This study aims to address the problem of medical text data privacy protection in the context of extensive development of cloud computing. This paper comprehensively researches the relevant literature and technical progress in recent years on privacy protection in medical scenarios using homomorphic encryption and other advanced cryptography techniques, and synthesizes the scalability of cloud computing, the timeliness of edge computing, and the inerrancy of blockchain technology to achieve the privacy protection of medical text data through the cloud storage of medical data and the dense state computation, and protects the privacy of patient's medical data in order to achieve the purpose of protecting individual privacy, property security, and security. It protects the privacy of patients' medical data to realize the purpose of protecting personal privacy and property security. By changing the encryption parameters of the existing DGHV multi-key homomorphic encryption scheme to realize the characteristics of the adapted scheme, and at the same time, the public key parity restriction can be eliminated. In addition, this paper also discusses the application of blockchain technology in homomorphic encryption key management, and proposes a blockchain-based key security storage system to ensure the key's tamperability and security. The privacy security problem in medical data transmission, storage and processing is solved by constructing this medical text data privacy protection system based on cloud-edge cooperative computing and homomorphic encryption. Simulation experiments verify that this scheme is practically feasible, while the correct parameters and the choice of the edge computing approach take into account both security and feasibility.