Optimal key-trees for tree-based private authentication

Abstract

Key-tree based private authentication has been proposed by Molnar and Wagner as a neat way to efficiently solve the problem of privacy preserving authentication based on symmetric key cryptography. However, in the key-tree based approach, the level of privacy provided by the system to its members may decrease considerably if some members are compromised. In this paper, we analyze this problem, and show that careful design of the tree can help to minimize this loss of privacy. First, we introduce a benchmark metric for measuring the resistance of the system to a single compromised member. This metric is based on the well-known concept of anonymity sets. Then, we show how the parameters of the key-tree should be chosen in order to maximize the system's resistance to single member compromise under some constraints on the authentication delay. In the general case, when any member can be compromised, we give a lower bound on the level of privacy provided by the system. We also present some simulation results that show that this lower bound is quite sharp. The results of this paper can be directly used by system designers to construct optimal key-trees in practice; indeed, we consider this as the main contribution of our work. © 2006 Springer-Verlag.