A secure protocol for computing dot-products in clustered and distributed environments

Dot-products form the basis of various applications ranging from scientific computations to commercial applications in data mining and transaction processing. Typical scientific computations utilizing sparse iterative solvers use repeated matrix-vector products. These can be viewed as dot-products of sparse vectors. In database applications, dot-products take the form of counting operations. With widespread use of clustered and distributed platforms, these operations are increasingly being performed across networked hosts. Traditional APIs for messaging are susceptible to sniffing, and the data being transferred between hosts is often enough to compromise the entire computation. Due to the large computational requirements of underlying applications, it is highly desirable that secure protocols add minimal overhead to the original algorithm. Finally, by its very nature, dot-products leak limited amounts of information - one of the parties can detect an entry of the other party's vector by simply probing it with a vector with a I in a particular location and zeros elsewhere. We present an extremely efficient and sufficiently secure protocol for computing the dot-product of two vectors using linear algebraic techniques. Using analytical as well as experimental results, we demonstrate superior performance in terms of computational overhead, numerical stability, and security. We show that the overhead of a two-party dot-product computation using MPI as the messaging API across two high-end workstations connected via a Gigabit ethernet approaches multiple 4.69 over an unsecured dot-product. We also show that the average relative error in dot-products across a large number of random (normalized) vectors was roughly 4.5 × 10^-9.