## 7 Application in Outsourcing Computing in Cloud Computing  
Cloud computing has strong computing power and storage capacity of big data. However, the cloud service provider (CSP) is not trusted by the user, and may steal the user's private information or deceive the user. Cloud computing allows resource-constrained users to outsource expensive computations to the CSP. Hence, it is very important to ensure the integrity of the computing task and the authenticity of the remote user's identity. Due to the limited computing ability of the user, the heavy computing task is outsourced to the CSP to complete. The CSP is able to authenticate a computing task outsourced by the user through a signature-based protocol. For the protection of private information, the user wants the designated CSP to be the only entity that can verify the legality of the signature on a computing task, and the CSP cannot reveal the signature to any third party at will. Since the ordinary digital signature has public verifiability and transferability, anyone can verify the validity of signatures by using the public key of the signer and obtain the real identity of the signer. Obviously, the ordinary digital signature scheme is not suitable for this scenario. The SDVS scheme is considered as one of the solutions to these problems, which can provide secret authentication service to the user in an outsourcing computation task. SDVS guarantees that a designated CSP can validate the user's signature on a computing task. At the same time, it ensures that the designated CSP does not convince others that the user is involved in a computing task. However, most of the SDVS schemes cannot identify the real signature generator when the user and the cloud service provider dispute a signature, which may cause huge economic losses to the user or the CSP. Hence, the SDVS scheme without undeniability cannot handle a controversial computing task. For example, if the user denies the submission of a computing task for some reasons, then the CSP is forced to stop it. At the same time, if the CSP forges a user's signature on the computing task, then the user will take on the responsibility to pay for expensive computing cost. These economic losses are undesirable to the user or the CSP. The SDVS-USU scheme given in Section 3.2 is undeniable and strongly unforgeable, so it is more suitable for outsourcing computation in a cloud computing environment. The system model of outsourcing computation in cloud computing based on the SDVS-USU scheme is shown in Figure 5.  
Figure 4: Comparison of time cost of verifying. There are three entities in the system: the user, the CSP and the arbiter. The process of outsourcing calculation is as follows. 1. A user with limited computing resources uses his private key and the SDVS-USU scheme to generate a signature \(\sigma_{1}\) for a computing task \(m_{1}\) and sends \((m_{1},\sigma_{1})\) to the CSP. 2. The CSP has powerful computing power. After verifying the validity of the signature \(\sigma_{1}\) on \(m_{1}\) to confirm this submission, the CSP performs the computational task of \(m_{1}\). Then, the CSP uses its private key and the SDVS-USU scheme to generate the signature \(\sigma_{2}\) of the corresponding calculation result \(m_{2}\), and returns \((m_{2},\sigma_{2})\) to the user. 3. If \(\sigma_{2}\) is the valid signature of \(m_{2}\), the user accepts the calculation result returned by the CSP; otherwise, the user refuses to accept \(m_{2}\) and accuses the CSP of malicious behavior. 4. For a controversial computing task, the arbiter determines whether the user or the CSP is responsible for the economic loss of the computing task based on \((m_{1},\sigma_{1})\) and \((m_{2},\sigma_{2})\). The SDVS-USU scheme is easily implemented as a software in cloud computing environments. For example, the signature algorithm \(\mathbf{Sign}\) is installed on the user side, and the verification algorithm \(\mathbf{Veffy}\) is installed on the CSP side.