Browsing Bergen Open Research Archive by Author "Calderini, Marco"
Now showing items 1-14 of 14
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Constructing APN functions through isotopic shifts
Budaghyan, Lilya; Calderini, Marco; Carlet, Claude; Coulter, Robert; Villa, Irene (Journal article; Peer reviewed, 2020)Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, mathematics and information theory. In this paper we deduce a new method ... -
Differentially low uniform permutations from known 4-uniform functions
Calderini, Marco (Journal article; Peer reviewed, 2021)Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low ... -
Generalized isotopic shift construction for APN functions
Budaghyan, Lilya; Calderini, Marco; Carlet, Claude Michael; Coulter, Robert; Villa, Irene (Journal article; Peer reviewed, 2021)In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (IEEE Trans Inform Theory 66:5299–5309, 2020), when the initial function is a Gold function. In ... -
A note on some algebraic trapdoors for block ciphers
Calderini, Marco (Peer reviewed; Journal article, 2018)We provide sufficient conditions to guarantee that a translation based cipher is not vulnerable with respect to the partition-based trapdoor. This trapdoor has been introduced, recently, by Bannier et al. (2016) and it ... -
On construction and (non)existence of c-(almost) perfect nonlinear functions
Bartoli, Daniele; Calderini, Marco (Journal article; Peer reviewed, 2021)Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low c-differential uniformity attracted lots of attention. In particular, so-called APcN and PcN functions ... -
On equivalence between known families of quadratic APN functions
Budaghyan, Lilya; Calderini, Marco; Villa, Irene (Journal article; Peer reviewed, 2020)This paper is dedicated to a question whether the currently known families of quadratic APN polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these families to those CCZ-inequivalent to each ... -
On Isotopic Shift Construction for Planar Functions
Budaghyan, Lilya; Calderini, Marco; Carlet, Claude; Coulter, Robert; Villa, Irene (Chapter; Peer reviewed, 2019)CCZ-equivalence is the most general currently known equivalence relation for functions over finite fields preserving planarity and APN properties. However, for the particular case of quadratic planar functions isotopic ... -
On properties of translation groups in the affine general linear group with applications to cryptography
Calderini, Marco; Civino, Roberto; Sala, Massimiliano (Journal article; Peer reviewed, 2021)The affine general linear group acting on a vector space over a prime field is a well-understood mathematical object. Its elementary abelian regular subgroups have recently drawn attention in applied mathematics thanks to ... -
On relations between CCZ- and EA-equivalences
Villa, Irene; Calderini, Marco; Budaghyan, Lilya (Peer reviewed; Journal article, 2020)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 permutations. ... -
On the Boomerang Uniformity of some Permutation Polynomials
Calderini, Marco; Villa, Irene (Journal article; Peer reviewed, 2020)The boomerang attack, introduced by Wagner in 1999, is a cryptanalysis technique against block ciphers based on differential cryptanalysis. In particular it takes into consideration two differentials, one for the upper ... -
On the EA-classes of known APN functions in small dimensions
Calderini, Marco (Journal article; Peer reviewed, 2020)Recently Budaghyan et al. (Cryptogr. Commun. 12, 85–100, 2020) introduced a procedure for investigating if CCZ-equivalence can be more general than EA-equivalence together with inverse transformation (when applicable). In ... -
On Two Fundamental Problems on APN Power Functions
Budaghyan, Lilya; Calderini, Marco; Carlet, Claude Michael; Davidova, Diana; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2022)The six infinite families of power APN functions are among the oldest known instances of APN functions, and it has been conjectured in 2000 that they exhaust all possible power APN functions. Another long-standing open ... -
Some group-theoretical results on Feistel Networks in a long-key scenario
Aragona, Riccardo; Calderini, Marco; Civino, Roberto (Journal article; Peer reviewed, 2020)The study of the trapdoors that can be hidden in a block cipher is and has always been a high-interest topic in symmetric cryptography. In this paper we focus on Feistel-network-like ciphers in a classical long-key scenario ... -
Wave-shaped round functions and primitive groups
Aragona, Riccardo; Calderini, Marco; Civino, Roberto; Sala, Massimiliano; Zappatore, Ilaria (Peer reviewed; Journal article, 2019)Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks (SPN) and Feistel Networks (FN), are often obtained as the composition of different layers. The ...