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KSII Transactions on Internet and Information Systems

An Analysis of Group Key Agreement Schemes based on the Bellare-Rogaway Model in Multi-party Setting

Meng-Hui Lim, Bok‐Min Goi, Sang Gon Lee

Published Jan 1, 2011• 11 citations
Publisher

Abstract

Group key agreement protocols derive a shared secret key for a group of users to ensure data confidentiality or/and integrity among the users in the subsequent communications.In this paper, we inspect two group key agreement schemes which have been proposed by Shi et al. and Zheng et al. in 2005 and 2007 respectively.Although both schemes were claimed to be secure in a heuristic way, we reveal several flaws using the Bellare-Rogaway security model extended to multi-party setting by Bresson et al.These flaws are found to be originated from inappropriate selection of key derivation function, inadvertent exclusion of partners' identities from the protocol specification and insufficient consideration in preserving known temporary information security and key freshness properties.Furthermore, we suggest and discuss proper countermeasures to address such flaws.

DOI
10.3837/tiis.2011.04.011

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Group key agreement protocols derive a shared secret key for a group of users to ensure data confidentiality or/and integrity among the users in the subsequent communications.In this paper, we inspect two group key agreement schemes which have been proposed by Shi et al. and Zheng et al. in 2005 and 2007 respectively.Although both schemes were claimed to be secure in a heuristic way, we reveal several flaws using the Bellare-Rogaway security model extended to multi-party setting by Bresson et al.These flaws are found to be originated from inappropriate selection of key derivation function, inadvertent exclusion of partners' identities from the protocol specification and insufficient consideration in preserving known temporary information security and key freshness properties.Furthermore, we suggest and discuss proper countermeasures to address such flaws.
We study the problem of secure key establishment. We critically examine the security models of Bellare and Rogaway (1993) and Canetti and Krawczyk (2001) in the computational complexity approach, as these models are central in the understanding of the provable security paradigm. We show that the partnership definition used in the three-party key distribution (3PKD) protocol of Bellare and Rogaway (1995) is flawed, which invalidates the proof for the 3PKD protocol. We present an improved protocol with a new proof of security. We identify several variants of the key sharing requirement (i.e., two entities who have completed matching sessions, partners, are required to accept the same session key). We then present a brief discussion about the key sharing requirement. We identify several variants of the Bellare and Rogaway (1993) model. We present a comparative study of the relative strengths of security notions between the several variants of the Bellare-Rogaway model and the Canetti-Krawczyk model. In our comparative study, we reveal a drawback in the Bellare, Pointcheval, and Rogaway (2000) model with the protocol of Abdalla and Pointcheval (2005) as a case study. We prove a revised protocol of Boyd (1996) secure in the Bellare-Rogaway model. We then extend the model in order to allow more realistic adversary capabilities by incorporating the notion of resetting the long-term compromised key of some entity. This allows us to detect a known weakness of the protocol that cannot be captured in the original model. We also present an alternative protocol that is efficient in both messages and rounds. We prove the protocol secure in the extended model. We point out previously unknown flaws in several published protocols and a message authenticator of Bellare, Canetti, and Krawczyk (1998) by refuting claimed proofs of security. We also point out corresponding flaws in their existing proofs. We propose fixes to these protocols and their proofs. In some cases, we present new protocols with full proofs of security. We examine the role of session key construction in key establishment protocols, and demonstrate that a small change to the way that session keys are constructed can have significant benefits. Protocols that were proven secure in a restricted Bellare-Rogaway model can then be proven secure in the full model. We present a brief discussion on ways to construct session keys in key establishment protocols and also prove the protocol of Chen and Kudla (2003) secure in a less restrictive Bellare-Rogaway model. To complement the computational complexity approach, we provide a formal specification and machine analysis of the Bellare-Pointcheval-Rogaway model using an automated model checker, Simple Homomorphism Verification Tool (SHVT). We demonstrate that structural flaws in protocols can be revealed using our framework. We reveal previously unknown flaws in the unpublished preproceedings version of the protocol due to Jakobsson and Pointcheval (2001) and several published protocols with only heuristic security arguments. We conclude this thesis with a listing of some open problems that were encountered in the study.
A flaw lied in the security definition of the Bellare-Rogaway 3PKD model,which was proposed by Bellare and Rogaway for three-party key distribution in 1995,was discovered.To reveal it,a new three-party key distribution proto-col P-Flaw was proposed.The protocol was provably secure under the Bellare-Rogaway 3PKD model.However the pro-tocol was not secure enough to withstand the server spoofing attack,known session key attack,and replay attack.The absence of the origin recognition for the distributed session key accounts for the flaw.Accordingly,the security definition of the Bellare-Rogaway 3PKD model was corrected based on matching conversation.
The main goal of cryptography is to enable secure communication over a public channel; often a secret shared among the communicating parties is used to achieve this. The process by which these parties agree on such a shared secret is called key agreement. In this thesis, we focus on two-party key agreement protocols in the public-key setting and study the various methods used to establish and validate public keys. We pay particular attention to certificateless key agreement schemes and attempt to formalize a relevant notion of security. To that end, we give a possible extension of the existing extended Canetti-Krawzcyk security model applicable to the certificateless setting. We observe that none of the certificateless protocols we have seen in the literature are secure in this model; it is an open question whether such schemes exist. We analyze several published certificateless key agreement protocols, demonstrating the existence of key compromise impersonation attacks and even a man-in-the-middle attack in one case, contrary to the claims of the authors. We also briefly describe weaknesses exhibited by these protocols in the context of our suggested security model.
In an open and distributed environment, authenticated key agreement protocol, as an important cryptographic primitive, is used to authenticate entities and establish session key in order to provide secure communications. Key escrow is essential in situations where confidentiality and audit trail are legal requirements, whilst perfect forward secrecy and known session-specific temporary information secrecy attributes are desirable to provide stronger security. In this paper, we give a cryptanalysis on the scheme due to Wang et al., which is based on the identity-based encryption scheme proposed by Gentry (Eurocrypt'06), and then present an enhanced secure two-party identity-based authenticated key agreement protocol. The new proposed protocol achieves most of the required security attributes and can be used properly in the escrow mode. Security analysis shows that it achieves the attributes of known-key secrecy, key-compromise impersonation resilience, unknown key-share resilience and no key control. In addition, it captures the perfect forward secrecy and known session-specific temporary information secrecy attributes.