Publicly verifiable delegation of set intersection

We study the verifiable delegation of set intersection in the model of authenticated data structures, where a weak client in storage and computation stores its dataset composed of some sets into a powerful server. The client can issue update and set intersection query over outsourced data. The server returns the result and a proof of its correctness. Our scheme allows any entity to publicly verify the correctness of set intersection query, and requires no secret key. Based on characteristic polynomials of sets, our authenticated data structure firstly provides a practical and specific method for set intersection through polynomial evaluations. It achieves optimal verification and proof complexity, as well as optimal update complexity without bearing any extra space overhead. The overhead for computing actual answer and proofs is reduced significantly in contrast with previous methods based on bilinear-map accumulators. The intersection query comes up in keyword search, database queries and other applications. Indeed, our scheme can be effectively used in such scenarios. The security of our constructions is based on co-Computational Diffie-Hellman assumption.