We present a novel approach for guaranteeing access privacy to data stored at an external cloud provider. Our solution relies on the grouping of resources into buckets then organized with a binary search tree. The tree is built on an index computed in a non-invertible non-order preserving way, and supports efficient key-based retrieval. Our approach to provide access privacy builds on this data organization providing uniform observability to the server in access execution and dynamically changing not only the physical storage allocation, but also the logical structure itself. Our analysis and experimental evaluation show the effectiveness of our approach.