Grid technologies have proven to be very successful in tackling challenging problems in which data access and processing is a bottleneck. Notwithstanding the benefits that Grid technologies could have in Health applications, privacy leakages of current DataGrid technologies due to the sharing of data in VOs and the use of remote resources, compromise its widespreading. Privacy control for Grid technology has become a key requirement for the adoption of Grids in the Healthcare sector. Encrypted storage of confidential data effectively reduces the risk of disclosure. A self-enforcing scheme for encrypted data storage can be achieved by combining Grid security systems with distributed key management and classical cryptography techniques. Virtual Organizations, as the main unit of user management in Grid, can provide a way to organize key sharing, access control lists and secure encryption management. This paper provides programming models and discusses the value, costs and behavior of such a system implemented on top of one of the latest Grid middlewares. This work is partially funded by the Spanish Ministry of Science and Technology in the frame of the project Investigación y Desarrollo de Servicios GRID: Aplicación a Modelos Cliente-Servidor, Colaborativos y de Alta Productividad, with reference TIC2003-01318.