A Class of Quadrinomial Permutations With Boomerang Uniformity Four
Ziran Tu, Nian Li, Xiangyong Zeng, Junchao Zhou
Abstract
In Eurocrypt'18, Cid et al. proposed a new cryptanalysis tool called Boomerang Connectivity Table (BCT), to evaluate S-boxes of block ciphers. Later, Boura and Canteaut further investigated the new parameter Boomerang uniformity for cryptographic S-boxes. It is of great interest to find new S-boxes with low Boomerang uniformity for even dimensions. In this paper, we prove that a class of permutation quadrinomials over F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2(2m)</sub> with m odd has Boomerang uniformity four, which gives the fifth class of such kind of permutation polynomials. Further, the occurrences of 0 and 4 in the BCTs of the investigated permutation polynomials are also completely determined.