A password-based cryptographic method is effected between a first party with a specified identity and secret password and a second party with a master secret. During a registration phase, a long-term password-based public key is generated for the first party from its password and the master secret of the second party. Subsequently, to generate matching keys, asymmetric or symmetric, for the parties for a specific interaction, the first party generates short-term secret x, and computes a short-term password-based public key that requires for its computation direct knowledge of the first party's password and secrets x; the second party then transforms this short-term password-based public key into an clement X, complimentary to x, by using its master secret and at least a first-party-specific constituent of the first party's long-term password-based public key. The secret x and element X are then used to provide matching keys for the parties.