With a key that is truly random, the result is a one-time pad, which is unbreakable even in theory. They probably meant XOR is reversible, unlike either AND or OR.

What's the inverse of XOR?

XOR stands for eXclusive OR. As can be seen, the output values of XNOR are simply the inverse of the corresponding output values of XOR.

What is the opposite of XOR gate?

XNOR stands for "eXclusive NOR". It is the opposite of the XOR operation. It is sometimes called XAND ("eXclusive AND").