On Almost Perfect Nonlinear mappings
Thierry Berger, Anne Canteaut, Pascale Charpin
LACO (university of Limoges) and INRIA (projet CODES)
Presented at ISIT 2005, Adelaide, Australie.
To appear in IEEE Trans. Inform. Theory.
We investigate some open problems on Almost Perfect Nonlinear (APN)
functions over a finite field of characteristic 2. We provide new
characterizations of APN mappings and of APN permutations by means of
their component functions. We also focus on the case of quadratic
functions. Most notably, we prove that a class of quadratic
functions cannot be APN. Our result strengthens the conjecture that
all quadratic APN functions are power functions, up to equivalence.
Almost bent mapping, almost perfect nonlinear
mapping, power mapping, permutation polynomial.