Peer-to-Peer (P2P) systems enable efficient multimedia file sharing and are inherently scalable on the Internet. However, the absence of a centralized authority and a suitable Digital Right Management (DRM) mechanism prompts many securities-related challenges and discourages the widespread use of P2P networks for distributing copyright-protected multimedia files. To address these issues, we adopt the concept of a group Diffie-Hellman group key and threshold scheme to propose a novel anonymous DRM scheme for P2P users that wish to share multimedia files. Our scheme has four features: (1) the P2P users remain anonymous while sharing their files, (2) no online server is needed to perform the DRM operations, (3) an adjustable mechanism exists for efficiently distributing multimedia files with different popularities, and (4) users enjoy low communication and computation costs. In addition to explaining the operations of this scheme, we also compare its performance and security with Zhang et al.'s design, TLMS and Lua's Scheme within the context of this study.