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loosely coupled, or when the connectivity between members is poor, or just
simply when the most common behaviour of a member is to be off-line. In these
cases it can be too expensive to assume that members are (implicitly) evicted
as they go off-line.
Our approach to deal with off-line members benefits from the fact that, when
a group member becomes active again, he is usually just interested in the key
currently used by the group, and not in all the intermediate keys that were in
use while he was off-line. Therefore, we have devised a data structure that we
call the Key History Tree (KHT) that uses this property to merge all the key
updates multicast by a KM into a very compact representation. KHTs contain
only publicly available information, i.e., encrypted keys, so that they can be
safely cached in different parts of the network. This simplifies the way that the
manager of the KHT receives updates reliably from the KM, ensuring that its
information is easily multicast to members when they are back online.
Moreover, off-line members keep state associated with previously known keys,
and this can help us to prune the KHT. In particular, we define the KHT Working
Set (KHT-WS) to be the minimal subset of this tree that is needed so that all
the valid group members can obtain the current key. Unfortunately, to compute
the WS, we need to know the exact rekeying status of our group members and
some of them are off-line. Therefore, we provide a set of heuristics to prune the
KHT that give us an estimate of this WS without needing global knowledge.
These heuristics are based on previous behaviour, relative importance of the
nodes, and “ageing” information associated with the node keys.
KHT is particularly suited for Anonymous Group Content Delivery (AGCD).
On the one hand, the server enforces that content is only visible to current group
members. On the other hand, the group members want to avoid the server track-
ing what content they access. As the group membership can be very dynamic,
ecient delivery should allow multicast or cached content, and most members
are likely to be off-line most of the time. Encrypting all content with a group
key is an obvious solution, but the management of this shared key must handle
off-line members well. Our solution annotates the subscribed content with an
estimate of the KHT-WS to facilitate the handling of off-line members.
The rest of this paper is organized as follows: Section 2 discusses related
work. Section 3 explains in more detail the KHT data structure and algorithms.
Section 4 describes an implementation of AGCD using a KHT. Section 5 presents
some simulation results showing the performance of KHT for the AGCD appli-
cation discussed above. Finally, Section 6 discusses our conclusions.
2
Related Work
Secure multicast and scalable re-keying for dynamic groups is a well established
field [2,3,4]. In particular, we are building on the work on LKH described in [1].
On-going standardization efforts will provide seamless integration of these algo-
rithms with commonly used network security protocols, e.g., IPSEC [5,6].
Reliability of group re-keying, with a focus on key recovery for on-line mem-
bers when there are failures in the multicast transport is discussed in [7]. Their
