Ccz equivalence of power functions
WebF210 (resp. F212) to itself, which is proved to be CCZ-inequivalent to any power function. The exhibition of this function also disproves the third of the conjectures recalled above. This (quadratic) function is isolated and this leaves open the question of knowing whether a whole inflnite class of APN functions being not CCZ-equivalent to ... WebSep 1, 2024 · Two infinite classes of quadratic crooked multinomials on fields of order 22m are introduced and it is proved that the two classes of crooked functions constructed in …
Ccz equivalence of power functions
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WebJan 1, 2024 · A function F from F p ⁿ to itself is planar if for any [Formula: see text] the function F(x+a)-F(x) is a permutation. CCZ-equivalence is the most general known equivalence relation of functions ... WebJan 1, 2001 · In the case of power functions, CCZ-equivalence (as well as EA-equivalence) coincides with cyclotomic equivalence. Two power functions F (x) = x d and G(x) = x e over F 2 n , where d, e, n are ...
WebUp to this work only a few classes of APN and AB functions had been known and all these classes happened to be extended affine equivalent (EA-equivalent) to power functions. In this work we constructed the first classes of APN and AB polynomials EA-inequivalent to power mappings by using the equivalence relation (which we call CCZ-equivalence). WebDOI: 10.1016/j.ffa.2024.102190 Corpus ID: 257473857; Extending two families of bivariate APN functions @article{Calderini2024ExtendingTF, title={Extending two families of bivariate APN functions}, author={Marco Calderini and Kangquan Li and Irene Villa}, journal={Finite Fields and Their Applications}, year={2024} }
WebAug 26, 2008 · Abstract: This paper introduces the first found infinite classes of almost perfect nonlinear (APN) polynomials which are not Carlet-Charpin-Zinoviev (CCZ)-equivalent to power functions (at least for some values of the number of variables). These are two classes of APN binomials from F 2n to F 2n (for n divisible by 3, resp., 4). We … WebEA-equivalence is a particular case of CCZ-equivalence and every permutation is CCZ-equivalent to its inverse. The algebraic degree of a function (if it is not affine) is invariant under EA-equivalence but, in general, it is not preserved by CCZ-equivalence. There are six known infinite families of power APN functions. They are pre-sented in ...
WebMar 1, 2024 · Although the CCZ-equivalence between power APN functions has been completely characterized, a similar theoretical analysis between polynomial APN functions and power APN functions is still missing.
WebApr 13, 2024 · We show that a power function , with , on is an APN function of degree which is CCZ-equivalent to Kasami functions of degrees and . Comments: My … mark snapchat stories daus constineWebMar 1, 2024 · The research of equivalence of APN functions is focused on the equivalence between power functions [22], [5], [19], [12]. In 2024, Dempwolff gave a … marks nails cantonWebApr 13, 2024 · A power APN function CCZ-equivalent to Kasami function in even dimension. Let n be an even number such that n≡ 0 4. We show that a power function … mark smythe nflWebApr 13, 2024 · A power APN function CCZ-equivalent to Kasami function in even dimension. Let n be an even number such that n≡ 0 4. We show that a power function x^d, with d=2^n+2/2+2^n-2/2-1, on F_2^n is an APN function of degree n/2 which is CCZ-equivalent to Kasami function of degrees n/2 and (n+4)/2. marks myvegas comp roomsWebOct 1, 2024 · Almost perfect nonlinear (APN) function is an important type of function in cryptography, especially quadratic APN function. Since the notion of CCZ-equivalence developed, the construction of CCZ transform for APN functions to obtain new APN functions became a critical issue in cryptography. Inspired by the result of Budaghyan … navy white living roomWebWe prove hereby that for non-quadratic APN functions CCZ-equivalence can be more general (by studying the only known APN function which is CCZ-inequivalent to both power functions and quadratics). On the contrary, we prove that for power non-Gold APN functions, CCZ equivalence coincides with EA-equivalence and inverse transformation … navy white living room decorWebAug 26, 2008 · This paper introduces the first found infinite classes of almost perfect nonlinear (APN) polynomials which are not Carlet-Charpin-Zinoviev (CCZ)-equivalent to … mark smyth psychologist