Those interested in predicate encryption might also enjoy 

Group Authentication Using The Naccache-Stern Public-Key Cryptosystem

which takes a different approach and handles negation.

A group authentication protocol authenticates pre-defined groups of
individuals such that: 
- No individual is identified 
- No knowledge of which groups can be successfully authenticated is known to
the verifier 
- No sensitive data is exposed 
The paper presents a group authentication protocol based on splitting the
private keys of the Naccache-Stern public-key cryptosystem in such a way
that the Boolean expression defining the authenticable groups is implicit in
the split

Shamelessly, Scott

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