• CCZ-equivalence of bent vectorial functions and related constructions 

      Budaghyan, Lilya; Carlet, Claude (Peer reviewed; Journal article, 2011-01-06)
      We observe that the CCZ-equivalence of bent vectorial functions over F2nFn2 (n even) reduces to their EA-equivalence. Then we show that in spite of this fact, CCZ-equivalence can be used for constructing bent functions ...
    • Classification of quadratic APN functions with coefficients in F2 for dimensions up to 9 

      Yu, Yuyin; Kaleyski, Nikolay Stoyanov; Budaghyan, Lilya; Li, Yongqiang (Journal article; Peer reviewed, 2020)
      Almost perfect nonlinear (APN) and almost bent (AB) functions are integral components of modern block ciphers and play a fundamental role in symmetric cryptography. In this paper, we describe a procedure for searching for ...
    • 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 ...
    • A New Family of APN Quadrinomials 

      Budaghyan, Lilya; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2020)
      The binomial B(x) = x 3 +βx 36 (where β is primitive in F 2 2) over F 2 10 is the first known example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a power function, and has remained unclassified ...
    • 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 Distance Between APN Functions 

      Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2020)
      We investigate the differential properties of a vectorial Boolean function G obtained by modifying an APN function F . This generalizes previous constructions where a function is modified at a few points. We characterize ...
    • Partially APN functions with APN-like polynomial representations 

      Budaghyan, Lilya; Kaleyski, Nikolay Stoyanov; Riera, Constanza Susana; Stănică, Pantelimon (Journal article; Peer reviewed, 2020)
      In this paper we investigate several families of monomial functions with APN-like exponents that are not APN, but are partially 0-APN for infinitely many extensions of the binary field F2. We also investigate the differential ...