[Paper Review] Secure and Privacy-Preserving Consensus

Minghao Ruan, Huan Gao+1 more|arXiv (Cornell University)|Jul 12, 2017

Distributed systems and fault tolerance34 references3 citations

TL;DR

This paper proposes a decentralized, privacy-preserving consensus protocol for undirected networks using partial homomorphic cryptography to enable secure average consensus without an aggregator. By encrypting state exchanges and ensuring convergence to the exact average (within quantization error), the method protects node privacy even against passive eavesdroppers and supports dynamic topologies, with validation via simulations and Raspberry Pi hardware experiments.

ABSTRACT

Consensus is fundamental for distributed systems since it underpins key functionalities of such systems ranging from distributed information fusion, decision-making, to decentralized control. In order to reach an agreement, existing consensus algorithms require each agent to exchange explicit state information with its neighbors. This leads to the disclosure of private state information, which is undesirable in cases where privacy is of concern. In this paper, we propose a novel approach that enables secure and privacy-preserving average consensus in a decentralized architecture in the absence of an aggregator or third-party. By leveraging partial homomorphic cryptography to embed secrecy in pairwise interaction dynamics, our approach can guarantee consensus to the exact value in a deterministic manner without disclosing a node's state to its neighbors. In addition to enabling resilience to passive attackers aiming to steal state information, the approach also allows easy incorporation of defending mechanisms against active attackers which try to alter the content of exchanged messages. Furthermore, in contrast to existing noise-injection based privacy-preserving mechanisms which have to reconfigure the entire network when the topology or number of nodes varies, our approach is applicable to dynamic environments with time-varying coupling topologies. This secure and privacy-preservation approach is also applicable to weighted average consensus as well as maximum/minimum consensus under a new update rule. The approach is light-weight in computation and communication. Implementation details and numerical examples are provided to demonstrate the capability of our approach.

Motivation & Objective

• Address the privacy leakage inherent in conventional consensus algorithms that require explicit exchange of node states.
• Overcome limitations of noise-injection methods, which sacrifice accuracy or fail under eavesdropping and assume static topologies.
• Enable secure, deterministic convergence to the average consensus value in decentralized networks without a trusted third party.
• Provide resilience against both passive eavesdroppers and active attackers attempting to alter messages.
• Extend the approach to weighted average and maximum/minimum consensus under new update rules.

Proposed method

• Leverage partial homomorphic encryption (specifically Paillier cryptosystem) to encrypt state values during pairwise interactions.
• Design a novel pairwise interaction protocol where nodes exchange encrypted state differences to compute updates without revealing raw states.
• Introduce a counter-based synchronization mechanism to handle concurrent requests and responses in multi-node networks using parallel threads.
• Use digital signatures to defend against active attackers modifying messages during transmission.
• Ensure convergence to the exact average (up to quantization error) through deterministic, homomorphic operations on encrypted data.
• Formulate a new privacy definition for dynamical systems based on the presence of at least one honest neighbor who follows the protocol faithfully.

Experimental results

Research questions

• RQ1 Can a decentralized consensus protocol guarantee convergence to the exact average while preserving node privacy without relying on a trusted third party?
• RQ2 How can privacy be formally defined and proven in the context of dynamical consensus systems under adversarial observation?
• RQ3 Can the proposed method resist passive eavesdroppers who monitor communication channels?
• RQ4 How does the protocol perform in dynamic networks with time-varying topologies compared to noise-based obfuscation methods?
• RQ5 Can the approach be extended to support weighted average and maximum/minimum consensus under secure update rules?

Key findings

• The proposed protocol achieves deterministic convergence to the average consensus value (within quantization error) without requiring noise injection.
• Numerical simulations confirm that the method is resilient to passive eavesdroppers, unlike correlated-noise-based approaches that are vulnerable to naive observers.
• Hardware experiments on a six-node Raspberry Pi network demonstrate convergence to the average value of 580.67 in approximately 13 steps with an average processing latency of 7.8 ms per interaction.
• The approach supports dynamic topologies and does not require network reconfiguration when node count or coupling structure changes.
• The computational overhead of encryption (7.8 ms per interaction on Raspberry Pi) is deemed acceptable for real-time control systems.
• The protocol can be extended to support weighted average consensus and maximum/minimum consensus using new update rules, maintaining security and privacy.