This MAC did not magically appear from GCM, it is a variant of Carter-Wegman MAC. It's in the same class as Poly1305 and UMAC, VMAC. It was combined with CTR mo

This MAC did not magically appear from GCM, it is a variant of Carter-Wegman MAC. It's in the same class as Poly1305 and UMAC, VMAC. It was combined with CTR mode to create GCM. Poly1305 as used in NaCl (XSalsa20-Poly1305) or in TLS (ChaCha20-Poly1305) also will give different results, especially compared to the original proposal Poly1305-AES MAC, but this doesn't mean that those two are not compositions of a cipher and MAC.