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Lecture notes in computer science

Strongly Authenticated Key Exchange Protocol from Bilinear Groups without Random Oracles

Zheng Yang, Jörg Schwenk

Published Jan 1, 2012• 7 citations
Publisher
DOI
10.1007/978-3-642-33272-2_17

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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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Strongly Authenticated Key Exchange Protocol from Bilinear Groups without Random Oracles.

Zheng Yang, Jörg Schwenk

Malicious insider security of authenticated key exchange (AKE) protocol addresses the situation that an AKE protocol is secure even with existing dishonest parties established by adversary in corresponding security experiment. In the eCK model, the EstablishParty query is used to model the malicious insider setting. However such strong query is not clearly formalized so far. We show that the proof of possession assumptions for registering public keys are of prime importance to malicious insider security. In contrast to previous schemes, we present an eCK secure protocol in the standard model, without assuming impractical, strong, concurrent zero-knowledge proofs of knowledge of secret keys done to the CA at key registration. The security proof of our scheme is based on standard pairing assumption, collision resistant hash functions, bilinear decision Diffie-Hellman (BDDH) and decision linear Diffie-Hellman (DLIN) assumptions, and pseudo-random functions with pairwise independent random source πPRF [14].

•Jan 1, 2012•0 citations
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.
Recently, several identity (ID)-based authenticated group key exchange (IDAGKE) protocols from bilinear pairings were proposed. However, they all suffered from different types of insider (participants) colluding attacks. In this paper, we present a new IDAGKE protocol from bilinear pairings. In the random oracle model and under some security assumptions, we demonstrate that the proposed protocol is a provably secure IDAGKE protocol providing forward secrecy. Meanwhile, it is secure against insider attacks.
Malicious insider security of authenticated key exchange (AKE) protocol addresses the situation that an AKE protocol is secure even with existing dishonest parties established by adversary in corresponding security experiment. In the eCK model, the EstablishParty query is used to model the malicious insider setting. However such strong query is not clearly formalized so far. We show that the proof of possession assumptions for registering public keys are of prime importance to malicious insider security. In contrast to previous schemes, we present an eCK secure protocol in the standard model, without assuming impractical, strong, concurrent zero-knowledge proofs of knowledge of secret keys done to the CA at key registration. The security proof of our scheme is based on standard pairing assumption, collision resistant hash functions, bilinear decision Diffie-Hellman (BDDH) and decision linear Diffie-Hellman (DLIN) assumptions, and pseudo-random functions with pairwise independent random source πPRF [14].