Tag deduplication is an emerging technique to eliminate redundancy in cloud storage, which works by signing integrity tags with a content-associated key instead of user-associated secret key. To achieve public auditability in this scenario, the linkage between cloud users and their integrity tags is firstly re-established in current solutions, which provides a potential side channel to malicious third-party auditor to steal the existence privacy of a certain target file. Such kind of attack, which is also possible among classic public auditing schemes, still cannot be well resisted and is now becoming a big obstacle in using this technique. In this paper, we propose a secure aggregation-based tag deduplication scheme (ATDS), which takes the lead to consider resistance against side channel attack during the process of public verification. To deal with this problem, we define a user-associated integrity tag based on the defined content-associated polynomial and devise a Lagrangian interpolation-based aggregation strategy to achieve tag deduplication. With the help of this technique, content-associated public key is able to be utilized instead of a user-associated one to achieve auditing. Once the verification is passed, the TPA is just only able to make sure that the verified data are correctly corresponding to at least a group of users in cloud storage, rather than determining specific owners. The security analysis and experiment results show that the proposed scheme is able to resist side channel attack and is more efficient compared with the state of the art.