Full domain hash from (leveled) multilinear maps and identity-based aggregate signatures
Susan Hohenberger, Amit Sahai, Brent R. Waters · 2013
In this work, we explore building constructions with full domain hash structure, but with standard model proofs that do not employ the random oracle heuristic. The launching point for our results will be the utilization of a “leveled ” multilinear map setting for which Garg, Gentry, and Halevi (GGH) recently gave an approximate candidate. Our first step is the creation of a standard model signature scheme that exhibits the structure of the Boneh, Lynn and Shacham signatures. In particular, this gives us a signature that admits unrestricted aggregation. We build on this result to offer the first identity-based aggregate signature scheme that admits unrestricted aggregation. In our construction, an arbitrary-sized set of signatures on identity/message pairs can be aggregated into a single group element, which authenticates the entire set. The identity-based setting has important advantages over regular aggregate signatures in that it eliminates the considerable burden of having to store, retrieve or verify a set of verification keys, and minimizes the total cryptographic overhead that must be attached to a set of signer/message pairs. While identity-based signatures are trivial to achieve, their aggregate counterparts are not. To the best of our knowledge, no prior candidate for realizing unrestricted