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SUMMARYA cross-realm client-to-client password-authenticated key agreement (C2C-PAKA) protocol allows network clients from different realms managed by different servers to agree on a session key in an authentic manner based on easily memorizable passwords. In this paper, we present a generic framework for constructing a cross-realm C2C-PAKA protocol from any secure smart card-based password authentication (PA-SC) protocol. The security proof of our construction can be derived from the underlying PA-SC protocol employing the same assumptions. Our generic framework appears to be the first one with provable security. In addition, compared with similar protocols, the instantiation of our construction achieves improved efficiency.