A structured aggregate signature scheme

In multisignature scheme, verifiying the signing order is sometimes very important. A multisignature scheme in which generated signatures reflect the structure of signers, e.g. signing order, is called structured multisignature scheme and many such schemes have been proposed so far. Structured multisignature schemes are dedicated to represent not only serial/parallel signer structures but also mixture of serial and parallel signer structures. In most structured schemes, the signature size depends on the number of signers. There are some structured schemes which can generate fixed-size signatures, but these schemes do not have order-flexibility, i.e. public keys arranged for one signer structure cannot be used for other signer structure. On the other hand, a sequential multisignature scheme is one type of structured multisignature schemes, which is dedicated to represent the serial signer structure. Some sequential multisig-nature scheme like sequential aggregate signature schemes can generate fixed-size signatures and have order-flexibility but no structured aggregate signature scheme has been proposed so far. In this paper, we construct a structured aggregate scheme which provides order-flexiblity, the fixed-size signature and applicability to mixed signer structures by extending the sequential aggregate signature scheme by Boldyreva et al.