Unidirectional proxy re-encryption (PRE) can be used to realize an efficient and secure shared storage. However, this type of storage does not yet protect its users’ privacy: to retrieve some data a user must give his identity and his query to the proxy. We propose two secure data storage systems that allow authorized users to anonymously get access to the content of encrypted data on a storage. Each scheme corresponds to a certain economic model. In the first one, a user has to pay for each downloaded file, whereas in the second one, users pay each month a subscription to get an unlimited access to all their files.