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Lecture notes in computer science

eCK Secure Single Round ID-Based Authenticated Key Exchange Protocols with Master Perfect Forward Secrecy

Tapas Pandit, Rana Barua, Somanath Tripathy

Published Jan 1, 2014• 5 citations
Publisher
DOI
10.1007/978-3-319-11698-3_33

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

Tapas Pandit, Rana Barua, Somanath Tripathy

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.

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Abstract. This paper investigates the two-pass authenticated key exchange protocol in the enhanced Canetti-Krawczyk (eCK) with perfect forward security. Currently, there exist no authenticated key exchange protocols which are provably secure in eCK model and meanwhile achieve perfect forward security against active adversary in one round. We propose a new two-pass authenticated key exchange protocol which enjoys following desirable properties. First, our protocol is shown secure in the eCK model under the gap Diffie-Hellman (GDH) assumption. Moreover, our protocol does not use the NAXOS transformation, the drawback of which will be discussed in the introduction. Second, under the same assumption, we prove that our protocol achieves perfect forward security against active adversary in one round. To the best of our knowledge, our proposal is first two-pass (one round) AKE protocol provably secure in the eCK model and achieving perfect forward security against active adversary.

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One-round group authenticated key exchange (GAKE) protocols typically provide implicit authentication and appealing bandwidth efficiency. As a special case of GAKE – the pairing-based one-round tripartite authenticated key exchange (3AKE), recently gains much attention of research community due to its strong security. Several pairing-based one-round 3AKE protocols have recently been proposed to achieve provable security in the g-eCK model. In contrast to earlier GAKE models, the g-eCK model particularly formulates the security properties regarding resilience to the leakage of various combinations of long-term key and ephemeral session state, and provision of weak perfect forward secrecy in a single model. However, the g-eCK security proofs of previous protocols are only given under the random oracle model. In this work, we give a new construction for pairing-based one-round 3AKE protocol which is provably secure in the g-eCK model without random oracles. Security of proposed protocol is reduced to the hardness of Cube Bilinear Decisional Diffie-Hellman (CBDDH) problem for symmetric pairing. We also extend the proposed 3AKE scheme to a GAKE scheme with more than three group members, based on multilinear maps. We prove g-eCK security of our GAKE scheme in the standard model under the natural multilinear generalization of the CBDDH assumption.

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Chinese Journal of Computers•May 17, 2011•2 citations
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.
Abstract. This paper investigates the two-pass authenticated key exchange protocol in the enhanced Canetti-Krawczyk (eCK) with perfect forward security. Currently, there exist no authenticated key exchange protocols which are provably secure in eCK model and meanwhile achieve perfect forward security against active adversary in one round. We propose a new two-pass authenticated key exchange protocol which enjoys following desirable properties. First, our protocol is shown secure in the eCK model under the gap Diffie-Hellman (GDH) assumption. Moreover, our protocol does not use the NAXOS transformation, the drawback of which will be discussed in the introduction. Second, under the same assumption, we prove that our protocol achieves perfect forward security against active adversary in one round. To the best of our knowledge, our proposal is first two-pass (one round) AKE protocol provably secure in the eCK model and achieving perfect forward security against active adversary.
One-round group authenticated key exchange (GAKE) protocols typically provide implicit authentication and appealing bandwidth efficiency. As a special case of GAKE – the pairing-based one-round tripartite authenticated key exchange (3AKE), recently gains much attention of research community due to its strong security. Several pairing-based one-round 3AKE protocols have recently been proposed to achieve provable security in the g-eCK model. In contrast to earlier GAKE models, the g-eCK model particularly formulates the security properties regarding resilience to the leakage of various combinations of long-term key and ephemeral session state, and provision of weak perfect forward secrecy in a single model. However, the g-eCK security proofs of previous protocols are only given under the random oracle model. In this work, we give a new construction for pairing-based one-round 3AKE protocol which is provably secure in the g-eCK model without random oracles. Security of proposed protocol is reduced to the hardness of Cube Bilinear Decisional Diffie-Hellman (CBDDH) problem for symmetric pairing. We also extend the proposed 3AKE scheme to a GAKE scheme with more than three group members, based on multilinear maps. We prove g-eCK security of our GAKE scheme in the standard model under the natural multilinear generalization of the CBDDH assumption.