Paper 2024/1511

Some Classes of Cubic Monomial Boolean Functions with Good Second-Order Nonlinearity

Abstract

It is well known that estimating a sharp lower bound on the second-order nonlinearity of a general class of cubic Booleanfunction is a difficult task. In this paper for a given integer $n\ge 4$, some values of $s$ and $t$ are determined for which cubic monomial Boolean functions of the form $h_{\mu }(x)=Tr(\mu x^{2^s+2^t+1})$ $(n>s>t\ge 1)$ possess good lower bounds on their second-order nonlinearity. The obtained functions are worth considering for securing symmetric cryptosystems against various quadratic approximation attacks and fast algebraic attacks.