In-network caching is an appealing solution to cope with the increasing bandwidth demand of video, audio, and data transfer over the Internet. Nonetheless, in order to protect consumer privacy and their own business, content providers (CPs) increasingly deliver encrypted content, thereby preventing Internet service providers (ISPs) from employing traditional caching strategies, which require the knowledge of the objects being transmitted. To overcome this emerging tussle between security and efficiency, in this paper we propose an architecture in which the ISP partitions the cache space into slices, assigns each slice to a different CP, and lets the CPs remotely manage their slices. This architecture enables transparent caching of encrypted content and can be deployed in the very edge of the ISP's network (i.e., base stations and femtocells), while allowing CPs to maintain exclusive control over their content. We propose an algorithm, called SDCP, for partitioning the cache storage into slices so as to maximize the bandwidth savings provided by the cache. A distinctive feature of our algorithm is that ISPs only need to measure the aggregated miss rates of each CP, but they need not know the individual objects that are requested. We prove that the SDCP algorithm converges to a partitioning that is close to the optimal, and we bound its optimality gap. We use simulations to evaluate SDCP's convergence rate under stationary and nonstationary content popularity. Finally, we show that SDCP significantly outperforms traditional reactive caching techniques, considering both CPs with perfect and with imperfect knowledge of their content popularity.