**Constructing new superclasses of bent functions from known ones**

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

**Abstract: **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.

**Category / Keywords: **C class, D class, Completed Maiorana-McFarland class M#, CD class, Weakly normal bent functions, Bent duals, 4-bent decomposition

**Date: **received 9 Feb 2022

**Contact author: **amar bapic at famnit upr si

**Available format(s): **PDF | BibTeX Citation

**Version: **20220212:064459 (All versions of this report)

**Short URL: **ia.cr/2022/147

[ Cryptology ePrint archive ]