomerang Uniformity of Power Permutations x2k−1 over F2n

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 F
_2n
. 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 x
⁷
is completely determined.