Identity-based aggregate and verifiably encrypted signatures from bilinear pairing

Aggregate signatures are digital signatures that allow n players to sign n different messages and all these signatures can be aggregated into a single signature. This single signature enables the verifier to determine whether the n players have signed the n original messages. Verifiably encrypted signatures are used when Alice wants to sign a message for Bob but does not want Bob to possess her signature on the message until a later date. In this paper, we first propose an identity (ID)-based signature scheme from bilinear pairing and show that such a scheme can be used to generate an ID-based aggregate signature. Then, combining this ID-based signature with the short signature given by Boneh, Lynn and Shacham, we come up with an ID-based verifiably encrypted signature. Due to the nice properties of the bilinear pairing, the proposed signatures are simple, efficient and have short signature size.