Privacy preserving mechanisms for optimizing cross-organizational collaborative decisions based on the Karmarkar algorithm

Cross-organizational collaborative decision-making involves a great deal of private information which companies are often reluctant to disclose, even when they need to analyze data collaboratively. The lack of effective privacy-preserving mechanisms for optimizing cross-organizational collaborative decisions has become a challenge for both researchers and practitioners. It is even more challenging in the era of big data, since data encryption and decryption inevitably increase the complexity of calculation. In order to address this issue, in this study we introduce the Karmarkar algorithm as a way of dealing with the privacy-preserving distributed linear programming (LP) needed for secure multi-party computation (SMC) and secure two-party computation (STC) in scenarios characterised by mutual distrust and semi-honest participants without the aid of a trusted third party. We conduct two simulations to test the effectiveness and efficiency of the proposed protocols by revising the Karmarkar algorithm. The first simulation indicates that the proposed protocol can obtain the same outcome values compared to no-encryption algorithms. Our second simulation shows that the computational time in the proposed protocol can be reduced, especially for a high-dimensional constraint matrix (e.g., from 100 × 100 to 1000 × 1000). As such, we demonstrate the effectiveness and efficiency that can be achieved in the revised Karmarkar algorithm when it is applied in SMC. The proposed protocols can be used for collaborative optimization as well as privacy protection. Our simulations highlight the efficiency of the proposed protocols for large data sets in particular.