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 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 a much more efficient one, and it has well fairness. Simulated experiment results intuitively indicate the good performance of our novel 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 present a simple application case of EDSPP.