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Recording and keeping account of the usage of cloud resources in a trustworthy way are vital requirement for widespread cloud deployment and availability. To provide a trustworthiness of cloud service contracts, we identified that the frequent cryptographic operations for the trustworthy contracts lead to excessive computations and a bottleneck of contract transactions. As a remedy for these limitations, we propose a trustworthy contract system for cloud computing environment. The system, which introduces the concept of a Cloud Notary Authority (CNA) for the supervision of contract, makes contract more objective and acceptable to users and cloud service providers. CNA generates trustworthy binding information that can be used to resolve future disputes between a user and a cloud service provider. Because our contract system drastically minimizes the asymmetric key operations of cloud users and service providers, it provides a level of security that is identical to that of a Public Key Infrastructure (PKI) and it minimizes the latency of contract transactions. This work was undertaken on a real cloud computing service called iCubeCloud.