> That is because rainbow tables cannot practically attack long passwords. It's trivial to create a rainbow table that attacks passphrases. This statement is w

> That is because rainbow tables cannot practically attack long passwords. It's trivial to create a rainbow table that attacks passphrases. This statement is wrong. You example 1000102772901 is easily within rainbow tables. Trivially so, it's worse than a passphrase. > it defends against comparing one user's hashed password to a second user's hashed password, This has zero value. I can only suggest you do a course on hash functions on Coursera, the mathematics is somewhat easy and interesting to know. It's fun to follow up with a Blockchain course also has very interesting mathematics around hash functions, I really enjoyed this. I can't suggest which, the one I did isn't available, but check Google reviews there's a few out there.