On the linear structures of balanced functions and quadratic APN functions
نویسندگان
چکیده
منابع مشابه
On 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 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 zero-difference balanced functions, APN functions and strongly regular graphs
Let F be a function from Fpn to itself and δ a positive integer. F is called zerodifference δ-balanced if the equation F (x+a)−F (x) = 0 has exactly δ solutions for all nonzero a ∈ Fpn . As a particular case, all known quadratic planar functions are zero-difference 1-balanced; and some quadratic APN functions over F2n are zerodifference 2-balanced. In this paper, we study the relationship betwe...
متن کاملBinary quasi-perfect linear codes from APN quadratic functions
A mapping f from F2m to itself is almost perfect nonlinear (APN) if its directional derivatives in nonzero directions are all 2-to-1. Let Cf be the binary linear code of length 2 − 1, whose parity check matrix has its j-th column [ π f(π) ] , where π is a primitive element in F2m and j = 0, 1, · · · , 2 − 2. For m ≥ 3 and any quadratic APN function f(x) = ∑m−1 i,j=0 ai,jx 2+2 , ai,j ∈ F2m , it ...
متن کاملSome Results on the Known Classes of Quadratic APN Functions
In this paper, we determine theWalsh spectra of three classes of quadratic APN functions and we prove that the class of quadratic trinomial APN functions constructed by Göloğlu is affine equivalent to Gold functions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Cryptography and Communications
سال: 2020
ISSN: 1936-2447,1936-2455
DOI: 10.1007/s12095-020-00431-5