With the development of the internet, recommending interesting products to users has become a highly valuable research topic for businesses. Recommendation systems play a crucial role in addressing this issue. To prevent the leakage of each user's (client's) private data, Federated Recommendation Systems (FedRec) have been proposed and widely used. However, extensive research has shown that FedRec suffers from security issues such as data privacy leakage, and it is challenging to train effective models with FedRec when each client only holds interaction information for a single user. To address these two problems, this paper proposes a new privacy-preserving recommendation system (PRSI), which includes a preprocessing module and two main phases. The preprocessing module employs split vectors and fake interaction items to protect clients' interaction information and recommendation results. The two main phases are: (1) the collection of interaction information and (2) the sending of recommendation results. In the interaction information collection phase, each client uses the preprocessing module and random communication methods (according to the designed interactive protocol) to protect their ID information and IP addresses. In the recommendation results sending phase, the central server uses the preprocessing module and triplets to distribute recommendation results to each client under secure conditions, following the designed interactive protocol. Finally, we conducted multiple sets of experiments to verify the security, accuracy, and communication cost of the proposed method.