Polynomials with maximal differential uniformity and the exceptional APN conjecture
نویسندگان
چکیده
منابع مشابه
A Conjecture on Exceptional Orthogonal Polynomials
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials introduced by Cariñena et al., [3]. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical...
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We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer t ≥ 3 is said to be exceptional if f(x) = xt is APN (Almost Perfect Nonlinear) over F2n for infinitely many values of n. Equivalently, t is exceptional if the binary cyclic code of length 2n − 1 with two zeros ω, ωt has minimum distanc...
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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 = F2n . A conjecture of Janwa-Wilson and McGuireJanwa-Wilson (1993/1996), settled in 2011, was that the only monomial exceptional APN functions are the monomials ...
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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 : F2n → F2n is called exceptional APN if it is APN on infinitely many extensions of F2n . Aubry, McGuire and Rodier conjectured that the only exceptional APN functions are the Gold and the Kasami-Welch monomial...
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 ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2023
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2023.07.017