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With the escalation of multimedia data, cloud technology has played a very important role in its management with its promising computing and storage capabilities. Cloud computing leverages high scalability, resources, and on-demand services, which have a remarkable impact on assisting multimedia data storage. Meanwhile, any alteration in the outsourced multimedia data is a severe menace. Numerous researchers have focused on providing validation of integrity through the auditing mechanism. Regrettably, their mechanisms are focused on the traditional public-key cryptosystem and cannot withstand quantum attacks. Additionally, the centralised approach of completely relying on a third-party auditor (TPA) of existing mechanisms may lead to biased auditing results. Hence, employing the advantage of resistance against quantum attack and removing the liability of certificates with lattice cryptography and an identity-based cryptosystem, we have presented a new auditing framework by utilising blockchain technology. Blockchain technology is employed in order to track the activities of the cloud service provider and TPA, resulting less dependency on TPA. Security analysis portrays security of the framework under the random oracle model, which depends is based on the Shortest Integer Solution (SIS) problem of the lattices. Reduced computation, communication and storage overheads with efficient features and performance is observed for the proposed mechanism through analysis conducted with similar mechanisms. As a result, better operability is achieved by the proposed mechanism.