Constructions of 2-Rotation Symmetric Semi-Bent Functions with Degree Bigger than 2

Semi-bent functions have important applications in cryptography and coding theory. 2-rotation symmetric semi-bent functions are a class of semi-bent functions with the simplicity for efficient computation because of their invariance under 2-cyclic shift. However, no construction of 2-rotation symmetric semi-bent functions with algebraic degree bigger than 2 has been presented in the literature. In this paper, we introduce four classes of 2m-variable 2-rotation symmetric semi-bent functions including balanced ones. Two classes of 2-rotation symmetric semi-bent functions have algebraic degree from 3 to m for odd m≥3, and the other two classes have algebraic degree from 3 to m/2 for even m≥6 with m/2 being odd.