Methods and apparatus are provided for authenticated hierarchical set operations. A third party server processes a query q (possibly from a client) on outsourced data sets S1, . . . , Sn on behalf of a source of the data. The query q comprises a hierarchical set operation. Authenticated Set Operation techniques for flat set operations can be iteratively applied for hierarchical set operations. In addition, bilinear accumulators are extended to provide an extractable accumulation scheme comprising a primary bilinear accumulator and a secondary bilinear accumulator. In addition, a query q is parsed as a tree and for each tree node, a Union/Intersection argument is provided that is related to one or more accumulation values associated with the corresponding tree node. The client receives an answer to the query and a verification proof comprising, for example, subset witnesses, completeness witnesses, and/or accumulation values, but not necessarily intermediate results associated with the internal tree nodes of the query q.