The notion of aggregation of data in 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 compact aggregate signature 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.