Database outsourcing is an emerging data management paradigm which has the potential to transform the IT operations of corporations. In this paper we address privacy threats in database outsourcing scenarios where trust in the service provider is limited. Specifically, we analyze the data partitioning (bucketization) technique and algorithmically develop this technique to build privacy-preserving indices on sensitive attributes of a relational table. Such indices enable an untrusted server to evaluate obfuscated range queries with minimal information leakage. We analyze the worst-case scenario of inference attacks that can potentially lead to breach of privacy (e.g., estimating the value of a data element within a small error margin) and identify statistical measures of data privacy in the context of these attacks. We also investigate precise privacy guarantees of data partitioning which form the basic building blocks of our index. We then develop a model for the fundamental privacy-...