Client authentication with a collection of open source distributed servers

With a collection of open source distributed servers, all sharing every users data. How can the user authenticate with any server, without the passwords being compromised by malicious servers?

Also, in order to store the users data on the network securely, is the best approach to store the user's public key, private key encrypted with the users password and the users data encrypted with the public key. Then these three values are then passed to the client for decryption using the password?