The public cloud data integrity auditing technique is used to check the integrity of cloud data through the Third Party Auditor. In order to make it more practical, we propose a new paradigm called integrity auditing based on the keyword with sensitive information privacy for encrypted cloud data. This paradigm is designed for one of the most common scenario, that is, the user concerns the integrity of a portion of encrypted cloud files that contain his/her interested keywords. In our proposed scheme, the TPA who is only provided with the encrypted keyword, can audit the integrity of all encrypted cloud files that contain the user's interested keyword. Meanwhile, the TPA cannot deduce the sensitive information about which files contain the keyword and how many files contain this keyword. These salient features are realized by leveraging a newly proposed Relation Authentication Label (RAL). The RAL can not only authenticate the relation that files contain the queried keyword, but also be used to generate the auditing proof without sensitive information exposure. We give concrete security analysis showing that the proposed scheme satisfies correctness, auditing soundness and sensitive information privacy. We also conduct the detailed experiments to show the efficiency of our scheme.