EA-equivalence classes and the more general CCZ-equivalence classes of functions over GF (2) each preserve APN and AB properties desirable for S-box functions. We show that they can be related to subsets c[T ] and g[T ] of equivalence classes [T ] of transversals, respectively, thus clarifying their relationship and providing a new approach to their study. We derive a formula which characterise...

Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Ou...

We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n ≥ 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZ-inequivalent to any known APN function, and in particular for n = 12,...

A detailed overview of the problems, solutions and experience of the first international student’s Olympiad in cryptography, NSUCRYPTO’2014, is given. We start with rules of participation and description of rounds. All 15 problems of the Olympiad and their solutions are considered in detail. There are discussed solutions of the mathematical problems related to cipher constructing such as studyi...

The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n = 2m − 1 for small m, m ≤ 22, is given. As far as we know, for m ∈ {5, 7, 11, 13, 17, 19}, all given self-embeddings in closed surfaces are new. Moreover, they are cyclic for all m and nonorientable at least for all m ≤ 19. For any non prime m, the nonexistence o...

Generalized resources are defined as multisets of Petri net vertices. Here places represent material resources (designated by tokens residing in these places). Transitions correspond to activity resources represented by transition firings. Two generalized resources are called similar if in any Petri net marking one resource can be replaced by another without changing the observable system’s beh...

We present in this paper the algorithm which performs the translation of MSC’2000 diagrams into Petri net modulo strong bisimulation. The correctness of this algorithm is justified. Here we supplement MSC’2000 standard supplying it with formal definition of MSC element by means of process algebra. We would mention here that this translation algorithm is the part of the automated ver...

Recently, many new almost perfect nonlinear (APN) and almost bent (AB) functions have been constructed. These functions F n 2 → F n 2 play an important role in cryptography. In this article, we will summarize different concepts of equivalence between these functions, and discuss some invariants. Two codes can be associated with APN and AB functions. This is useful to distinguish functions up to...

It is known that crooked functions can be used to construct many interesting combinatorial objects, and a quadratic function is crooked if and only if it is almost perfect nonlinear (APN). In this paper, we introduce two infinite classes of quadratic crooked multinomials on fields of order 2. One class of APN functions constructed in [7] is a particular case of the one we construct in Theorem 1...

Two resources (submarkings) are called similar if in any marking any one of them can be replaced by another one without affecting the net’s behaviour (modulo marking bisimulation). It is known that resource similarity is undecidable for general labelled Petri nets. In this paper we study the properties of resource similarity and resource bisimulation (a subset of complete similarity relation, c...