Impossibility of unconditionally secure scalar products

The ability to perform scalar products of two vectors, each known to a different party, is a central problem in privacy preserving data mining and other multi-party computation problems. Ongoing search for both efficient and secure scalar product protocols has revealed that this task is not easy. In this paper we show that, indeed, scalar products can never be made secure in the information theoretical sense. We show that any attempt to make unconditionally secure scalar products will inevitably allow one of the parties to learn the other parties input vector with high probability. On the other hand, we show that under various assumptions, such as the existence of a trusted third party or the difficulty of discrete logarithms, both efficient and secure scalar products do exist. We proposed two new protocols for secure scalar products and compare their performance with existing secure scalar products.