The notion of aggregation of data in Industrial Internet of Things (IIoT) environment is a common practice. It shortens the data and associated signatures to reduce the bandwidth requirement. The compact aggregate signature (CAS) scheme creates a constant length aggregate signature (AS). Thus, the length of the CAS is independent of the number of messages or signatures to be aggregated. This article presents the first pairing-free CAS scheme in certificate-based settings. Due to the certificate-based approach, the proposed scheme is free from key escrow and key distribution problems inherited in identity-based cryptography (IDC) and certificate-less cryptography (CLC), respectively. Being compact and pairing free, it is the least bandwidth-consuming and the most efficient provably secure aggregation method. The length and computational cost analysis show that the scheme is the most appealing to use in the IIoT environment.