• 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 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; Conference object; 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 ...
    • 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 ...