Systematic Constructions of Rotation Symmetric Bent Functions, 2-Rotation Symmetric Bent Functions, and Bent Idempotent Functions

Rotation symmetric bent functions and their generation two-rotation symmetric bent functions are two classes of cryptographically significant Boolean functions. However, few constructions have been presented in the literature, which either have restriction on integer n or have algebraic degree no more than 4. In this paper, for any even integer n ≥ 4, three classes of bent functions are presented respectively. Most notably, the proposed n-variable rotation symmetric bent functions and two-rotation symmetric bent functions can have any possible algebraic degree ranging from 2 to n/2. Besides, we obtain bent idempotent functions with the maximal algebraic degree n/2.