Ccz equivalence of power functions
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 … WebAug 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 …
Ccz equivalence of power functions
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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). WebCCZ-equivalent if there exists an affine permutation of F 2 ×F 2 such that {︀ ( , ( )), ∈F 2}︀ = (︀{︀ ( , ( )), ∈F 2}︀)︀. As EA-equivalence and CCZ-equivalence are equivalence relations, and since EA-equivalence is a particular case of CCZ-equivalence, it is possible to partition the space of all functions F
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.
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} } 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 ...
WebApr 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 …
WebMetrics. The inverse function on is one of the most studied functions in cryptography due to its widespread use as an S-box in block ciphers like AES. In this paper, we show that, if , every function that is CCZ-equivalent to the inverse function is already EA-equivalent to it. This confirms a conjecture by Budaghyan, Calderini and Villa. shows in iowa cityWebAs EA-equivalence and CCZ-equivalence are equivalence relations, and since EA-equivalence is a particular case of CCZ-equivalence, it is possible to partition the space … shows in in las vegasWebDec 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 … shows in islingtonWebWe 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 … shows in indianapolis 2021WebApr 9, 2024 · The boomerang uniformity is invariant for affine equivalence but not for extended affine and CCZ-equivalence [ 2 ]. It has been proved that \delta \le \beta for any function F [ 5 ]. Additionally, \delta = 2 if and only if \beta = 2. Moreover, for n=4, the lowest boomerang uniformity that can be achieved is 6. shows in iowaWebAug 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 … shows in indio caWebAPN 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 … shows in indianapolis this weekend