模2n-1加法最佳线性逼近研究

Best Linear Approximation of Addition Modulo 2n - 1

模2n-1加法是密码算法中一种基本的算术运算,研究了它的最佳线性逼近问题,利用矩阵之间的特殊关系,给出单个输出比特、连续2个、连续3个及连续4个输出比特组合时的最佳线性逼近集及其对应的最大逼近优势。研究初步显示二元模2n-1加法最佳线性逼近的内在规律,有助于更好地认识它的非线性性质。

Addition modulo 2n -1 is a basic arithmetic operation in cryptographic algorithms, andits best linear approximation is studied in this paper. By using the special relationship among thematrixes, the best linear approximation sets and the maximum approximation advantage of the singleoutput bit, two adjacent output bits, three adjacent output bits and four adjacent output bits are pro-posed. This paper shows the inner principle of the best linear approximation of addition modulo 2n -1, which will help us learn its nonlinear property better.