• Binary Linear Codes With Few Weights From Two-to-One Functions 

      Li, Kangquan; Li, Chunlei; Helleseth, Tor; Qu, Longjiang (Journal article; Peer reviewed, 2021)
      In this paper, we apply two-to-one functions over b F 2n in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) (x 2t +x) e with ...
    • Bounds on the nonlinearity of differentially uniform functions by means of their image set size, and on their distance to affine functions 

      Carlet, Claude Michael (Journal article; Peer reviewed, 2021)
      We revisit and take a closer look at a (not so well known) result of a 2017 paper, showing that the differential uniformity of any vectorial function is bounded from below by an expression depending on the size of its image ...
    • 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 ...
    • 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 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 ...