Efficient scalar product protocol and its privacy-preserving application

Scalar product protocol aims at securely computing the dot product of two private vectors. As a basic tool, the protocol has been widely used in privacy preserving distributed collaborative computations. In this paper, at the expense of disclosing partial sum of some private data, we propose a linearly efficient even-dimension scalar product protocol (EDSPP) without employing expensive homomorphic crypto-system and any third party. The correctness and security of EDSPP are confirmed by theoretical analysis. In comparison with six most frequently-used schemes of scalar product protocol (to the best of our knowledge), the new scheme is the most efficient one, and it has good fairness. Simulated experiment results intuitively indicate the good performance of our scheme. Consequently, in the situations where divulging very limited information about private data is acceptable, EDSPP is an extremely competitive candidate secure primitive to achieve practical schemes of privacy preserving distributed cooperative computations. We also discuss the application of EDSPP, and present a secure distance comparison protocol based on EDSPP, which can be used in many privacy-preserving computations, such as privacy-preserving k-nearest neighbours computation. Additionally, a hybrid scheme is put forward to securely compute the scalar product of arbitrary-length private vectors.