A Note on &#x201C;Differential Properties of <formula formulatype="inline"><tex Notation="TeX">$x \mapsto x^{2^{t}-1}$</tex></formula>&#x201D;

  • F. Gologlu
  • Published 2012 in IEEE Transactions on Information Theory


Blondeau and colleagues recently conjectured a characterization of when <i>x</i><sup>2t-1</sup> is an almost perfect nonlinear function on F<sub>2</sub><i>n</i>. In this paper, we will prove the conjecture when <i>n</i> is even. The short proof uses a theorem of Hou and colleagues concerning reversed Dickson polynomials and a theorem of Payne.