Peer-To-Peer (P2P) systems have been very successful for large-scale data sharing. However, sharing sensitive data, like in online social networks, without appropriate access control, can have undesirable impact on data privacy. Data can be accessed by everyone (by potentially untrusted peers) and used for everything (e.g., for marketing or activities against the owner's preferences or ethics). Hippocratic DataBases (HDB) provides an effective solution to this problem, by integrating purpose based access control for privacy protection. However, the use of HDB has been restricted to centralized systems. This paper gives an overview of current solutions for supporting data privacy in P2P systems, and develops in more details a complete solution based on HDB.