Privacy-preserving analysis of vertically partitioned data using secure matrix products

Reluctance of statistical agencies and other data owners to share possibly confidential or proprietary data with others who own related databases is a serious impediment to conducting mutually beneficial analyses. In this article, we propose a protocol for conducting secure regressions and similar analyses on vertically partitioned data – databases with identical records but disjoint sets of attributes. This protocol allows data owners to estimate coefficients and standard errors of linear regressions, and to examine regression model diagnostics, without disclosing the values of their attributes to each other. No third parties are involved. The protocol can be used to perform other procedures for which sample means and covariances are sufficient statistics. The basis is an algorithm for secure matrix multiplication, which is used by pairs of owners to compute off-diagonal blocks of the full data covariance matrix. Key words: Distributed databases; secure matrix product; vertically partitioned data; regression; data confidentiality. 1