I'm pretty unfamiliar with the subject, so my reply may not be very helpful, but I'm wondering: is addition the same as XOR and multiplication the same as AND? This would lead to

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0

0 * 0 = 0

0 * 1 = 0

1 * 0 = 0

1 * 1 = 1

If so, then a (probably slow) way of solving is to construct an 8-row truth table and then find a simpler expression from that. I'm curious to see what people more experienced with these problems post.