A Note on “Differential Properties of $x mapsto x^{2^{t}-1}$”

摘要

Blondeau and colleagues recently conjectured a characterization of when $x^{2^{t}-1}$ is an almost perfect nonlinear function on $ BBF _{ 2^{n}}$. In this paper, we will prove the conjecture when $n$ is even. The short proof uses a theorem of Hou and colleagues concerning reversed Dickson polynomials and a theorem of Payne.