On the Linear Structures of Cryptographic Rotation Symmetric Boolean Functions

Due to its richness in terms of cryptographically properties along with its small search space 2^2n/n comparable to the whole space 2²ⁿ, the class of rotation symmetric Boolean functions (RSBFs) has become the main focus on searching for a Boolean function with good properties. Additionally, there are some other characteristics these functions might have which considered failure and should be avoided. For instance, the linear structure in Boolean function other than all-zero is regarded as a weakness and the function posses this characteristic is considered fragile and should be excluded from using in the cryptographic algorithms. Therefore, in this paper we examine the existence of linear structures in RSBFs, and then we categorize them based on the number of input variables and their algebraic degree.