Provable Data Possession (PDP) is an alternative technique that guarantees the integrity of remote data. However, most current PDP schemes are inapplicable to similarity-like data checking with the same attribute, i.e., when there are numerous similar files to be checked by Data Owners (DOs). Some traditional models cannot resist the corrupt auditors who always generate biased challenge information. Besides, a copy-summation attack exists in some schemes, which means the Cloud Server (CS) can bypass the verification by storing the median value instead of initial data via summation operation. To address the issues above, in this work, we propose a keyword searchable PDP scheme for large similar data checking. To achieve searchability, we introduce the notion of a keyword in PDP and design a specific index structure to match the authenticator. The scheme enables all matched files to be auditable and verifiable, while guaranteeing privacy protections. Unlike existing methods, our Third Party Auditor (TPA) checks all similar data containing the same keyword simultaneously. We utilize unpredictable yet verifiable public information on the blockchain to generate challenge information, rather than relying on a centralized TPA. The proposed scheme can resist copy-summation attacks. Theoretical analysis demonstrates that the proposed scheme satisfies the security requirements, and our evaluations demonstrate its efficiency.