I have a rather enlightening chat with Yvo Desmedt after the Cambridge Security Protocol‘s Workshop, who was kind enough to give me an overview and insight into the group key agreement protocols of the ’90s. As part of an on-going conversation on secure chat, I am trying to understand the genealogy, and requirement, for key group agreements to be “contributory” — namely ensure all participants contribute to the final group key, even under malice. It seems that there is also a preference for symmetric schemes, where all participants perform the same operations.

Yvo’s classic Eurocrypt paper [BD94] is the basis of GOTR [LVH13], which manages to complicate it considerably. The original paper had a O(N) broadcasts cost, and was “peer-to-peer”, meaning that everyone just does the same thing. However it did not consider an active adversary, and was also not “contributory” meaning that an insider (active) adversary could force the key to anything they liked. Interestingly, Yvo points me to [BD96], which he thinks is superior to [BD94]. This paper really illustrates that there is no magic to group key agreement: a master key for the group is determined and then propagated using a key-sharing graph. This reduces the cost from O(N) broadcasts to just O(N) point to point messages — which to me seems optimal.

Now, the idea that schemes must be “contributory” (ie. no participant is special in determining the key — no one can force the key to be some specific value) emerged sometime in the late ’90s. The first reference I found to this property is [BW98], where the authors look at the round complexity of key agreement. However they state that “If the group key is generated and distributed by a central trusted party, then it is not necessary to discuss the communication complexity“. Then, they just launch into those schemes with no justification as to the reason centralized distribution may be a problem …

Katz and Young [KY03] also state that “(we exclude here centralized protocols in which a designated group manager is assumed; such asymmetric, non-contributory schemes place an unfairly high burden on one participant who is a single point of failure and who must also be trusted to properly generate keys)“. So it seems that the security issue contributory schemes try to mitigate is a flawed RNG. However this is a marginal threat — if the RNG is bad, than it may be likely the adversary can also corrupt other aspects of the platform to extract keys. In any case the flawed RNG threat can be dealt with by including some entropy from other participants assuming that they do not act in an adaptive malicious manner (if they do they can just leak the key to the adversary). I find it strange that KY03 argue that a single participant must not be burdened, when this results in proposed protocols that burden all participants to a great extent instead.

Around 2000 a number of works spring up that attempt to extend key agreement to dynamic membership setting, including [STW00] and [KPT00]. It is not at all clear to me whether those are in fact superior to running the key exchange multiple times, or even having a central party distributing keys.

Finally, Goldberg and others [GUGC09] propose extensions to OTR for a multi-user setting. These focus on deniability and signatures (and call a generic key exchange protocol) and a shared authentic transcript. This is a fine property, however I am a bit surprised the protocols are (a) so complex to establish ephemeral signatures and (b) so simple if they are to establish transcript consistency. My understanding is that they rely on the channel to offer consistent ordering, and then simply cryptographically ensure it was not tampered by an adversary — however I only read the paper obliquely.

Conclusion: It seems that a lot of the literature on group key exchange is based on the premise that the protocols need to be symmetric and contributory. Yet, I fail to see any justification beyond the fact that centralized schemes are simple and efficient, and no one could possibly write an academic paper about them. All schemes I have seem rely on the honest channel offering ordering, and being reliable. If that is not the case some of them detect it and hard fail (for example the integrity checks fail, with no hint that it is due to missing messages). This means that they assume some ordering happens on the outside of the crypto, which is dubious without some leader election. Few works have dealt with how you determine the group, which would either go the admin way or the voting way (can of worms).

References:

[BD94] Mike Burmester, Yvo Desmedt: A Secure and Efficient Conference Key Distribution System (Extended Abstract). EUROCRYPT 1994: 275-286

[LVH13] Hong Liu, Eugene Y. Vasserman, Nicholas Hopper: Improved group off-the-record messaging. WPES 2013: 249-254

[BD96] Mike Burmester, Yvo Desmedt: Efficient and Secure Conference-Key Distribution. Security Protocols Workshop 1996: 119-129

[GUGC09] Ian Goldberg, Berkant Ustaoglu, Matthew Van Gundy, Hao Chen: Multi-party off-the-record messaging. ACM Conference on Computer and Communications Security 2009: 358-368

[KY03] Katz, Jonathan, and Moti Yung. “Scalable protocols for authenticated group key exchange.” Advances in cryptology-CRYPTO 2003. Springer Berlin Heidelberg, 2003. 110-125.

[BW98] Becker, Klaus, and Uta Wille. “Communication complexity of group key distribution.” Proceedings of the 5th ACM conference on Computer and communications security. ACM, 1998.

[STW00] Steiner, Michael, Gene Tsudik, and Michael Waidner. “Key agreement in dynamic peer groups.” Parallel and Distributed Systems, IEEE Transactions on 11.8 (2000): 769-780.

[KPT00] Kim, Yongdae, Adrian Perrig, and Gene Tsudik. “Simple and fault-tolerant key agreement for dynamic collaborative groups.” Proceedings of the 7th ACM conference on Computer and communications security. ACM, 2000.

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I read today a brief missive about the Russian government’s intent to replace US sourced CPUs, the heart of a modern computer, with domestically produced ones. This is presumably a move to protect their critical infrastructure from hardware back doors, that are difficult to detect or eliminate. This is a good opportunity to share my thoughts on what is at stake in the current debate about the NSA’s and GCHQ’s pervasive surveillance infrastructure, including historic attempts to prevent the development and widespread use of security and cryptology technologies, and their current active compromise of international communications and end-users.

A lot has been written about the right to privacy of American citizens, and to some extent now British subjects. In my opinion, this important domestic issue lies on the insignificant end of the global impact of the Snowden revelations. It is also the only issue that may be resolved through better oversight and stronger privacy guarantees in national laws (with the caveats relating to the “liberal fallacy“).

What is truly at stake is whether a small number of technologically-advanced countries, including the US and the UK, but also others with a domestic technology industry, should be in a position to absolutely dominate the “cyber-space” of smaller nations. About 20 years ago, this may have been a minor concern as few things were critically dependent on IP or mobile networks. Today, most social and economic interactions are mediated through such technologies, or could economically benefit from being so, if only due to “security and privacy concerns”.

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