Thesis

2.2. Resistance to single member compromise
key-tree should look like. In this chapter, I address this problem, and I show how to find optimal
key-trees.
In this chapter, after finding the optimal key-tree, I go further and I present a novel symmetrickey
private authentication scheme that provides a higher level of privacy and achieves better
efficiency than the key-tree based approach. This approach is called the group based approach.
More precisely, the complexity of the group based scheme for the reader can be set to be O(log N)
(i.e., the same as in the key-tree based approach), while the complexity for the tags is always a
constant (in contrast to O(log N) of the key-tree based approach). Hence, the group based scheme
is better than the key-tree based scheme both in terms of privacy and efficiency, and therefore, it
is a serious alternative to the key-tree based scheme to be considered by the RFID community.
More precisely, the main contributions are the following:
I propose a benchmark metric for measuring the resistance of the system to a single compromised
member based on the concept of anonymity sets. To the best of my knowledge,
anonymity sets have not been used in the context of private authentication yet. I prove that
this simply defined metric is equivalent to a metric widely used in cryptography with a much
more complex definition. The real contribution of the metric, is that its definition simplifies
the usage of the metric without losing any details of the more complex metric.
I introduce the idea of using different branching factors at different levels of the key-tree;
the advantage is that the system’s resistance to single member compromise can be increased
while still keeping the authentication delay short. To the best of my knowledge, key-trees
with variable branching factors have not been proposed yet for private authentication.
I present an algorithm for determining the optimal parameters of the key-tree, where optimal
means that resistance to single member compromise is maximized, while the authentication
delay is kept below a predefined threshold.
In the general case, when any member can be compromised, I give a lower bound on the
level of privacy provided by the system, and present some simulation results that show that
this lower bound is quite sharp. This allows me to compare different systems based on their
lower bounds.
I introduce a group based approach, which is superior to the tree-based approach in many
properties.
In summary, I propose practically usable techniques for designers of RFID based authentication
systems.
The outline of the chapter is the following: in Section 2.2, I introduce my benchmark metric
to measure the level of privacy provided by key-tree or group based authentication systems, and
I illustrate, through an example, how this metric can be used to compare systems with different
parameters. By the same token, I also show that key-trees with variable branching factors can be
better than key-trees with a constant branching factor at every level. In Section 2.3, I formulate
the problem of finding the best key-tree with respect to my benchmark metric as an optimization
problem, and I present an algorithm that solves that optimization problem. In Section 2.4, I
consider the general case, when any number of members can be compromised, and I derive a useful
lower bound on the level of privacy provided by the system. After finding the optimal key-tree, I
describe the operation of my group based scheme in Section 2.5, and I quantify the level of privacy
that it provides in Section 2.6. I compare the group based scheme to the key-tree based approach
in Section 2.7. Finally, in Section 2.8, I report on some related work, and in Section 2.9, I conclude
the chapter.
2.2 Resistance to single member compromise
There are different ways to measure the level of anonymity provided by a system [Diaz et al., 2002;
Serjantov and Danezis, 2003]. Here the concept of anonymity sets [Chaum, 1988] is used. The
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