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

Abstract

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 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$O(r\log^2 n)$</tex> </formula> algorithm is obtained to compute the average transmission overhead for any layering-based scheme where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$r$</tex> </formula> out of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> 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.