Zero-pole cancellation for identity-based aggregators: a constant-size designated verifier-set signature

In this paper we present a designated verifier-set signature (DVSS), in which the signer allows to designate many verifiers rather than one verifier, and each designated verifier can verify the validity of signature by himself. Our research starts from identity-based aggregator (IBA) that compresses a designated set of verifier’s identities to a constant-size random string in cryptographic space. The IBA is constructed by mapping the hash of verifier’s identity into zero or pole of a target curve, and extracting one curve’s point as the result of aggregation according to a specific secret. Considering the different types of target curves, these two IBAs are called as zeros-based aggregator and poles-based aggregator, respectively. Based on them, we propose a practical DVSS scheme constructed from the zero-pole cancellation method which can eliminate the same elements between zeros-based aggregator and poles-based aggregator. Due to this design, our DVSS scheme has some distinct advantages: (1) the signature supporting arbitrary dynamic verifiers extracted from a large number of users; and (2) the signature with short and constant length. We rigorously prove that our DVSS scheme satisfies the security properties: correctness, consistency, unforgeability and exclusivity.