On the (Im)possibility of privately outsourcing linear programming

In this paper we study the security definitions and methods for transformation-based outsourcing of linear programming. The recent attacks have shown the deficiencies of existing security definitions; thus we propose a stronger, indistinguishability-based definition of security of problem transformations that is very similar to IND-CPA security of encryption systems. We will study the realizability of this definition for linear programming and find that barring radically new ideas, there cannot exist transformations that are secure information-theoretically or even computationally. We conclude that for solving linear programming problems in privacy-preserving manner, cryptographic methods for securely implementing Simplex or some other linear programming solving algorithm are the only viable approach.

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