The definition of cloud computing grows from the narrow one including Virtualization, Utility Computing, IaaS, PaaS, and SaaS to the wide one, which mode focuses on the exchange and the usage of the services and products. Under the transaction mode of cloud computing, the server providing services or products can record the private data of the users without their allowance. This has violated the privacy regulation. Thus, we aim to figure out a novel oblivious transfer scheme to realize the private transactions in cloud computing environment based on Aryabhata remainder theorem. We have implemented the system to show its feasibility, as well as evaluate the time consumption in different cases out of the seller's and the buyer's views, respectively.