Deduplication is a technique used to reduce the amount of storage needed by service providers. It is based on the intuition that several users may want (for different reasons) to store the same content. Hence, storing a single copy of these files would be sufficient. Albeit simple in theory, the implementation of this concept introduces many security risks. In this paper, we address the most severe one: an adversary, possessing only a fraction of the original file, or colluding with a rightful owner who leaks arbitrary portions of it, becomes able to claim possession of the entire file. The paper's contributions are manifold: first, we review the security issues introduced by deduplication, and model related security threats; second, we introduce a novel Proof of Ownership (POW) scheme with all the features of the state-of-the-art solution and only a fraction of its overhead. We also show that the security of the proposed mechanisms relies on information-theoretical rather than computational assumptions, and propose viable optimization techniques that further improve the scheme's performance. Finally, the quality of our proposal is supported by extensive benchmarking.