Due to perceived fairness and allocation efficiency, cloud auctions for resource allocation and pricing have recently attracted significant attention. As an important economic property, truthfulness makes bidders reveal their true valuations for cloud resources to maximize their utilities. However, disclosure of one's true value causes numerous security vulnerabilities. Therefore, privacy-preserving cloud auctions are called for to prevent such information leakage. In this paper, we demonstrate how to perform privacy-preserving auctions in clouds that do not leak any information other than the auction results to anyone. Specifically, we design a privacy-preserving cloud auction framework that addresses the challenges posed by the cloud auction context by leveraging the techniques in garbled circuits and homomorphic encryption. As foundations of our privacy preserving cloud auction framework, we develop data-oblivious cloud auction algorithm and basic operations (e.g., comparison, swapping etc.), such that the execution path does not depend on the input. In practical systems with a large number of users and constrained resources, we develop an improved version with a computational complexity of O(n log2 n) in the number of bidders n. We further fully implement our framework and theoretically and experimentally show that it preserves privacy by incurring only limited computation and communication overhead.