I was reading the paper, entitled "Multiparty Key Exchange, Efficient Traitor Tracing, and More from Indistinguishability Obfuscation", by Boneh et al. On page 23, the authors have claimed the following.
"Remark 6.2. We note that for private linear broadcast, there are only a polynomial number of recipient sets, meaning selective and adaptive security are equivalent."
How can we prove this Remark? Is it possible to transform a selective secure private linear broadcast encryption scheme to an adaptive secure scheme (for the system which can accommodate at most a polynomial number of users)?