## 1 Introduction  
Cloud computing comes with different deployment models (private, public, community, and hybrid). Depending on the cloud client's (CC) preferred infrastructure, cloud computing is offered as IaaS (infrastructure as a service), PaaS (platform as a service), and SaaS (software as a service) [1].  
The cloud service provider's (CSP) responsibility for security is correlated with the level of infrastructure offered to the CC. In the case of IaaS and PaaS, the CSP offers the necessary tools, but it is up to the CC to adopt them correctly. A service-level agreement allows to manage the relationship between the CSP and the CC [1].  
Cybersecurity is a cause for struggle among individuals and companies who want to keep their data safe. For computer networking, the confidentiality, integrity, and availability (CIA) triad and authentication, authorization, and accounting (AAA) security model, has been introduced to provide a concrete model on what should be observed in terms of security [2]. Cloud computing comes with its own security issues, such as colluding attacks, Byzantine attacks, malicious data, and so on [3; 4].  
To ensure conformity with the current standards and compliance with their security mainframe; nowadays, information technology (IT) auditing is a common practice for midsize and large corporations. In cloud computing, a TPA is introduced to assume the function of an \"on-the-fly\" audit. This audit encompasses the security of the communication between the cloud client and, as the cloud service provider, as well as the cloud client's data integrity [5; 6].  
As defined in [7], privacy preserving consists of making sure that the three cloud stakeholders are not involved in any malicious activities coming from insiders at the CSP level, as well as remediating to the TPA vulnerabilities and checking that the CC is not deceitfully affecting other clients.  
Cloud storage is a flexible platform that allows the CCs to store their confidential data from their local servers to the cloud platform; nowadays, many CCs have embraced the cloud realm. Nonetheless, the cloud platform introduces new concerns and security trials. To overcome these concerns, a TPA is introduced to safeguard the confidential data and restore CC's confidence [7]. The TPA, as an individual or an organization, has the skills and proficiency necessary for exposing and evaluating the malicious threats encountered by the CSP. On the other hand, the TPA could be dishonest and become an adversary. As a result, the TPA's malicious role could cause significant damage by sharing the CC's confidential and private data with illegitimate parties and altering the CC's privacy, to obtain financial gains as well as other benefits [8]. Therefore, to preserve the CC's privacy, we need to be able to detect whether the TPA has a dishonest role while performing the audit of the CC's confidential information and private data. There are some existing protocols available in the literature to keep the check and balance on the possible malicious activities of the TPA [9; 10; 11; 12]. However, computational and communicational overheads are not fully addressed in those existing protocols [13; 14], leaving room for possible malicious activities from the TPA. Hence, there is a need for a lightweight protocol to preserve the CC's privacy and detect the TPA's malicious activities, on the occasion that there are any.  
The next sections of the paper will be presented as follows: Section 2 evaluates the existing approaches that have tried to solve the same problem. Section 3 presents the proposed lightweight, accountable, privacy-preserving protocol. Section 4 explains the privacy-preserving polynomial model generation, where we demonstrate mathematically how our privacy-preserving polynomes are generated and verified. Section 5 presents the simulation setup and experimental results. In Section 6, we discuss these results; and finally, Section 7 concludes the paper and provides a hint of the planned future work.