With the rapid development of wireless communication and big data analysis technologies, the storage of massive amounts of data relies on third-party trusted storage, such as cloud storage. However, once data are stored on third-party servers, data owners lose physical control over their data, making it challenging to ensure data integrity and security. To address this issue, researchers have proposed integrity auditing mechanisms that allow for the auditing of data integrity on cloud servers without retrieving all the data. To further enhance the availability of data stored on cloud servers, multiple replicas of the original data are stored on the server. However, in existing multi-replica auditing schemes, there is a problem of server fraud, where the server does not actually store the corresponding data replicas. To tackle this issue, this paper presents a formal definition of authentic replicas along with a security model for the authentic-replica sampling mechanism. Based on time-lock puzzles, identity-based encryption (IBE) mechanisms, and succinct proof techniques, we design an authentic replica auditing mechanism. This mechanism ensures the authenticity of replicas and can resist outsourcing attacks and generation attacks. Additionally, our schemes replace the combination of random numbers and replica correspondence tables with Linear Feedback Shift Registers (LFSRs), optimizing the original client-side generation and uploading of replica parameters from being linearly related to the number of replicas to a constant level. Furthermore, our schemes allow for the public recovery of replica parameters, enabling any third party to verify the replicas through these parameters. As a result, the schemes achieve public verifiability and meet the efficiency requirements for authentic-replica sampling in multi-cloud environments. This makes our scheme more suitable for distributed storage environments. The experiments show that our scheme makes the time for generating copy parameters negligible while also greatly optimizing the time required for replica generation. As the amount of replica data increases, the time spent does not grow linearly. Due to the multi-party aggregation design, the verification time is also optimal. Compared to the latest schemes, the verification time is reduced by approximately 30%.
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