The authenticity of outsourced data may be effectively checked using the remote data possession checking method, which can be classified into both private and public verification. Public verification can be verified by any cloud user, however, private verification can only be verified by the data owner. However, In the majority of real-world scenarios, the data owner anticipates that just a specific verifier will be able to carry out integrity-checking duties and that the verifier won't be able to learn anything about the data. Yan et al. suggest a remote data possession verification scheme with a designated validator to make sure that only the designated verifier can guarantee the data's integrity and that others cannot. However, this strategy makes use of public-key technology and disregards privacy-related concerns. To overcome these shortcomings, we propose an identity-based remote data possession checking method that fulfills the data owner's demand to select a unique verifier. This method also employs a Merkle hash tree for dynamic data updating and a randomized integer for blind data integrity verification that protects user privacy. Our method can be used to get around the public key infrastructure's burdensome certificate administration. We showed that our system is secure using the computing Diffie-Hellman assumptions and the discrete optimization assumption. Our plan is practical and effective in practical contexts, as shown by conceptual analysis and experimental results.