Cloud-based Quadratic Optimization with Partially Homomorphic Encryption

TL;DR

This paper presents a cloud-based protocol for privacy-preserving quadratic optimization using partially homomorphic encryption and secure multi-party computation, balancing privacy and communication efficiency.

Contribution

It introduces a novel cryptographic protocol for distributed quadratic optimization that ensures computational privacy and analyzes its complexity and privacy trade-offs.

Findings

Protocol achieves computational privacy under cryptographic definitions.

A variant reduces communication complexity with weaker privacy guarantees.

Theoretical and implementation results demonstrate effectiveness and efficiency.

Abstract

The development of large-scale distributed control systems has led to the outsourcing of costly computations to cloud-computing platforms, as well as to concerns about privacy of the collected sensitive data. This paper develops a cloud-based protocol for a quadratic optimization problem involving multiple parties, each holding information it seeks to maintain private. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure multi-party computation techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy, i.e., there is no computationally efficient algorithm that any involved party can employ to obtain private information beyond what can be inferred from the party's inputs and outputs only. In order to reduce the communication complexity of the proposed protocol, we introduced a variant that achieves this objective at the expense of weaker privacy guarantees. We discuss in detail the computational and communication complexity properties of both algorithms theoretically and also through implementations. We conclude the paper with a discussion on computational privacy and other notions of privacy such as the non-unique retrieval of the private information from the protocol outputs.