Binomial differentially 4 uniform permutations with high nonlinearity

Differentially 4 uniform permutations with high nonlinearity on fields of even degree are crucial to the design of S-boxes in many symmetric cryptographic algorithms. Until now, there are not many known such functions and all functions known are power functions. In this paper, we construct the first class of binomial differentially 4 uniform permutations with high nonlinearity on F26m, where m is an odd integer. This result gives a positive answer to an open problem proposed in Bracken and Leander (2010) [7].