中文摘要：

记0〈sj〈[n/2]为整数,j=0,1,…,r-1,称fn（x0,…,xn-1）=∑r-1j=0∑n-1i=0xixi＋sj为多圈旋转对称布尔函数。定义S（e（fn（X）））=∑X∈Fn2e（fn（X））,其中,e（x）=（-1）x。利用差分分析的方法和勒让德符号等数论知识,计算多圈旋转对称布尔函数的指数和。对于奇素数p,建立了S（e（fn（X）））与S（e（fpn（X）））取值之间的联系,从而实际上给出了一种计算这类函数指数和的方法。同时给出特殊条件下2圈旋转对称布尔函数的指数和。

英文摘要：

An n-variable multi-orbit rotation symmetric Boolean function（RSBF） is an n-variable Boolean function such as fn（x0,…,xn-1）=∑r-1j=0∑n-1i=0xixi＋sj,where 0sjn2 are r integers,j=0,1,…,r-1.This paper shows that the exponential sums of multi-orbit RSBFs can be calculated in terms of differential cryptanalysis and some number theory such as the Legendre Symbol techingue.Furthermore,the relation between S（e（fn（X）））and S（e（fpn（X））） is studied and this relation can be used to calculate the exponential sums of such fpn（X） in practice,where p is an odd prime.Finally,the exact exponential sums of 2-orbit RSBFs under special conditions are calculated.