This paper investigates privacy threats in big data and proposes the use of FHE and other encryption methods to guarantee privacy and security of user data. It discusses the challenges and issues faced, the methodology of research and a proposed approach, before evaluating performance and drawing conclusions. The paper reviews related work, identifies data breaches and abuse as being major big data privacy issues, and proposes controlled storage management, with encryption, restricted access to data, and securing the networks through which big data is managed. The paper is relevant to subjects such as computer science, data science, and information technology.