A tale of two clouds: Computing on data encrypted under multiple keys

Cloud computing provides a convenient platform for big data computation such as machine learning and data mining. However, privacy conscious users often encrypt their data with their own keys before uploading them to the cloud. Existing techniques for computation on encrypted data are either in the single key setting or far from practical. In this paper, we show how two non-colluding servers can leverage proxy re-encryption to jointly compute arithmetic functions over the ciphertexts of multiple users without learning the inputs, intermediate or final results. Moreover, the computation is non-interactive to users and only requires minimal server-to-server interactions. Experimental results demonstrate that our schemes significantly improve the efficiency of outsourced computation when compared to the existing approach.