Systems and methods for verifying membership in one or more sets that are subsets of a global set are provided. The method compromises representing members of the global set by mapping each member to a distinct Boolean variable of length d, wherein 2d is not less than the number of members in the global set; representing each of the given subsets of the global set by a Boolean expression which evaluates to a first value for any of the assignments to the Boolean variables which represent members of the subset, and which evaluates to a second value for any of the assignments to the Boolean variables which represent members of the global set that are not members of the subset.