# How to compare security between S-Box and Addition in the block ciphers?

I'm studying a block cipher based on ARX(Addition, Rotation, XOR).

In a block cipher, nonlinearity comes from S-box or modular addition($Z=X\boxplus Y$ mod $2^n$).

As far as I know, in the case of S-Box, its security can be explained in the algebraic aspect.

How to explain the modular addition($\boxplus$ mod $2^n$) in the algebraic aspect?

So you have addition with carry bitwise if the sum is smaller than $2^n-1$ as well as the subtraction of $2^n$ if the sum is greater than $2^n-1.$