Obtaining mutual nonrepudiation between the user and service provider is crucial in cloud storage. One of the solutions for mutual nonrepudiation is based on logging attestations, which are signed messages. For every request, clients and service provider exchange attestations. These attestations will be used in an auditing protocol to verify their behavior. The chain-hashing scheme chains attestations and stores them in service provider for supporting write serializability and read freshness of files. However, the chain-hashing scheme is inefficient when files in an account can be accessed by multiple client devices interchangeably. In this paper we first show that the chain-hashing scheme cannot resist roll-back attack from service provider unless client devices keep all the attestations or there exists a way to broadcast the last attestation to all the client devices. We propose a scheme that can guarantee mutual nonrepudiation between the user and service provider without requiring the client devices to exchange any messages, and each client device only has to store the last attestation it received. We also propose how to apply the hash tree to remove accumulated attestations. The results from related experiments demonstrate the feasibility of the proposed scheme. A service provider of cloud storage can use the proposed scheme to provide a mutual nonrepudiation guarantee in their service-level agreement.