Cloud data security and privacy have garnered significant attention in recent years, with data integrity being a key concern. Most existing auditing protocols overlook the unforgeability of integrity proofs against Man-in-the-Middle (MitM) attacks. Specifically, MitM attackers can forge integrity proofs to conceal tampering with the data, misleading the data owner (DO) into believing the data is unchanged. This could lead to more severe consequences when the DO unknowingly uses compromised data. In this paper, we propose PSCIA, a privacy-preserving, secure and certificate-based integrity auditing protocol for cloud storage. Firstly, PSCIA provides unforgeability for the integrity proofs to resist MitM attackers. Secondly, we introduce a novel privacy attack during auditing that can reveal whether DOs have modified the cloud data, and then propose a defense method. Thirdly, by employing the certificate-based cryptosystem, PSCIA eliminates the need for secure channels, resolves the key escrow problem, and reduces certificate management burden. Furthermore, we formally prove that PSCIA is secure in the random oracle model. Finally, theoretical analysis and experiments demonstrate that PSCIA improves computational efficiency over related schemes, reducing the number of bilinear pairings computed by the DO and CSP from linear to constant complexity.