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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 = F 2 n. A conjecture of Janwa-Wilson and McGuire-Janwa-Wilson (1993/1996), settled in 2011, was that the only exceptional(More)
Almost Perfect Nonlinear (APN) functions are very useful in cryptography , when they are used as S-Boxes, because of their good resistance to differential cryptanalysis. An APN function f : F 2 n → F 2 n is called exceptional APN if it is APN on infinitely many extensions of F 2 n. Aubry, McGuire and Rodier conjectured that the only exceptional APN(More)
This is a brief description of the GAP package automata, a package designed to work with finite state automata and with rational languages. The package automata [DLM05] started with an attempt to implement, in GAP [GAP04] (GAP 3, at the time), an algorithm coming from semi-group theory, namely an algorithm to compute the abelian kernel of a finite monoid(More)
On the absolute irreducibility of hyperplane sections of generalized Fermat varieties in P 3 and the conjecture on exceptional APN functions: the Kasami-Welch degree case Abstract Let f be a function on a finite field F. The decomposition of the generalized Fermat variety X defined by the multivariate polynomial of degree n, φ(x, y, z) = f (x) + f (y) + f(More)
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