On the best linear approximation of addition modulo 2n

In this paper, the best linear approximations of addition modulo 2n are studied. Let x = (xn−1, xn−2,…,x0) and y = (yn−1, yn−2,…,y0) be any two n-bit integers, and let z = x + y (mod 2n). Firstly, all the correlations of a single bit zi approximated by xj’s and yj’s (0 ≤ i, j ≤ n − 1) are characterized, and similar results are obtained for the linear approximation of the xoring of the neighboring bits of zi’s. Then the maximum correlations and the best linear approximations are presented when these zj’s (0 ≤ j ≤ n − 1) are xored in any given means.