Secure and Privacy-Preserving Consensus (1707.04491v4)

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.

• The paper introduces a consensus protocol that leverages partial homomorphic cryptography, preserving node privacy without using noise injection.
• It employs the additive properties of the Paillier cryptosystem to secure pairwise interactions in decentralized and dynamic network settings.
• Experimental results on a Raspberry-Pi network confirm the approach's computational feasibility and robust security against various attacks.

Summary of "Secure and Privacy-Preserving Consensus"

The paper "Secure and Privacy-Preserving Consensus" by Minghao Ruan, Huan Gao, and Yongqiang Wang presents an innovative approach to achieve secure and privacy-preserving consensus in distributed systems, specifically focusing on undirected networks. Such networks are vital components of various modern applications, including distributed information fusion, decision-making, and decentralized control. The challenge in existing consensus algorithms lies in their requirement for explicit state information exchange among agents, which can lead to privacy breaches when these exchanges occur in plain text. To address this, the authors propose a novel consensus protocol leveraging partial homomorphic cryptography without relying on third-party aggregators or noise injection mechanisms typical of previous methods.

Key Contributions and Methodology

The proposed method introduces a decentralized architecture employing homomorphic encryption to secure pairwise interactions. This ensures that the privacy of each node's state is maintained by encrypting the messages exchanged between neighboring nodes, using the Paillier cryptosystem for its additive homomorphic properties. Their protocol permits nodes to conduct necessary calculations for reaching consensus while preserving privacy and ensuring resistance to both passive and active attackers.

A distinct privacy definition relevant to dynamical systems is provided within the paper. It rigorously demonstrates, under this framework, that a node's privacy can be maintained if it has at least one legitimate neighboring node faithfully executing the protocol. The authors clarify that compared to noise-injection methods, their approach does not compromise consensus accuracy. Furthermore, their method accommodates dynamic environments, allowing for time-varying network topologies without the necessity of reconfiguration.

Notably, this protocol extends beyond average consensus, addressing weighted average, maximum, and minimum consensus by adopting variant update rules compatible with the overarching framework. The authors also implemented the protocol on a Raspberry-Pi micro-controller network to verify its efficiency and computational feasibility, demonstrating the practicality of their solution in real-time scenarios.

Numerical Results and Comparisons

The paper provides strong numerical evidence and simulations to back up its claims. It shows that the proposed method can achieve the desired consensus while preserving the privacy and security of initial states, outperforming existing methods that rely on noise injection. The comparison with approaches like decaying-noise and correlated-noise mechanisms reveals their vulnerability to external eavesdroppers, as these noise-based methods often involve a trade-off between privacy and accuracy, which the proposed cryptography-based approach effectively mitigates.

Implications and Future Directions

The implications of this research are considerable for fields heavily reliant on secure and decentralized operations, such as sensor networks, IoT, and autonomous control systems. The ability to maintain privacy without compromising accuracy is a substantial advancement, making distributed systems more resilient to privacy concerns and cyber threats. As a future trajectory, expanding this consensus protocol to encompass other network scenarios and further reducing computational overheads could enhance the applicability and adoption of this method. Additionally, developments in cryptographic research could provide opportunities to refine and optimize the underlying cryptographic techniques used in such secure algorithms.

In summary, this paper significantly contributes to secure consensus methods within distributed systems. It provides a robust framework that balances security, privacy, and computational feasibility, presenting a viable solution to the pivotal concerns of consensus processes in decentralized architectures.