Computing encrypted cloud data efficiently under multiple keys

The emergence of cloud computing brings users abundant opportunities to utilize the power of cloud to perform computation on data contributed by multiple users. These cloud data should be encrypted under multiple keys due to privacy concerns. However, existing secure computation techniques are either limited to single key or still far from practical. In this paper, we design two efficient schemes for secure outsourced computation over cloud data encrypted under multiple keys. Our schemes employ two non-colluding cloud servers to jointly compute polynomial functions over multiple users' encrypted cloud data without learning the inputs, intermediate or final results, and require only minimal interactions between the two cloud servers but not the users. We demonstrate our schemes' efficiency experimentally via applications in machine learning. Our schemes are also applicable to privacy-preserving data aggregation such as in smart metering.