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Remote Data Integrity Checking Protocol (RDC) is an interactive protocol allowing a client to verify that a storage service provider (SSP) faithfully stores a file. Existing protocols are mainly built from homomorphic identification protocols. In this paper, we first present a RDC protocol (HH-RDC) from a homomorphic hash function. The key technique is treating the file as a set of integers other than elements in some large field in previous protocol. The proposed protocol support public verifiability, data dynamic and privacy against verifiers. We then present a variant (V-HH-RDC) of HH-RDC by fixing and simplifying some parameters. Compared with HH-RDC, V-HH-RDC obtains a significant improvement in computation and communication at the sacrifice of losing feature of public verifiability. V-HH-RDC is very suitable for low-power devices, such as cell phones. After that, theoretical analysis and experimental results show that the proposed protocols have good performances.