Research on the Best Linear Approximation of Addition Modulo 2n

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.