Privacy-preserving consensus averaging

Abstract

Consensus problem has been a topic of interest for many research areas allowing multiple agents to reach an agreement through local information exchange. The explicit share of the state variables, however, may cause privacy issues due to the confidentiality of the initial values. In this work, asynchronous privacy-preserving consensus average algorithms are proposed which enables the agents to reach the exact average of their initial values while preserving the privacy of them. The research aims to reduce the convergence time and computational complexity compared to the cryptographic solutions. Three methods are proposed and compared. The state decomposition and noise-obfuscation methods preserve the privacy of the initial values given that the semi-honest adversary is not able to listen to one of the neighboring nodes of the targeted node. The hybrid state decomposition approach proposes a way to overcome this assumption by using a minimum number of encryption operations. The initial values are shown to be private against an eavesdropper who is able to tap all communication channels as well as a semi-honest adversary in the system. It has been shown in all proposed approaches that as the noise variance goes to infinity, the adversary does not have any range to estimate the initial value. The noise obfuscation technique futures the same convergence rate as the standard averaging approach while providing a linear increase in the variance of the adversary's estimate with the increasing noise variance. On the other hand, the state decomposition technique futures a lower convergence rate compared to the standard averaging approach while providing an exponential increase in the variance of the adversary's estimate with the increasing noise variance. By optimizing the algorithm, it has been shown that the same convergence rate as the standard randomized gossip can be obtained. The state decomposition approach requires the addition of noise for a bounded amount whereas, the noise obfuscation method requires the addition of noise at each iteration. All three approaches, converges faster than a fully cryptographic approach while promising statistical security guarantees.