RUS  ENG
Full version
JOURNALS // Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography] // Archive

Mat. Vopr. Kriptogr., 2016 Volume 7, Issue 4, Pages 51–66 (Mi mvk203)

Investigation of some subclasses of multiaffine, bijunctive, weakly positive and weakly negative Boolean functions

S. P. Gorshkov

Academy of Cryptography of the Russian Federation, Moscow

Abstract: Sets of multiaffine (denoted by $A$), bijunctive ($2$-CNF, $Bi$), weakly positive (or anti-Horn, $WP$) and weakly negative (or Horn, $WN$) Boolean functions generate classes of polynomially solvable systems of equations. We investigate functional classes $A\cap B$, $Bi\cap B$, where $B$ is the set of bent functions. Sets of possible values of algebraic nonlinearity degree of functions from $A$, $Bi$, $WP$, $WN$ are described. Problems of construction of functions from classes $WP$, $WN$ by means of functions of smaller number of variables are considered.

Key words: bent functions, multiaffine functions, $2$-CNF, Horn Boolean functions.

UDC: 519.716.39+519.719.2

Received 30.V.2016

DOI: 10.4213/mvk203



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025