Fast, privacy preserving linear regression over distributed datasets based on pre-distributed data

This work proposes a protocol for performing linear regression over a dataset that is distributed over multiple parties. The parties will jointly compute a linear regression model without actually sharing their own private datasets. We provide security definitions, a protocol, and security proofs. Our solution is information-theoretically secure and is based on the assumption that a Trusted Initializer pre-distributes random, correlated data to the parties during a setup phase. The actual computation happens later on, during an online phase, and does not involve the trusted initializer. Our online protocol is orders of magnitude faster than previous solutions. In the case where a trusted initializer is not available, we propose a computationally secure two-party protocol based on additive homomorphic encryption that substitutes the trusted initializer. In this case, the online phase remains the same and the offine phase is computationally heavy. However, because the computations in the offine phase happen over random data, the overall problem is embarrassingly parallelizable, making it faster than existing solutions for processors with an appropriate number of cores.