Cloud-based quadratic optimization with partially homomorphic encryption

This paper 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 the paper with a discussion on privacy notions.