模2~n加法最佳线性逼近关系研究

Research on the Best Linear Approximation of Addition Modulo 2n

该文研究了模2n加法运算的最佳线性逼近问题。利用权位分量函数的线性逼近关系,该文首先给出了模2n加法最佳线性逼近相关值的计算公式。其次通过递归构造得到了模2n加法最佳线性逼近集的生成方法。该文的研究从理论上更清楚地刻画了二元模2n加法最佳线性逼近的内在规律,有助于更好地利用该线性逼近关系实现对实际密码算法的有效分析。

In this paper, the best linear approximation of addition modulo 2n is studied. Firstly, the formula for maximum correlations of addition modulo 2n is proposed by using the linear approximation of the coordinate functions of addition modulo 2n. Moreover, a method to construct the best linear approximation set of addition modulo 2n is given in a recursive way. The paper characterizes the inner principle of best linear approximation of addition modulo 2n theoretically~ which will help to use the linear approximation relation to realize an effective analysis of cryptographic algorithms.