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Authenticated Key Exchange Secure under the Computational Diffie-Hellman Assumption.

Jooyoung Lee, Je Hong Park

Published Jan 1, 2008• 46 citations
OpenAlex

Abstract

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

Related papers

Efficient and Secure Authenticated Key Exchange Protocols in the eCK Model

Jooyoung Lee, Je Hong Park

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.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2011•0 citations

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

Hai Huang

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.

International Journal of Communication Systems•Sep 23, 2013•8 citations

Strongly-secure and Efficient Authenticated Key Exchange Protocol

Jinyue Xia

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.

Jisuanji gongcheng•Jan 1, 2010•0 citations

An eCK-secure Authenticated Key Exchange Protocol Without Random Oracles

Daisuke Moriyama, Tatsuaki Okamoto

Two-party key exchange protocol is a mechanism in which two parties communicate with each other over an insecure channel and output the same session key.A key exchange protocol that is secure against an active adversary who can control and modify the exchanged messages is called authenticated key exchange (AKE) protocol.LaMacchia, Lauter and Mityagin presented a strong security definition for public key infrastructure (PKI) based two-pass protocol, which we call the extended Canetti-Krawczyk (eCK) security model, and some researchers have provided eCK-secure AKE protocols in recent years.However, almost all protocols are provably secure in the random oracle model or rely on a special implementation technique so-called the NAXOS trick.In this paper, we present a PKI-based two-pass AKE protocol that is secure in the eCK security model.The security of the proposed protocol is proven without random oracles (under three assumptions), and does not rely on implementation techniques such as the NAXOS trick.

KSII Transactions on Internet and Information Systems•Jan 1, 2011•11 citations

Strongly Secure Authenticated Key Exchange without NAXOS' Approach under Computational Diffie-Hellman Assumption

Minkyu Kim, Atsushi Fujioka, Berkant Ustaoğlu

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.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2012•6 citations

An efficient strongly secure authenticated key exchange protocol without random oracles

Zheng Yang

Abstract Since the introduction of extended Canetti–Krawczyk (eCK) security model for two‐party key exchange, many protocols have been proposed to provide eCK security. However, most of those protocols are provably secure in the random oracle model or rely on special design technique, which is well known as the NAXOS trick. In contrast to previous schemes, we present an eCK secure protocol in the standard model, without NAXOS trick and without knowledge of secret key assumption for public key registration. The security proof of our scheme is based on standard pairing assumption, collision‐resistant hash functions, Bilinear Decision Diffie–Hellman and Decision Linear Diffie–Hellman assumptions, and pseudo‐random functions with pairwise independent random source. Although our proposed protocol is based on bilinear groups, it does not require any pairing operation during key exchange procedure. Copyright © 2014 John Wiley & Sons, Ltd.

Security and Communication Networks•Aug 28, 2014•0 citations
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.
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.
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.
Two-party key exchange protocol is a mechanism in which two parties communicate with each other over an insecure channel and output the same session key.A key exchange protocol that is secure against an active adversary who can control and modify the exchanged messages is called authenticated key exchange (AKE) protocol.LaMacchia, Lauter and Mityagin presented a strong security definition for public key infrastructure (PKI) based two-pass protocol, which we call the extended Canetti-Krawczyk (eCK) security model, and some researchers have provided eCK-secure AKE protocols in recent years.However, almost all protocols are provably secure in the random oracle model or rely on a special implementation technique so-called the NAXOS trick.In this paper, we present a PKI-based two-pass AKE protocol that is secure in the eCK security model.The security of the proposed protocol is proven without random oracles (under three assumptions), and does not rely on implementation techniques such as the NAXOS trick.
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.
Abstract Since the introduction of extended Canetti–Krawczyk (eCK) security model for two‐party key exchange, many protocols have been proposed to provide eCK security. However, most of those protocols are provably secure in the random oracle model or rely on special design technique, which is well known as the NAXOS trick. In contrast to previous schemes, we present an eCK secure protocol in the standard model, without NAXOS trick and without knowledge of secret key assumption for public key registration. The security proof of our scheme is based on standard pairing assumption, collision‐resistant hash functions, Bilinear Decision Diffie–Hellman and Decision Linear Diffie–Hellman assumptions, and pseudo‐random functions with pairwise independent random source. Although our proposed protocol is based on bilinear groups, it does not require any pairing operation during key exchange procedure. Copyright © 2014 John Wiley & Sons, Ltd.