Walsh spectrum properties of rotation symmetric boolean function

Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric(RotS) function is special. For a RotSn variables functionf(x ₁,x₂,···,x_n) we havef(π _n ^k (x₁,x₂,···,x_n)=f(x ₁,x₂,···,x_n) fork=0,1,…n−1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary. Foundation item: Supported by the National Natural Science Foundation of China (90104035) Biography: WANG Yongjuan (1982-), female, Ph. D. candidate, research direction: cryptographic theory.