Secure dot product of outsourced encrypted vectors and its application to SVM

It is getting popular for users to outsource their data to a cloud system as well as leverage the high-speed computing power of this third-party platform to process the data. For the sake of data privacy, outsourced data from different users is usually encrypted under different keys. To enable users to run data mining algorithms collaboratively in the cloud, we need an efficient scheme to process the encrypted data under multiple keys. Dot product is one of the most important building blocks of data mining algorithms. In this paper, we show how to give the cloud the permission to decrypt the encrypted dot product of two encrypted vectors without compromising the privacy of the data owners. We propose the first feasible scheme that trains a SVM (Support Vector Machine) classifier for both horizontally and vertically partitioned datasets using only one server. Existing schemes either can only handle a much simpler classifier (linear mean classifier) with two non-colluding servers or can only be applied to vertically partitioned dataset. We also show that our scheme not only preserves data privacy but also runs faster than existing schemes.