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on member compromise/leave.
• We propose new key identifier assignment method
which generates unambiguous key identifiers for
nodes in the tree.
• We provide modified PUT operation which reduce
rekey cost on member join. Finally, we show that
our method reduces the rekey cost compared to
LKH and PLKH.
Organization of the Paper. The paper is organized
as follows. In Section 2, we describe various methods
available in literature to optimize LKH scheme. In
Section 3, we discuss various problems with PLKH.
In Section 4, we describe our scheme. In section 5,
we present the simulation results and analysis of the
results. Finally, in Section 6, we conclude our work.
2 RELATED WORK
There are many optimization schemes proposed in
literature for LKH. Some of them optimize network
bandwidth, some reduce rekeycost and others restruc-
ture LKH tree.
The OFC(R. Canetti and Pinkas, 1999) proposed
a variation of LKH which reduces the communication
overhead from LKH’s 2(log
2
N)– 1 to (log
2
N); but it
is limited to the binary key tree case. The Bezawada
scheme(Bezawada and Kulkarni, 2004) proposed a
key distribution algorithm for distributing keys to
only those users who need them. It proposes a com-
pact descendant tracking scheme to track the descen-
dants of the intermediate nodes in the multicast tree.
In the schemes (S. Setia, 2000)(Y. Yang and Lam,
2001), the groups are rekeyed periodically instead of
on every membership change which reduce both the
processing and communication overhead at the key
server.
The scheme in (Sencun Zhu and Jajodia, 2003),
proposed to partition the key tree using temporal pat-
terns of group members which reduce the overhead of
rekeying. The tree is partitioned into S–partition for
short duration members and L–partition for long du-
ration members. In (Onen and Molva, 2004) scheme,
the key server partitions members in different cate-
gories based on their membership duration.
In Refined LKH scheme(Xu and Sun, 2005), on
member join the member behavior namely active and
non–active is used to partition the member. On leave
by a member, “dirty path” is set in the path from
leaving node to root and rekeying is delayed until a
join operation in the same path of leaving member.
This scheme tries to merge leave operation rekey cost
with next join operation in that sub tree. But the per-
formance of algorithm is not adequate in all circum-
stances.
Probabilistic optimization of LKH (Selc¸uk and
Sidhu, 2000), called PLKH, show that it could be ben-
eficial to use an unbalanced key tree in some cases.
The idea in PLKH is to organize the key tree with re-
spect to the compromise probabilities of members, in
a spirit similar to data compression algorithms such
as Huffman and Shannon-Fano coding. Basically, the
key server places members who are is more likely to
be revoked closer to the root of the key tree. PLKH
ensures that the keys each member is holding after an
insert operation is same as those it was holding before
the insertion.
3 SHORTCOMINGS OF PLKH
Although the PLKH scheme reduces the rekeying
cost compared to LKH, it has some shortcomings
too. PLKH has three shortcomings which we are dis-
cussing below.
3.1 Strict Binary Tree Structure
On membership change, PLKH always ensures that
tree formed is strict binary tree. On member join,
PLKH balances the tree such that all the nodes will
have either two child or none. This increases the
depth of newly inserted member node which in turn
increases rekey cost. On deletion of a node, any node
with single child is also removed from tree. This ad-
versely affects the probability value of that deleted
node.
3.2 Probability Considered
PLKH considers cumulative probability i.e. X.p is
equal to the probability of the corresponding mem-
ber if X is a leaf node, and it is equal to X.left.p +
X.right.p, if X is an internal node. The insert oper-
ations proposed check this cumulative probability for
insert operation. This pushes new node down the tree,
even though new node may have higher rekey proba-
bility than some of the nodes on its path to tree root.
Another main problem with cumulative probabil-
ity is that it changes on every membership change
done in the subtree. On membership change, the key
held by nodes in the path from changed member node
to root are refreshed and their cumulative probability
field gets updated to reflect the membership changes.
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