Two certificateless aggregate signatures from bilinear maps

In this paper we propose two certificateless aggregate signature schemes, which are the first aggregate signature schemes in the CL-PKC. The first scheme CAS-1 reduces the costs of communication and signer-side computation but loses on storage, while CAS-2 minimizes the storage but sacrifices the communication. We can choose one of the above schemes by the consideration of the implementation requirement. Our schemes do not need the public key certificate anymore and achieve the trust level 3, the same level with traditional PKI. Both of the schemes are proven secure in the random oracle model(ROM) by assuming the intractability of the computational Diffie-Hellman(CDH) problem over groups with bilinear maps.