New broadcast encryption scheme using tree-based circle

Since broadcast encryption was first introduced in 1993 by Fiat and Naor, many broadcast encryption schemes have been developed. Among these, schemes based on tree structure and linear structure are notable. The subset difference (SD) scheme and layered subset difference (LSD) scheme based on tree structure have small user-key size and small transmission overhead when the number r of revoked users is very small. The punctured interval (PI) scheme based on linear (or circular) structure has better transmission over-head when r is not too small. In this paper, we propose a new broadcast encryption scheme, called the tree-based circle (TC) scheme, combining tree structure and circular structure. In this scheme, the transmission overhead is proportional to r like in the SD scheme for small r and becomes asymptotically same as that of the PI scheme when r grows, keeping the computation cost and the storage size small. The TC scheme also inherits the flexibility of the PI scheme. We further improve the transmission overhead of the TC scheme, when r is very small, by adopting the notion of cascade arc.