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Recently, LaMacchia, Lauter and Mityagin proposed the extended Canetti-Krawczyk (eCK) model for Authenticated Key Exchange (AKE) protocols that covers many attacks on existing models. An ID-based AKE protocol with Perfect Forward Secrecy (PFS) (respectively Master Perfect Forward Secrecy (MPFS)) ensures that revelation of the static keys of the parties (respectively the master secret key of the private key generator), must not compromise even a single bit of the session keys of the past sessions between the parties. Currently, to the best of our knowledge, there is no ID-based eCK secure single round AKE protocol with either PFS or MPFS. In our preliminary version [18] we have proposed, without proofs, ID-based eCK secure single round AKE protocols with PFS and MPFS in the random oracle model. To achieve this, we also have constructed ID-based eCK secure single round AKE protocols, one without Master Forward Secrecy (MFS) and one with MFS, almost at the same computational cost as the existing efficient ID-based eCK Secure Single Round AKE protocols. In this full version, we provide proofs to show that all of our protocols are secure under the Gap Bilinear Diffie-Hellman (GBDH) problem.

eCK Secure Single Round ID-based Authenticated Key Exchange Protocols with Master Perfect Forward Secrecy (Extended Version).