On the Conjecture on APN Functions

@article{Delgado2012OnTC,
  title={On the Conjecture on APN Functions},
  author={Moises Delgado and Heeralal Janwa},
  journal={CoRR},
  year={2012},
  volume={abs/1207.5528}
}
An almost perfect nonlinear (APN) function (necessarily a polynomial function) on a finite field F is called exceptional APN, if it is also APN on infinitely many extensions of F. In this article we consider the most studied case of F = F2n. A conjecture of Janwa-Wilson and McGuire-Janwa-Wilson (1993/1996), settled in 2011, was that the only exceptional monomial APN functions are the monomials x, where n = 2 + 1 or n = 2 − 2 + 1 (the Gold or the Kasami exponents respectively). A subsequent… CONTINUE READING