  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 obfuscation 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 analyze the protocol for
correctness, security, and efficiency.
