Privacy-preserving vertically partitioned linear program with nonnegativity constraints

We propose a simple privacy-preserving reformulation of a linear program with inequality constraints and nonnegativity constraints. By employing two random matrix transformation we construct a secure linear program based on the privately held data without revealing that data. The secure linear program has the same minimum value as the original linear program. Component groups of the solution of the transformed problem can be decoded and made public only by the original group that owns the corresponding columns of the constraint matrix and can be combined to give an exact solution vector of the original linear program.