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The most important contribution of modern cryptography is the invention of digital signatures. To deal with specific application scenarios, digital signature schemes have been evolved with different variants. One of such variants is the aggregate signature scheme, which allows aggregation of different signatures by different users on different messages, to achieve computational and communication efficiency. Such schemes are useful in the design of Wireless Sensor Networks, Mobile Ad-hoc Networks, and Vehicular Ad-hoc Networks, where storage, bandwidth, and computational complexity are major constraints. In order to improve the computational and communicational efficiency along with security, in this paper, we propose a novel Certificateless Aggregate Signature (CLAS) scheme and extended it to achieve full aggregation. The proposed CLAS scheme uses bilinear pairings over elliptic curves and is proven secure in the Random Oracle Model under the assumption that Computational Diffie–Hellman Problem is hard. The security of the proposed CLAS scheme is proven without using forking lemma to achieve tight security. We compared our scheme with well-known existing schemes. Efficiency analysis shows that our scheme is much efficient than existing schemes in terms of communication and computational costs. [ABSTRACT FROM AUTHOR]