> unbreakable like Vigenere is

Please stop saying this. Vigenere is breakable. What you are describing is more correctly referred to as a one time pad (as other have suggested) .

There are a number of problems with implementing effective one time pad solutions, e.g.

1) securely communicating the key to the recipient
2) key must be kept secure
2) key must only be used once
3) key must be completely random
4) key must be at least as long as the message

Basically, as Steve Bellini said: "As a practical person, I've observed that one-time pads are theoretically unbreakable, but practically very weak. By contrast, conventional ciphers are theoretically breakable, but practically strong."

It is doable, but only if (as in necessary, not sufficient) the key/password is typed by the user and never pre-stored on the phone. Even with a hardware keyboard like in the N900 you don't want to type 160 (or whatever) additional characters (for which no auto-completion will help, the key being truly random) every time you want to send an SMS.

So, doable in principle, but not in practice. Plus see @strongm above.

I don't think we assume the phone to be compromised here, so storing a very long key on the phone in advance and then using it piece by piece is not problematic, if we're only concerned about end-to-end security (i.e. that no malicious base station or similar can read the messages).

If we assume that the attacker also controls the phone anyway, then he can just see the message directly.

To be clear, the idea is still extremely impractical, but password entry should not be the problem.