A few more quadratic APN functions
نویسندگان
چکیده
منابع مشابه
A few more functions that are not APN infinitely often
We consider exceptional APN functions on F2m , which by definition are functions that are APN on infinitely many extensions of F2m . Our main result is that polynomial functions of odd degree are not exceptional, provided the degree is not a Gold number (2 +1) or a Kasami-Welch number (4 −2k +1). We also have partial results on functions of even degree, and functions that have degree 2 + 1. ∗Re...
متن کاملEquivalences of quadratic APN functions
The following conjecture due to Y. Edel is affirmatively solved: two quadratic APN (almost perfect nonlinear) functions are CCZ-equivalent if and only if they are extended affine equivalent.
متن کاملQuadratic Equations from APN Power Functions
We develop several tools to derive quadratic equations from algebraic S-boxes and to prove their linear independence. By applying them to all known almost perfect nonlinear (APN) power functions and the inverse function, we can estimate the resistance against algebraic attacks. As a result, we can show that APN functions have different resistance against algebraic attacks, and especially S-boxe...
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...
متن کاملA class of quadratic APN binomials inequivalent to power functions
We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n ≥ 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZ-inequivalent to any known APN function, and in particular for n = 12,...
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ژورنال
عنوان ژورنال: Cryptography and Communications
سال: 2010
ISSN: 1936-2447,1936-2455
DOI: 10.1007/s12095-010-0038-7