Blar i Bergen Open Research Archive på forfatter "Carlet, Claude Michael"

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    • 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 ...

    • 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 ...

    • Gold functions and switched cube functions are not 0-extendable in dimension n > 5 

      Beierle, Christof; Carlet, Claude Michael (Journal article; Peer reviewed, 2023)
      In the independent works by Kalgin and Idrisova and by Beierle, Leander and Perrin, it was observed that the Gold APN functions over \(\mathbb {F}_{2^5}\) give rise to a quadratic APN function in dimension 6 having maximum ...

    • 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 ...

    • Relation between o-equivalence and EA-equivalence for Niho bent functions 

      Davidova, Diana; Budaghyan, Lilya; Carlet, Claude Michael; Helleseth, Tor; Ihringer, Ferdinand; Penttila, Tim (Journal article; Peer reviewed, 2021)
      Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent ...

    • Simplicity conditions for binary orthogonal arrays 

      Carlet, Claude Michael; Kiss, Rebeka; Nagy, Gábor P. (Journal article; Peer reviewed, 2023)
      It is known that correlation-immune (CI) Boolean functions used in the framework of side channel attacks need to have low Hamming weights. The supports of CI functions are (equivalently) simple orthogonal arrays, when their ...

    • The weight spectrum of two families of Reed-Muller codes 

      Carlet, Claude Michael; Solé, Patrick (Journal article; Peer reviewed, 2023)
      We determine the weight spectra of the Reed-Muller codes RM (m− 3, m) for m ≥ 6 and RM (m − 4, m) for m ≥ 8. The technique used is induction on m, using that the sum of two weights in RM (r −1, m−1) is a weight in RM (r, ...