• Analysis, classification and construction of optimal cryptographic Boolean functions 

      Villa, Irene (Doctoral thesis, 2021-01-04)
      Modern cryptography is deeply founded on mathematical theory and vectorial Boolean functions play an important role in it. In this context, some cryptographic properties of Boolean functions are defined. In simple terms, ...
    • 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 ...
    • 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 ...
    • 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 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 ...