Paper 2022/147

Constructing new superclasses of bent functions from known ones

Amar Bapić, Enes Pasalic, Fengrong Zhang, and Samir Hodžić


Some recent research articles [23, 24] addressed an explicit specification of indicators that specify bent functions in the so-called $\mathcal{C}$ and $\mathcal{D}$ classes, derived from the Maiorana- McFarland ($\mathcal{M}$) class by C. Carlet in 1994 [5]. Many of these bent functions that belong to $\mathcal{C}$ or $\mathcal{D}$ are provably outside the completed $\mathcal{M}$ class. Nevertheless, these modifications are performed on affine subspaces, whereas modifying bent functions on suitable subsets may provide us with further classes of bent functions. In this article, we exactly specify new families of bent functions obtained by adding together indicators typical for the $\mathcal{C}$ and $\mathcal{D}$ class, thus essentially modifying bent functions in $\mathcal{M}$ on suitable subsets instead of subspaces. It is shown that the modification of certain bent functions in $\mathcal{M}$ gives rise to new bent functions which are provably outside the completed $\mathcal{M}$ class. Moreover, we consider the so-called 4-bent concatenation (using four different bent functions on the same variable space) of the (non)modified bent functions in $\mathcal{M}$ and show that we can generate new bent functions in this way which do not belong to the completed $\mathcal{M}$ class either. This result is obtained by specifying explicitly the duals of four constituent bent functions used in the concatenation. The question whether these bent functions are also excluded from the completed versions of $\mathcal{PS}$, $\mathcal{C}$ or $\mathcal{D}$ remains open and is considered difficult due to the lack of membership indicators for these classes.

Available format(s)
Publication info
Preprint. MINOR revision.
C classD classCompleted Maiorana-McFarland class M#CD classWeakly normal bent functionsBent duals4-bent decomposition
Contact author(s)
amar bapic @ famnit upr si
2022-02-12: received
Short URL
Creative Commons Attribution


      author = {Amar Bapić and Enes Pasalic and Fengrong Zhang and Samir Hodžić},
      title = {Constructing new superclasses of bent functions from known ones},
      howpublished = {Cryptology ePrint Archive, Paper 2022/147},
      year = {2022},
      note = {\url{}},
      url = {}
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