It should be noted that XOR is just (bitwise) subtraction modulo 2. There are many kinds of SUB instructions in the x86-64 ISA, which do subtraction modulo 2^64, modulo 2^32, modulo 2^16 or modulo 2^8. To produce a null result, any kind of subtraction can be used, and XOR is just a particular case of subtraction, it is not a different kind of operation. Unlike for bigger moduli, when operations are done modulo 2 addi…
It's different in that there's no carry propagation.