Bear in mind that the 128 bit space is not double the size of the 64 bit space - it's 2^64 times the size. Cryptography actually relies on there being a space

Bear in mind that the 128 bit space is not double the size of the 64 bit space - it's 2^64 times the size. Cryptography actually relies on there being a space that is too large to count though, even in parallel.