Per-se Privacy Preserving Distributed Optimization

Ensuring privacy is essential in various contexts, such as h ealthcare data, banks, e-commerce, government services, and social networks. In these contexts, it is common that different parties coordinate to solve a specific problem whose problem data is dispersed am ong the involved entities and that no entity wants to publish its data during the solution procedu re. Addressing these problems falls under the umbrella of well-known secured multiparty computation(SMC). Existing approaches for SMC are mostly based on cryptography. Surprisingly, little attent ion has been devoted thus far to develop efficient non-cryptographic approaches. In this paper, we investigate potential non-cryptographic methods based on mathematical optimization techniques . In particular, first, a unified framework to encapsulate existing non-cryptographic methods, which rely algebraic transformations to disguise sensitive problem data, is developed. The proposed framework capitalizes on key optimization techniques, such as change of variables and transformation of objective and constraint functions , for equivalent problem formation. Moreover, the privacy preserving properties that are inherent in the mathematical optimization techniques, including classical decomposition methods (e.g., primal and dual decomposition), and state-ofthe-art methods, such as alternating direction method of multipliers are investigated. A general definition for quantifying the privacy in the context of non-cryptographic approaches is proposed. A number of examples are provided to illustrate the importance of our proposed algorithms. It is concluded that the theory is in its infancy and that huge benefits can be achieved by a substantial development.