Lower Bounds for Subset Cover Based Broadcast Encryption

In this paper, we prove lower bounds for a large class of Subset Cover schemes (including all existing schemes based on pseudorandom sequence generators). In particular, we show that - For small r, bandwidth is Ω(r) - For some r, bandwidth is Ω(n/log(s)) - For large r, bandwidth is n - r where n is the number of users, r is the number of revoked users, and s is the space required per user. These bounds are all tight in the sense that they match known constructions up to small constants.

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