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ACM Asia Conference on Computer and Communications Security (ASIA CCS)

Securing group key exchange against strong corruptions

Emmanuel Bresson, Mark Manulis

Published Mar 18, 2008• 65 citations
Publisher

Abstract

When users run a group key exchange (GKE) protocol, they usually extract the key from some auxiliary (ephemeral) secret information generated during the execution. Strong corruptions are attacks by which an adversary can reveal these ephemeral secrets, in addition to the possibly used long-lived keys. Undoubtedly, security impact of strong corruptions is serious, and thus specifying appropriate security requirements and designing secure GKE protocols appears an interesting yet challenging task --- the aim of our paper.

DOI
10.1145/1368310.1368347

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When users run a group key exchange (GKE) protocol, they usually extract the key from some auxiliary (ephemeral) secret information generated during the execution. Strong corruptions are attacks by which an adversary can reveal these ephemeral secrets, in addition to the possibly used long-lived keys. Undoubtedly, security impact of strong corruptions is serious, and thus specifying appropriate security requirements and designing secure GKE protocols appears an interesting yet challenging task --- the aim of our paper.
In Group Key Exchange (GKE) protocols, users usually extract the group key using some auxiliary (ephemeral) secret information generated during the execution. Strong corruptions are attacks by which an adversary can reveal these ephemeral secrets, in addition to the possibly used long-lived keys. Undoubtedly, security impact of strong corruptions is serious, and thus specifying appropriate security requirements and designing secure GKE protocols appears an interesting yet challenging task – the aim of our article. We start by investigating the current setting of strong corruptions and derive some refinements like opening attacks that allow to reveal ephemeral secrets of users without their long-lived keys. This allows to consider even stronger attacks against honest, but 'opened' users. Further, we define strong security goals for GKE protocols in the presence of such powerful adversaries and propose a 3-round GKE protocol, named TDH1, which remains immune to their attacks under standard cryptographic assumptions. Our security definitions allow adversaries to register users and specify their long-lived keys, thus, in particular capture attacks of malicious insiders for the appropriate security goals such as Mutual Authentication, key confirmation, contributiveness, key control and key-replication resilience.
Recent advances in the design and analysis of secure two-party key exchange (2KE) such as the leakage of ephemeral secrets used during the attacked sessions remained unnoticed by the current models for group key exchange (GKE). Focusing on a special case of GKE | the tripartite key exchange (3KE) | that allows for ecient one-round protocols, we demonstrate how to incorporate these advances to the multi-party setting. From this perspective our work closes the most pronounced gap between provably secure 2KE and GKE protocols. The proposed 3KE protocol is an implicitly authenticated protocol with one communication round which remains secure even in the event of ephemeral secret leakage. It also signicantly improves upon currently known 3KE protocols, many of which are insecure. An optional key conrmation round can be added to our proposal to achieve the explicitly authenticated protocol variant.
When a group key exchange protocol is executed, the session key is typically extracted from two types of secrets: long-term keys (for authentication) and freshly generated (often random) values. The leakage of this latter so-called ephemeral keys has been extensively analysed in the 2-party case, yet very few works are concerned with it in the group setting. The authors provide a generic group key exchange construction that is strongly secure, meaning that the attacker is allowed to learn both long-term and ephemeral keys (but not both from the same participant, as this would trivially disclose the session key). Their design can be seen as a compiler, in the sense that it builds on a 2-party key exchange protocol which is strongly secure and transforms it into a strongly secure group key exchange protocol by adding only one extra round of communication. When applied to an existing 2-party protocol from Bergsma et al., the result is a 2-round group key exchange protocol which is strongly secure in the standard model, thus yielding the first construction with this property.
With the rapid development of cloud computing and mobile networks, more and more application scenarios require a secret group key for secure communication. Group Key Exchange (GKE) protocol provides a secret group key for three or more members. Burmester and Desmedt presented an influential GKE protocol, which has a broadcast version and a cyclic version. In this paper, we investigate the security weaknesses of the Burmester-Desmedt protocol. We report that both the broadcast version and the cyclic version of the Burmester-Desmedt protocol suffer member tampering attacks if the two members that belong to both group A and group B are corrupted. That is, two corrupted members can add some unknowing members of group A to group B and trick the legal members of group B to believe that these unknowing members share the secret group key with them after a protocol run. Furthermore, to defeat the member tampering attack, we propose digital signature-based improvements on the broadcast version and the cyclic version of the Burmester-Desmedt protocol. We hope our research results will encourage the development of more robust and effective GKE protocols that stand rigorous security analysis.
When a group key exchange protocol is executed, the session key is typically extracted from two types of secrets: long‐term keys (for authentication) and freshly generated (often random) values. The leakage of this latter so‐called ephemeral keys has been extensively analysed in the 2‐party case, yet very few works are concerned with it in the group setting. The authors provide a generic group key exchange construction that is strongly secure, meaning that the attacker is allowed to learn both long‐term and ephemeral keys (but not both from the same participant, as this would trivially disclose the session key). Their design can be seen as a compiler, in the sense that it builds on a 2‐party key exchange protocol which is strongly secure and transforms it into a strongly secure group key exchange protocol by adding only one extra round of communication. When applied to an existing 2‐party protocol from Bergsma et al ., the result is a 2‐round group key exchange protocol which is strongly secure in the standard model, thus yielding the first construction with this property.
Two-party key exchange (2PKE) protocols have been rigorously analyzed under various models considering different adversarial actions. However, the analysis of group key exchange (GKE) protocols has not been as extensive as that of 2PKE protocols. Particularly, an important security attribute called key compromise impersonation (KCI) resilience has been completely ignored for the case of GKE protocols. Informally, a protocol is said to provide KCI resilience if the compromise of the long-term secret key of a protocol participant A does not allow the adversary to impersonate an honest participant B to A. In this paper, we argue that KCI resilience for GKE protocols is at least as important as it is for 2PKE protocols. Our first contribution is revised definitions of security for GKE protocols considering KCI attacks by both outsider and insider adversaries. We also give a new proof of security for an existing two-round GKE protocol under the revised security definitions assuming random oracles. We then show how to achieve insider KCIR in a generic way using a known compiler in the literature. As one may expect, this additional security assurance comes at the cost of an extra round of communication. Finally, we show that a few existing protocols are not secure against outsider KCI attacks. The attacks on these protocols illustrate the necessity of considering KCI resilience for GKE protocols.