Optimal plateaued functions without linear structures

In this talk, we address the algebraic method to design plateaued functions with desirable cryptographic properties (such as maximal algebraic degree and balancedness) by employing the generalized Maiorana-McFarland class (GMM) of Boolean functions. We consider functions in the GMM class of the form $f(x,y)=x cdot phi(y) oplus h(y)$, where $x in F_2^{n/2+k}, y in F_2^{n/2 -k}$ and $phi(y): F_2^{n/2 -k} rightarrow F_2^{n/2 +k}$, and derive a set of sufficient conditions for designing optimal plateaued functions. We will show that under certain conditions designed optimal plateaued functions do not admit the linear structures. Furthermore, we will show that under specific conditions, the addition of an indicator ($1_{R}(x,y) = 1_{E_1}(x)1_{E_2}(y)$) to a function $g(x,y) = x cdot phi(y)$, we have that $f(x,y) = g(x,y) oplus  1_{R}(x,y)$ is a plateaued function.