On cryptography properties of algebraic thickness

Algebraic thickness is an important property of Boolean functions. In this paper we give the relationship between algebraic thickness of Boolean functions with disjoint variables and their algebraic thickness, and derive some algebraic thicknesses of special Boolean functions. Furthermore, we prove the restrictive relationship of algebraic thickness between Boolean function and complement Boolean function, by this result the upper bounds on algebraic thickness of Boolean functions with small hamming weights and their complement Boolean functions are given. Finally, we summarize some lower or upper bounds on algebraic thickness of common Boolean functions.