Construction of highly nonlinear permutations on [formula omitted] with differential uniformity at most 8

Abstract

In this paper, we propose a construction of permutations on Z2n having high nonlinearity by taking two highly nonlinear permutations on Zn, where n is odd. For n being prime, we identify a subclass of permutations whose differential uniformity is bounded above by 8. We further explore and show that the differential uniformity of such permutations on Z2p is at most 7 if p≡2(mod15) or p≡8(mod15).