On Algebraic Immunity of Boolean Functions by Concatenation

Algebraic immunity measures the resistance of a Boolean function against algebraic attack. To resist algebraic attack, a Boolean function should possess high algebraic immunity. Concatenation is an important method by which we can construct Boolean functions with good cryptographic properties. In this paper, we investigate certain classes of Boolean functions $g=f_{1}\Vert f_{2}\Vert f_{3}\Vert f_{4}$ for their algebraic immunity. When $n$ is even, we obtain two special classes ($n+2$)-variable Boolean functions with maximum algebraic immunity. Last, for an odd integer $n$, we get the divisibility result on the weights of Boolean functions with maximum possible algebraic immunity.