The intent of peer data management systems (PDMS) is to share as much data as possible. However, in many applications leveraging sensitive data, users demand adequate mechanisms to restrict the access to authorized parties. In this paper, we study a distributed access control model, where data items are stored, queried and authenticated in a totally decentralized fashion. Our contribution focuses on the design of a comprehensive framework for access control enforcement in PDMS sharing secure data, which blends policy rules defined in a declarative language with distributed key management schemes. The data owner peer decides which data to share and whom to share with by means of such policies, with the data encrypted accordingly. To defend against malicious attackers who can compromise the peers, the decryption keys are decomposed into pieces scattered amongst peers. We discuss the details of how to adapt distributed encryption schemes to PDMS to enforce robust and resilient access control, and demonstrate the efficiency and scalability of our approach by means of an extensive experimental study.