With the continuous increase of cloud storage adopters, data deduplication has become a necessity for cloud providers. By storing a unique copy of duplicate data, cloud providers greatly reduce their storage and data transfer costs. Unfortunately, deduplication introduces a number of new security challenges. We propose PerfectDedup, a novel scheme for secure data deduplication, which takes into account the popularity of the data segments and leverages the properties of Perfect Hashing in order to assure block-level deduplication and data condentiality at the same time. We show that the client-side overhead is minimal and the main computational load is outsourced to the cloud storage provider.