On APN-functions and division property of multisets
نویسندگان
چکیده
منابع مشابه
On a remarkable property of APN Gold functions
In [13] for a given vectorial Boolean function F from F2 to itself it was defined an associated Boolean function γF (a, b) in 2n variables that takes value 1 iff a 6= 0 and equation F (x) + F (x + a) = b has solutions. In this paper we introduce the notion of differentially equivalent functions as vectorial functions that have equal associated Boolean functions. It is an interesting open proble...
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We show that for an arbitrary mapping F on F2 to verify that it is APN, it is enough to consider the difference mappings of F defined by elements from an hyperplane.
متن کاملOn the Conjecture on APN Functions
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 ...
متن کاملOn differential equivalence of APN functions
For a given vectorial Boolean function F from F2 to itself it was defined an associated Boolean function γF (a, b) in 2n variables by C. Carlet, P. Charpin, V. Zinoviev in 1998 that takes value 1 iff a 6= 0 and equation F (x) +F (x+a) = b has solutions. In this paper we introduce the notion of differentially equivalent functions as vectorial functions that have equal associated Boolean function...
متن کاملOn the equivalence of quadratic APN functions
Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Ou...
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ژورنال
عنوان ژورنال: Prikladnaya diskretnaya matematika. Prilozhenie
سال: 2019
ISSN: 2226-308X
DOI: 10.17223/2226308x/12/65