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

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.