Unconditionally Secure Computation on Large Distributed Databases with Vanishing Cost

TL;DR

This paper demonstrates that in a network of distributed databases, any empirical statistic can be computed privately with negligible distortion and communication cost as database size grows, using secure multi-party computation techniques.

Contribution

It introduces a method combining dimensionality reduction and secure computation to achieve unconditionally secure, low-cost analysis of large distributed databases.

Findings

Perfect privacy against colluding parties

Communication cost approaches zero with large databases

Distortion in computed statistics vanishes as database size increases

Abstract

Consider a network of k parties, each holding a long sequence of n entries (a database), with minimum vertex-cut greater than t. We show that any empirical statistic across the network of databases can be computed by each party with perfect privacy, against any set of t < k/2 passively colluding parties, such that the worst-case distortion and communication cost (in bits per database entry) both go to zero as n, the number of entries in the databases, goes to infinity. This is based on combining a striking dimensionality reduction result for random sampling with unconditionally secure multi-party computation protocols.