Data storage is one of the most profitable applications on cloud computing platforms. Although a transparent service model provides flexibility and convenience, it also brings new challenges with respect to data security. For example, the existing vulnerabilities in some commercial cloud storage services can potentially lead to repudiation problems. In part I of this two-part chapter, a basic TPNR protocol is introduced that addresses disputes between an individual user and a service provider. In this chapter, we introduce a framework that supports a fair data transmission procedure without the risk of disputes in environments where data sharing among multiple users is required. An advanced MPNR protocol is presented. Fairness is achieved with the help of a TTP. Both parties can get evidence at the end of a round. In addition, taking advantage of the Merkle hash tree, the MPNR protocol can prevent rollback attacks by limiting the data access priorities of individual users. The rationale behind the new protocol’s design and its working modes are analyzed in detail. We also discuss its robustness under typical malicious network attacks.