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International Journal of Communication Systems

Authenticated key exchange protocol under computational Diffie–Hellman assumption from trapdoor test technique

Hai Huang

Published Sep 23, 2013• 8 citations
Publisher

Abstract

SUMMARY This paper investigates authenticated key exchange (AKE) protocol under computational Diffie–Hellman assumption in the extended Canetti–Krawczyk model. The core technical component of our protocol is the trapdoor test technique, which is originally introduced to remove the gap Diffie–Hellman (GDH) assumption for the public key encryption schemes. Our contributions are twofold.First, we clarify some misunderstandings of the usage of the trapdoor test technique in AKE protocols showing its adaptation to the AKE protocols is not trivial. We point out some errors in some recent work which attempts to make use of the trapdoor test technique to remove GDH assumption.Second, based on trapdoor test technique, we propose an efficient extended Canetti–Krawczyk secure AKE protocol under computational Diffie–Hellman assumption instead of GDH assumption. Additionally, our protocol does not make use of NAXOS trick and has a tight reduction. In comparison with all existing AKE protocols with the properties as previously mentioned, our protocol with only three exponentiations is most efficient. Copyright © 2013 John Wiley & Sons, Ltd.

DOI
10.1002/dac.2671

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SUMMARY This paper investigates authenticated key exchange (AKE) protocol under computational Diffie–Hellman assumption in the extended Canetti–Krawczyk model. The core technical component of our protocol is the trapdoor test technique, which is originally introduced to remove the gap Diffie–Hellman (GDH) assumption for the public key encryption schemes. Our contributions are twofold.First, we clarify some misunderstandings of the usage of the trapdoor test technique in AKE protocols showing its adaptation to the AKE protocols is not trivial. We point out some errors in some recent work which attempts to make use of the trapdoor test technique to remove GDH assumption.Second, based on trapdoor test technique, we propose an efficient extended Canetti–Krawczyk secure AKE protocol under computational Diffie–Hellman assumption instead of GDH assumption. Additionally, our protocol does not make use of NAXOS trick and has a tight reduction. In comparison with all existing AKE protocols with the properties as previously mentioned, our protocol with only three exponentiations is most efficient. Copyright © 2013 John Wiley & Sons, Ltd.
Abstract. In this paper, we present a new authenticated key exchange(AKE) protocol and prove its security under the random oracle assumption and the computational Diffie-Hellman(CDH) assumption. In the extended Canetti-Krawczyk model, there has been no known AKE protocol based on the CDH assumption. Our protocol, called NAXOS+, is obtained by slightly modifying the NAXOS protocol proposed by LaMacchia, Lauter and Mityagin. We establish a formal security proof of NAXOS+ in the extended Canetti-Krawczyk model using as a main tool the trapdoor test presented by Cash, Kiltz and Shoup. Key words: authenticated key exchange, trapdoor test, computational Diffie-Hellman assumption, extended Canetti-Krawzcyk model 1
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.
This paper presents an Authenticated Key Exchange(AKE) protocol,named AKE-1.Compared with previous protocols,the proposal is more efficient and proven to be safe in newly enhanced Canetti-Krawczyk(eCK07) model under the random oracle assumption and the Computational Diffie-Hellman(CDH) assumption.It uses a technique named trapdoor test,recently proposed by Cash,Kiltz and Shoup.In addition,it presents a one-pass variant(for only one entity on line) and three-pass variant(providing key confirmation) of AKE-1 for different applications.
In this paper, we propose an authenticated key exchange (AKE) protocol under the computational Diffie-Hellman (CDH) assumption with respect to the strengthened eCK-security (seCK-security) of Sarr et al.. To date, many AKE protocols either are provably secure under a rather strong and non-standard assumption named as the gap Diffie-Hellman (GDH) assumption, or fall to practical attacks on the intermediate result leakage which can be captured by the seCK model. In order to remove the gap assumption and achieve stronger security requirements, we present the TMQV protocol using the twinning technique and the MQV key derivation method. With the help of trapdoor test theorem, TMQV is provably seCK-secure under the standard CDH assumption in the random oracle model. Compared with the related works, TMQV achieves not only stronger security but also higher implementation efficiency with weaker cryptographic assumptions.
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.