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Communication anonymity is becoming an increasingly important, or even indispensable security requirement for many applications. The existing research in anonymous communications can largely be divided into two categories: mix- based systems and secure multi-party computation-based systems, originating from mixnet and DC-net respectively. However, they either cannot provide provable anonymity, or suffer from transmission collision problem. In this paper, we first propose a novel unconditionally secure source anonymous message authentication code (SA-MAC) that can be applied to any messages without relying on any trusted third parties. While ensuring message sender anonymity, SM-MAC can also provide message content authenticity. We then propose a novel communication protocol that can hide the senders and the receivers from each other, and thus can be used for secure file sharing. The security analysis demonstrates that the proposed protocol is secure against various attacks. Our analysis also shows it is efficient and practical.