On Permutation Quadrinomials and 4-Uniform BCT
Nian Li, Maosheng Xiong, Xiangyong Zeng · IEEE Transactions on Information Theory · 2021
Extending previous results, we study a class of general quadrinomials over the field of size 22mwith odd m and characterize conditions under which they are permutations with 4-uniform BCT, a new and important parameter related to boomerang-style attacks. These permutations are known to have the best known nonlinearity. Numerical data also show that the inverse of these functions all have large algebraic degree, making them desirable for applications.