Password managers (aka stores or vaults) allow a user to store and retrieve (usually high-entropy) passwords for her multiple password-protected services by interacting with a "device" serving the role of the manager (e.g., a smartphone or an online third-party service) on the basis of a single memorable (low-entropy) master password. Existing password managers work well to defeat offline dictionary attacks upon web service compromise, assuming the use of high-entropy passwords is enforced. However, they are vulnerable to leakage of all passwords in the event the device is compromised, due to the need to store the passwords encrypted under the master password and/or the need to input the master password to the device (as in smartphone managers). Evidence exists that password managers can be attractive attack targets. In this paper, we introduce a novel approach to password management, called SPHINX, which remains secure even when the password manager itself has been compromised. In SPHINX, the information stored on the device is information theoretically independent of the user's master password - an attacker breaking into the device learns no information about the master password or the user's site-specific passwords. Moreover, an attacker with full control of the device, even at the time the user interacts with it, learns nothing about the master password - the password is not entered into the device in plaintext form or in any other way that may leak information on it. Unlike existing managers, SPHINX produces strictly high-entropy passwords and makes it compulsory for the users to register these randomized passwords with the web services, hence fully defeating offline dictionary attack upon service compromise. The design and security of SPHINX is based on the device-enhanced PAKE model of Jarecki et al. that provides the theoretical basis for this construction and is backed by rigorous cryptographic proofs of security. While SPHINX is suitable for different device and online platforms, in this paper, we report on its concrete instantiation on smartphones given their popularity and trustworthiness as password managers (or even two-factor authentication). We present the design, implementation and performance evaluation of SPHINX, offering prototype browser plugins, smartphone apps and transparent device-client communication. Based on our inspection analysis, the overall user experience of SPHINX improves upon current managers. We also report on a lab-based usability study of SPHINX, which indicates that users' perception of SPHINX security and usability is high and satisfactory when compared to regular password-based authentication. Finally, we discuss how SPHINX may be extended to an online service for the purpose of back-up or as an independent password manager.