In recent years, the Internet of Things (IoT) devices have become increasingly deployed in many industries and generated a large amount of data that needs to be processed in a timely and efficient manner. Using aggregate signatures, it provides a secure and efficient way to handle large numbers of digital signatures with the same message. Recently, the privacy issue has been concerned about the topic of data sharing on the cloud. To provide the integrity, authenticity, authority, and privacy on the data sharing in the cloud storage, the notion of an aggregatable certificateless designated verifier signature scheme (ACLDVS) was proposed. ACLDVS also is a perfect tool to enable efficient privacy-preserving authentication systems for IoT and or the vehicular ad hoc networks (VANET). Our concrete scheme was proved to be secured underling of the Computational Diffie-Hellman assumption. Compared to other related schemes, our scheme is efficient, and the signature size is considerably short.