Sanjay Bhattacherjee

Complete tree subset difference broadcast encryption scheme and its analysis

The subset difference (SD) method proposed by Naor, Naor and Lotspiech is the most popular broadcast encryption (BE) scheme. It is suitable for real-time applications like Pay-TV and has been suggested for use by the AACS standard for digital rights management in Blu-Ray and HD-DVD discs. The SD method assumes the number of users to be a power of two. We propose the complete tree subset difference (CTSD) method that allows the system to support an arbitrary number of users. In particular, it subsumes the SD method and all results proved for the CTSD method also hold for the SD method. Recurrences are obtained for the CTSD scheme to count the number, N(n, r, h), of possible ways r users in the system of n users can be revoked to result in a transmission overhead or header length of h. The recurrences lead to a polynomial time dynamic programming algorithm for computing N(n, r, h). Further, they provide bounds on the maximum possible header length. A probabilistic analysis is performed to obtain an O(r log n) time algorithm to compute the expected header length in the CTSD scheme. Further, for the SD scheme we obtain an explicit limiting upper bound on the expected header length.

Concrete Analysis and Trade-Offs for the (Complete Tree) Layered Subset Difference Broadcast Encryption Scheme

Two key parameters of broadcast encryption (BE) schemes are the transmission size and the user storage. Naor-Naor-Lotspiech (2001) introduced the subset difference (SD) scheme achieving a good trade-off between these two parameters. Halevy-Shamir (2002) introduced the idea of layering to reduce user storage of the NNL scheme at the cost of increased transmission overhead. Here, we introduce several simple ideas to obtain new layering strategies with different trade-offs between user storage and transmission overhead. We define the notion of storage minimal layering and describe a dynamic programming algorithm to compute layering schemes for which the user storage is the minimum attainable using layerings. Further, the constrained minimization problem is considered. A method is described which yields BE schemes whose transmission overhead is not much more than the SD scheme but, whose user storage is still significantly lower. Finally, an O(r log2 n) algorithm is obtained to compute the average transmission overhead for any layering-based scheme where r out of n users are revoked. This algorithm works for any layering strategy and also for arbitrary number of users. The algorithm has been used here to generate all data for the average transmission overhead.

Tree based symmetric key broadcast encryption

The most influential broadcast encryption (BE) scheme till date was introduced in 2001 by Naor, Naor and Lotspiech (NNL) and is based on binary trees. This paper generalizes the ideas of NNL to obtain BE schemes based on k-ary trees for any k ? 2 . The treatment is uniform across all k and essentially provides a single scheme which is parameterized by the arity of the underlying tree. We perform an extensive analysis of the header length and user storage of the scheme. It is shown that for a k-ary tree with n users out of which r are revoked, the maximum header length is min ? ( 2 r - 1 , n - r , ? n / k ? ) . An expression for the expected header length is obtained and it is shown that the expression can be evaluated in O ( r log ? n ) time. Experimental results indicate that for values of r one would expect in applications such as pay TV systems, the average header length decreases as k increases. The number of keys to be stored by any user is shown to be at most ( ? k - 2 ) ? 0 ( ? 0 + 1 ) / 2 , where ? 0 = ? log k ? n ? and ? k is the number of cyclotomic cosets modulo 2 k - 1 . In particular, when the number of users is more than 1024, we prove that the user storage required for k = 3 is less than that of k = 2 . For higher values of k, the user storage is greater than that for binary trees. The option of choosing the value of k provides a designer of a BE system with a wider range of trade-offs between average header length and user storage. The effect of layering on the k-ary tree SD scheme is also explored.