• 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 ...
    • 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 ...
    • 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 ...
    • Towards a deeper understanding of APN functions and related longstanding problems 

      Kaleyski, Nikolay Stoyanov (Doctoral thesis, 2021-08-24)
      This dissertation is dedicated to the properties, construction and analysis of APN and AB functions. Being cryptographically optimal, these functions lack any general structure or patterns, which makes their study very ...