> For addition this is correct, I don't believe it's correct for multiplication because of the negative integers. That is, the ring described by signed n-bit si

> For addition this is correct, I don't believe it's correct for multiplication because of the negative integers. That is, the ring described by signed n-bit signed integers under multiplication and addition is not isomorphic to (Z_{2^n}, +, *). No, it is. It is in fact just Z modulo 2^n, just with the choice of representatives being { -2^(n-1), ..., 2^(n-1)-1 } instead of { 0, ..., 2^n-1 }. This is pretty easy to check... do you have an example to the contrary?