I'm not talking about tomorrow but rather distant future. The banks evolved somehow. Now it is really hard to "become" a bank. There are very strict regulations in place. If a bank goes bankrupt the personal savings are still guaranteed to be paid off. So this is just a matter of making some regulations and establishing proper hierarchy.
And about security as in privacy. I don't know what future holds. Perhaps you'd be implanted a token that you can use for accessing the data which can't be faked or copied. Who knows. I just wouldn't rule out the possibility of a "cloud world" completely.
[1] You say "cryptography". I say "Analog hole".