WebOn relations between CCZ and EA-equivalences Marco Calderini (joint work with Lilya Budaghyan and Irene Villa) University of Bergen Boolean Functions and their Applications June 17-22, 2024. Notations and de nitions PN and APN functions: Let F : Fn 2!Fm 2 be a Vectorial Boolean function. Web1 de mar. de 2024 · Furthermore, we show that it is possible to navigate between the EA-classes in the CCZ-class of a function using an operation which we call t-twisting, where …

On the EA-classes of known APN functions in small dimensions

Web1 de set. de 2024 · EA-equivalence is a particular case of CCZ-equivalence, which is the most general known equivalence relation preserving the differential uniformity. An important aspect of the study and the analysis of APN functions, and vectorial Boolean functions in general, is their classification with respect to these equivalence relations. 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 reach lms

On CCZ-equivalence, extended-affine equivalence, and

WebOn relations between CCZ- and EA-equivalence Lilya Budaghyan Marco Calderini Irene Villa Received: date / Accepted: date Abstract In the present paper we introduce some sufficient conditions and a procedure for checking whether, for a given function, CCZ-equivalence is more general than EA-equivalence together with taking inverses of … WebOn relations between CCZ- and EA-equivalences. Cryptography and Communications. 2024;12:85-100: eng: dc.identifier.issn: 1936-2455: en_US: dc.identifier.issn: 1936-2447: en ... we prove that for power non-Gold APN functions, CCZ equivalence coincides with EA-equivalence and inverse transformation for n ≤ 8. We conjecture that this is true for ... Webfor a given function, CCZ-equivalence is more general than EA-equivalence together with taking inverses of permutations. It is known from [8,6] that for quadratic APN … reach llc behavioral health