Aggregate signature is public-key signature that allows anyone to aggregate different signatures generated by different signers on different messages into a short (called aggregate) signature. The notion has many applications where compressing the signature space is important: secure routing protocols, compressed certificate chain signature, software module authentications, and secure high-scale repositories and logs for financial transactions. In spite of its importance, the state of the art of the primitive is that it has not been easy to devise a suitable aggregate signature scheme that satisfies the conditions of real applications, with reasonable parameters: short public key size, short aggregate signatures size, and efficient aggregate signing/verification. In this paper, we propose aggregate signature schemes based on the Camenisch-Lysyanskaya (CL) signature scheme (Crypto 2004) whose security is reduced to that of CL signature which substantially improve efficiency conditions for real applications.• We first propose an efficient sequential aggregate signature scheme with the shortest size public key, to date, and very efficient aggregate verification requiring only a constant number of pairing operations and l number of exponentiations (l being the number of signers).• Next, we propose an efficient synchronized aggregate signature scheme with a very short public key size, and with the shortest (to date) size of aggregate signatures among synchronized aggregate signature schemes. Signing and aggregate verification are very efficient: they take constant number of pairing operations and l number of exponentiations, as well.• Finally, we introduce a new notion of aggregate signature named combined aggregate signature that allows a signer to dynamically use two modes of aggregation "sequential" and "synchronized," employing the same private/public key. We also present an efficient combined aggregate signature based on our previous two aggregate signature schemes. This combined-mode scheme allows for application flexibility depending on real world scenario: For example, it can be used sequentially to sign incrementally generated legal documents, and synchronously to aggregate the end-of-day logs of all branches of an institute into a single location with a single aggregate signature.