Disclosed herein is a method for generating a high entropy password using a low entropy password and low-entropy login data comprising supplying the low entropy password to a system comprising a generating client and/or a recovery client; and at least n servers; submitting request data derived, at least in part, from the user's low entropy password, where the request data includes authentication data; engaging in a distributed protocol with at least t servers to generate high-entropy values based on stored cryptographic information and a set of authentication information stored on the at least n servers which is checked against the authentication data provided by the user and/or the generating client and/or a recovery client; and generating the high entropy password.