模m加法的一类线性逼近关系研究

摘要

该文研究模 m 加法的线性逼近问题，其中 m 为大于3的整数。利用分类计数方法，文中给出了任意 k个整数求和模 m 的最低两个比特异或值用每一个整数的最低两个比特异或值去逼近时概率值的精确计算公式。此外，对于 k ＝2、3或4，文中还进一步分析了这类线性逼近的效果。%The linear approximation of addition modulo m is studied in this paper,where m >3.Using classification counting method,an exact probability formula of the XOR of the lowest two bits of the summation of k integers modulo m approximate to the XOR of the lowest two bits of every integer is given in this paper.Moreover,the effect of this approximation is discussed for k=2,3 or 4.