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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Strongly Secure Identity-Based Key Exchange with Single Pairing Operation

Junichi Tomida, Atsushi Fujioka, 彰 永井, Koutarou Suzuki

Published Dec 31, 2020• 1 citation
Publisher

Abstract

This paper proposes an id-eCK secure identity-based authenticated key exchange (ID-AKE) scheme, where the id-eCK security implies that a scheme resists against leakage of all combinations of master, static, and ephemeral secret keys except ones trivially break the security. Most existing id-eCK secure ID-AKE schemes require two symmetric pairing operations or a greater number of asymmetric pairing, which is faster than symmetric one, operations to establish a session key. However, our scheme is realized with a single asymmetric pairing operation for each party, and this is an advantage in efficiency. The proposed scheme is based on the ID-AKE scheme by McCullagh and Barreto, which is vulnerable to an active attack. To achieve id-eCK security, we apply the HMQV construction and the NAXOS technique to the McCullagh-Barreto scheme. The id-eCK security is proved under the external Diffie-Hellman for target group assumption and the q-gap-bilinear collision attack assumption.

DOI
10.1587/transfun.2020cip0010

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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2011•0 citations
This paper proposes an id-eCK secure identity-based authenticated key exchange (ID-AKE) scheme, where the id-eCK security implies that a scheme resists against leakage of all combinations of master, static, and ephemeral secret keys except ones trivially break the security. Most existing id-eCK secure ID-AKE schemes require two symmetric pairing operations or a greater number of asymmetric pairing, which is faster than symmetric one, operations to establish a session key. However, our scheme is realized with a single asymmetric pairing operation for each party, and this is an advantage in efficiency. The proposed scheme is based on the ID-AKE scheme by McCullagh and Barreto, which is vulnerable to an active attack. To achieve id-eCK security, we apply the HMQV construction and the NAXOS technique to the McCullagh-Barreto scheme. The id-eCK security is proved under the external Diffie-Hellman for target group assumption and the q-gap-bilinear collision attack assumption.
Most of the existing Identity-based(ID) authenticated protocols are proven secure in the Canetti-Krawczyk(CK) model which is weaker than the extended Canetti-Krawczyk(eCK) model.Based on NAXOS trick,a new scheme using bilinear pairing was proposed.The security of the scheme was proven in the eCK model under the random oracle assumption and the Gap Bilinear Diffie-Hellman(GBDH) assumption.The proposed protocol was efficient in computational cost and communication round when compared with other solutions.The new protocol also satisfied master key forward security,perfect forward security and anti-key-leak disguise.
LaMacchia, Lauter and Mityagin [19] proposed a novel security definition for authenticate key exchange (AKE) that gives an adversary the power to obtain ephemeral information regarding a target test session. To demonstrate feasibility of secure protocols in the new definition, henceforth called eCK, the authors described a protocol called NAXOS. NAXOS combines an ephemeral private key x with a static private key a to generate an ephemeral public key X (more precisely in what we call the NAXOS' approach X=gH(x,a)). Thus no one is able to query the discrete logarithm of X without knowing both the ephemeral and static private keys. This idea is crucial in the security argument to guard against leaked ephemeral secrets belonging to the test session. Another important assumption is the gap assumption that allows the protocol to remain secure even in the presence of malicious insiders. Both ideas have been successfully used in creating various protocols secure in the eCK model. In this paper, we construct two eCK-secure protocols without the above mentioned ideas. KFU1 is secure under the GDH assumption without using the NAXOS' approach. KFU2 builds upon KFU1 and drops the gap requirement, thus it is secure under the CDH assumption. Efficiency and security of the proposed protocols are comparable to the well-known HMQV [15] protocol. Furthermore, unlike HMQV and NAXOS the use of the random oracle in KFU1 and KFU2 is restricted to the key derivation function making them more suitable for practical applications.
Identity-based authenticated key exchange (ID-AKE) protocol is an important cryptographic primitive, which is used to establish a session key between two communication participants while authenticating each other. Indeed, most of the existing ID-AKE protocols do not concern with side-channel attacks in the sense that adversaries could obtain partial information of ephemeral/permanent secret keys of users. Recently, several leakage-resilient ID-AKE (LR-ID-AKE) protocols have been proposed to address such attacks. However, these LR-ID-AKE protocols have a restriction that the total leakage information during the life time of the LR-ID-AKE protocol must be bounded to some ratio of ephemeral/permanent secret keys. In this paper, the authors define a new adversary model, termed as identity-based continuous-leakage extended Canetti-Krawczyk (ID-CL-eCK) model. Using the key refreshing procedure (i.e., the multiplicative blinding technique) of permanent secret keys, the first LR-ID-AKE protocol resilient to continuous key leakage is proposed, and it possesses overall unbounded leakage property. Comparisons are given to demonstrate that the proposed protocol is better than the previously proposed ID-AKE protocols in terms of security models and leakage properties. Under the generic bilinear group model, security analysis is made to show that the proposed LR-ID-AKE protocol is secure against adversaries in the new ID-CL-eCK model.
In this paper, we present a new ID-based two-party authenticated key exchange (AKE) protocol, which makes use of a new technique called twin Diffie-Hellman problem proposed by Cash, Kiltz and Shoup. We show that our scheme is secure under bilinear Diffie-Hellman (BDH) assumption in the enhanced Canetti-Krawczyk (eCK) model, which better supports the adversary's queries than previous AKE models. To the best of our knowledge, our scheme is the first ID-based AKE protocol provably secure in eCK model.
In this paper, we propose two authenticated key exchange (AKE) protocols and prove their security in the extended Canetti-Krawczyk model. The first protocol, called NAXOS+, is obtained by slightly modifying the NAXOS protocol proposed by LaMacchia, Lauter and Mityagin [15]. We prove its security under the Computational Diffie-Hellman (CDH) assumption by using the trapdoor test introduced in [6]. To the authors' knowledge, this is the first AKE protocol which is secure under the CDH assumption in the eCK model. The second protocol, called NETS, enjoys a simple and tight security reduction compared to existing schemes including HMQV and CMQV without using the Forking Lemma. Since each session of the NETS protocol requires only three exponentiations per party, its efficiency is also comparable to MQV, HMQV and CMQV.