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Formal Proof of Relative Strengths of Security between ECK2007 Model and other Proof Models for Key Agreement Protocols.

Jinyue Xia, Jiandong Wang, Liming Fang, Yongjun Ren, Shizhu Bian

Published Jan 1, 2008• 4 citations
OpenAlex

Abstract

In 2005, Choo, Boyd & Hitchcock compared four well-known indistinguishability-based proof models for key agreement protocols, which contains the Bellare & Rogaway (1993, 1995) model, the Bellare , Pointcheval & Rogaway 2000 model and the Canetti & Krawczyk (2001) model. After that, researchers from Microsoft presented a stronger security model, called Extended Canetti-Krawczyk model (2007). In this paper, we will point out the differences between the new proof model and the four previous models, and analyze the relative strengths of security of these models. To support the implication or non-implication relation between these models, we will provide proof or counter-example.

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Jisuanji gongcheng•Jan 1, 2008•0 citations
In 2005, Choo, Boyd & Hitchcock compared four well-known indistinguishability-based proof models for key agreement protocols, which contains the Bellare & Rogaway (1993, 1995) model, the Bellare , Pointcheval & Rogaway 2000 model and the Canetti & Krawczyk (2001) model. After that, researchers from Microsoft presented a stronger security model, called Extended Canetti-Krawczyk model (2007). In this paper, we will point out the differences between the new proof model and the four previous models, and analyze the relative strengths of security of these models. To support the implication or non-implication relation between these models, we will provide proof or counter-example.
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.
Since Bellare and Rogaway presented the first formal security model for authenticated key exchange (AKE) protocols in 1993, many formal security models have been proposed. The extended Canetti-Krawczyk (eCK) model proposed by LaMacchia et al. is currently regarded as the strongest security model for two-party AKE protocols. In this paper, we first generalize the eCK model for tripartite AKE protocols, called teCK model, and enhance the security of the new model by adding a new reveal query. In the teCK model, the adversary has stronger powers, and can learn more secret information. Then we present a new tripartite AKE protocol based on the NAXOS protocol, called T-NAXOS protocol, and analyze its security in the teCK model under the random oracle assumption.
Assessing the security of key exchange protocols is a crucial task and turned out to be highly non-trivial.Many protocols proposed in the past have subsequently been broken.In order to provide a formal framework for security proofs, various security models have been defined.In this thesis, we analyse several such security models for key exchange protocols using the paradigm of constructive cryptography.We examine the exact constructive security guarantees and semantics that these notions provide.In particular, we compare constructive security definitions with a model proposed by Bellare and Rogaway, SK-security by Canetti and Krawczyk and a formal model for secure key exchange proposed by Shoup.i
McCullagh and Barreto presented an identity-based authenticated key agreement protocol in CT-RSA 2005. Their protocol was found to be vulnerable to a key-compromise impersonation attack. In order to recover the weakness, McCullagh and Barreto, and Xie proposed two variants of the protocol respectively. In each of these works, a security proof of the proposed protocol was presented. In this paper, we revisit these three security proofs and show that all the reductions in these proofs are invalid, because the property of indistinguishability between their simulation and the real world was not held. As a replacement, we slightly modify the McCullagh and Barreto’s second protocol and then formally analyse the security of the modified scheme in the Bellare-Rogaway key agreement model.
Since Bellare and Rogaway's work in 1994, the indistinguishability-based security models of authenticated key agreement protocols in simple cases have been evolving for more than ten years. In this paper, we review and organize the models under a unified framework with some new extensions. By providing a new ability (the Coin query) to adversaries and redefining two key security notions, the framework fully exploits an adversary's capacity and can be used to prove all the commonly required security attributes of key agreement protocols with key confirmation. At the same time, the Coin query is also used to define a model which can be used to heuristically evaluate the security of a large category of authenticated protocols without key confirmation. We use the models to analyze a few identity-based authenticated key agreement protocols with pairings.