The utilization of cloud storage is increasingly prevalent as the field of cloud computing continues to expand. Several cloud data auditing schemes have been proposed within the academic community to guarantee the availability and integrity of cloud data. Nevertheless, several schemes rely on public key infrastructure and identity-based encryption, introducing intricate challenges associated with certificate management and key escrow. Consequently, we present a certificateless encryption-based blockchain-assisted public cloud data integrity auditing scheme for data integrity. Furthermore, our proposed scheme incorporates blockchain technology to oversee the activities of semi-trusted third-party auditors and resolve the concerns mentioned above. To enhance the efficiency of dynamic data updating and ensure data privacy security, we introduce a new data structure that combines a novel counting bloom filter and a Multi-Merkel hash tree approach. The assumption of the discrete logarithm issue determines the system's security. In contrast, the security model of the scheme is comprehensively delineated. In the part dedicated to performance analysis, we assess the scheme's functionality and computational cost within the framework of existing literature. The experimental results provide proof of the scheme's comprehensive functionality and effectiveness.