This article develops a cloud-based protocol for a constrained quadratic optimization problem involving multiple parties, each holding private data. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure communication techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy. We show the implementation results of the protocol and discuss its computational and communication complexity. We conclude this article with a discussion on privacy notions.

Real-world healthcare data sharing is instrumental in constructing broader-based and larger clinical datasets that may improve clinical decision-making research and outcomes. Stakeholders are frequently reluctant to share their data without guaranteed patient privacy, proper protection of their datasets, and control over the usage of their data. Fully homomorphic encryption (FHE) is a cryptographic capability that can address these issues by enabling computation on encrypted data without intermediate decryptions, so the analytics results are obtained without revealing the raw data. This work presents a toolset for collaborative privacy-preserving analysis of oncological data using multiparty FHE. Our toolset supports survival analysis, logistic regression training, and several common descriptive statistics. We demonstrate using oncological datasets that the toolset achieves high accuracy and practical performance, which scales well to larger datasets. As part of this work, we propose a cryptographic protocol for interactive bootstrapping in multiparty FHE, which is of independent interest. The toolset we develop is general-purpose and can be applied to other collaborative medical and healthcare application domains.