What key are you going to encrypt these passwords with? If you were to encrypt passwords in the cloud with a key that's stored on the device, you can't unlock the passwords on a different device (or the same device after flashing), which is the whole point of backing it up in the cloud. If you were to encrypt them with the user's Google Accounts password, the device would need to ask for that password on every startu…
One way to do it would be: 1) Your plaintext password is used to generate two derivative tokens. One for user authentication with Google, and one for encrypting data stored with Google. The authentication password token is PBKDF2(N, password) and the encryption token is PBKDF2(N-1, password). You give Google the authentication token on signup. They are not capable of deriving the encryption token from it, but the use…
Chances of me implementing a boolean on/off switch for the plaintext passwords correctly: 99%