Ccz equivalence of power functions
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 ...
Ccz equivalence of power functions
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WebOct 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 … WebMar 7, 2024 · CCZ equivalence of power functions Abstract. Let F\simeq { {\mathrm {GF}}} (p^n) be a finite field of characteristic p and p_k …
WebWe 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 … 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.
WebDec 1, 2024 · Running the search for n = 9 on a server operating with an Intel Xeon E5 CPU at 3.5G GHz took approximately 33 days and produced a list of 21504 functions. Partitioning them into CCZ-equivalence classes by the code isomorphism test was performed by running several parallel processes on a server with an Intel Xeon E5 CPU … 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 …
Web2 + A= G. EA-equivalence is a particular case of CCZ-equivalence, with the latter being strictly more general than EA-equivalence and taking inverses of permutations [9]. In the case of power functions, CCZ-equivalence (as well as EA-equivalence) coincides with cyclotomic equivalence [42]. Two power functions F(x) = xd and G(x) = xe over F
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 ... dubois va phone number on shaffer roadWebWe 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 … common shagWebSep 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 … dubois winnipegWebSep 1, 2024 · Equivalence plays an important role in research of cryptographic functions, because two functions have some identical cryptographic properties if they are equivalent. There are two famous equivalent relations in this area, i.e. , extended affine (EA) equivalence and Carlet-Charpin-Zinoviev (CCZ) equivalence [7] . du bois watchesWebIn this contribution we consider the stability of linearity and differential uniformity of vector Boolean functions under certain constructions and modifications. These include compositions with affine surjections onto the input space and with affine surjections from the output space, inversions, adding coordinate functions, forming direct sums and … commons hall tamuWebF210 (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 ... common shakespeare playsWebMar 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 … common shag bird