WebIt is known from Budaghyan et al. (IEEE Trans. Inf. Theory 52.3, 1141–1152 2006; Finite Fields Appl. 15(2), 150–159 2009) that for quadratic APN functions (both monomial and … Web1 de mar. de 2024 · 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 F2n→F2minto CCZ-equivalence classes and then to partition each CCZ-equivalence class into EA-equivalence classes.
On the EA-classes of known APN functions in small dimensions
Web1 de set. de 2024 · Paper 2024/796 On relations between CCZ- and EA-equivalences. Lilya Budaghyan, Marco Calderini, and Irene Villa Abstract. In the present paper we … It is easy to see that the set\Im (A_{2}^{*})iscontained inSF(see (3)). Along this section we denote by Span(v1,…,vm) the vector (sub)space over {\mathbb F}_{2} generated by the elements v_{1},\dots ,v_{m} \in {\mathbb F}_{2^n}. Now, to construct the possible functions F1 we should consider all the vector … Ver mais Without loss of generality, fixing any basis{u1,…,uk} ofU (where k is the dimension of U) and fixing a basis{β1,...,βn} of{\mathbb F}_{2^n}(asa vector space over{\mathbb F}_{2}),we can suppose … Ver mais For anyu ∈ U ∖{0} we considerthe set\mathcal {Z}\mathcal {W}(u), as definedbefore. To constructA1we need to determine the images of the vectorsβi’s.In order to do that, we … Ver mais As stated in [21, Theorem 2.3] for any linear polynomialL(x) we have that,given a basis {β1,...,βn} of{\mathbb F}_{2^n}, thereexist unique𝜃1,...,𝜃nin{\mathbb F}_{2^n}suchthatL(x)={\sum }_{i=1}^{n} \text {Tr}(\beta … Ver mais LetU be a subspace contained inSF, whereF is a function from{\mathbb F}_{2^n}toitself andSFdefined as in (4). Then, there exists a permutationof{\mathbb … Ver mais csc serviceworks marisa buzzanca
Recovering or Testing Extended-Affine Equivalence
Web1 de set. de 2024 · In fact, to the best of our knowledge, it is not known how to partition a CCZ-equivalence class into its Extended-Affine (EA) equivalence classes; EA-equivalence being a simple particular case of ... Websimple relation between special structures in the LAT of a function : F 2 →F 2 (or equivalently in its DDT) and the EA-classes of the functions CCZ-equivalent to it. … http://boolean.w.uib.no/files/2024/06/marco.pdf dyson cr01 fault f11