| Multicast is a key technology to support large group communications over the Internet. Security for multicast communication is provided by encrypting and authenticating the messages with a group key shared among the group members. For large multicast groups, efficient key management is a crucial issue. Currently, the most efficient protocols for multicast key management are based on the Logical Key Hierarchy (LKH) scheme. Traditionally, the key distribution tree in an LKH-based protocol is organized as a balanced binary tree, which gives a uniform O(log n) complexity for compromise recovery in an n-member group. In the first part of this thesis, we study improving the performance of LKH-based key distribution protocols by organizing the LKH tree with respect to the members' rekeying probabilities instead of keeping a uniform balanced tree. We propose two algorithms which combine ideas from data compression with the special requirements of multicast key management. Simulation results show that these algorithms can reduce the cost of multicast key management significantly, depending on the amount of variation in the rekey characteristics of the group members.; Linear cryptanalysis is one of the major analysis tools for symmetric-key block ciphers. In the second part of the thesis, we investigate some common but untested practices in linear cryptanalysis with an emphasis on the problem of estimating the bias, which is the main measure of security in linear cryptanalysis. We show by experiments on several ciphers that the bias estimates obtained by the Piling-Up Lemma (PUL) method, which is the de facto standard of bias estimation, can be far from the actual values. We investigate several alternative theories for bias estimation, including the correlation matrices, linear hulls, and statistical estimation by sampling. Some of the investigated techniques provide consistently better results than the PUL. However, they all fall short of a fully satisfactory solution. |
