Analysis of Addition Modulo 2n on Boolean Function

In order to analyze the impact on the security of cryptographic algorithm produced by the linear approximations of addition modulo 2
ⁿ
with XOR, this paper firstly translates the operation of addition modulo 2
ⁿ
into vector Boolean function with dimension of n. The component functions can be obtained through a recurrence formula which does not require a recall of the carry function. Then we explore the cryptographic properties of n-dimensional Boolean functions of addition modulo 2
ⁿ
, and the results indicate that the component functions are all kth-order quasi-Bent functions. The n-dimensional vector has the first order-correlation immunity, rather than the second-order correlation immunity.