Efficient Protocols for Principal Eigenvector Computation over Private Data

In this paper we present a protocol for computing the principal eigenvector of a collection of data matrices belonging to multiple semi-honest parties with privacy constraints. Our proposed protocol is based on secure multi-party computation with a semi-honest arbitrator who deals with data encrypted by the other parties using an additive homomorphic cryptosystem. We augment the protocol with randomization and oblivious transfer to make it difficult for any party to estimate properties of the data belonging to other parties from the intermediate steps. The previous approaches towards this problem were based on expensive QR decomposition of correlation matrices, we present an efficient algorithm using the power iteration method. We present an analysis of the correctness, security, and efficiency of protocol along with experimental results using a prototype implementation over simulated data and USPS handwritten digits dataset.