Secure consensus averaging in sensor networks using random offsets

Kefayati, M.; Talebi, Majid; Khalaj, Babak Hossein; Rabiee, Hamid R.

doi:10.1109/ictmicc.2007.4448699

Cited by 55 publications

(43 citation statements)

References 5 publications

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“…Proof 10 (Proof of Theorem 3.2): Given (5), it is straightforward to see that (6a) is necessary and sufficient for (4a). Next, we observe that using (5), we can write lim t→∞ t 0 R ⊤ (f (τ ) + D out g(τ ))dτ = R ⊤ β 1 · · · β N ⊤ . Then, it follows from the statement (b) of Lemma 7.2 that lim t→∞ t 0 e −L + (t−τ ) R ⊤ (f (τ ) + D out g(τ ))dτ = 0.…”

Section: Lemma 73 (Auxiliary Results 3)mentioning

confidence: 99%

“…The proof of Theorem 3.2 is given in the appendix. We refer to the admissible signals chosen according to (5) and (6) as the locally chosen admissible signals. For a given set of…”

Section: Problem Formulationmentioning

confidence: 99%

“…The only information available to the agents is that their collective choices should satisfy (4). Then, in light of Theorem 3.2, to ensure (4a) each agent i ∈ V chooses its local admissible perturbation signals according to (5) with β i = 0.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Any other choice of {β i } N i=1 and α needs an inter-agent coordination/agreement procedure. In case of the locally chosen admissible perturbation signals without interagent coordination, since the agents need to satisfy (5) and (6) with α = β i = 0, i ∈ V, these values will be known to the malicious agents. In case that the agents coordinate to choose non-zero values for α and {β} N i=1 such that (5) and (6) are satisfied, it is likely that these choices to be known to the malicious agents.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The proof of this lemma is given in the appendix. Lemma 4.2 (Privacy preservation for i ∈ V via a concealed β i ): Consider the modified static average consensus algorithm (3) with a set of locally chosen admissible perturbation signals {f j , g j } N j=1 over a strongly connected and weightbalanced digraph G. Let the knowledge set of the malicious agent 1 include the form of conditions (5) and (6), and also the parameter α that the agents agreed to use. Let agent 1 be the in-neighbor of agent i ∈ V and all the out-neighbors of agent i, i.e., agent 1 knows {y j (t)} j∈N i out+i , t ∈ R ≥0 .…”

Section: B Case 2 Knowledge Setmentioning

confidence: 99%

See 4 more Smart Citations

Privacy preservation in a continuous-time static average consensus algorithm over directed graphs

Rezazadeh

Kia

2018

2018 Annual American Control Conference (ACC)

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This paper considers the problem of privacy preservation against passive internal and external malicious agents in the continuous-time Laplacian average consensus algorithm over strongly connected and weight-balanced digraphs. For this problem, we evaluate the effectiveness of use of additive perturbation signals as a privacy preservation measure against malicious agents that know the graph topology. Our results include (a) identifying the necessary and sufficient conditions on admissible additive perturbation signals that do not perturb the convergence point of the algorithm from the average of initial values of the agents; (b) obtaining the necessary and sufficient condition on the knowledge set of a malicious agent that enables it to identify the initial value of another agent; (c) designing observers that internal and external malicious agents can use to identify the initial conditions of another agent when their knowledge set on that agent enables them to do so. We demonstrate our results through a numerical example.

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Section: Lemma 73 (Auxiliary Results 3)mentioning

confidence: 99%

“…The proof of Theorem 3.2 is given in the appendix. We refer to the admissible signals chosen according to (5) and (6) as the locally chosen admissible signals. For a given set of…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: B Case 2 Knowledge Setmentioning

confidence: 99%

See 3 more Smart Citations

Privacy preservation in a continuous-time static average consensus algorithm over directed graphs

Rezazadeh

Kia

2018

2018 Annual American Control Conference (ACC)

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Consensus with preserved privacy against neighbor collusion

Zhang

Timoudas

Dahleh

2020

Control Theory Technol.

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This paper proposes a privacy-preserving algorithm to solve the average consensus problem based on Shamir's secret sharing scheme, in which a network of agents reach an agreement on their states without exposing their individual state until an agreement is reached. Unlike other methods, the proposed algorithm renders the network resistant to the collusion of any given number of neighbors (even with all neighbors' colluding). Another virtue of this work is that such a method can protect the network consensus procedure from eavesdropping.

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Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design

2017

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This paper studies the multi-agent average consensus problem under the requirement of differential privacy of the agents' initial states against an adversary that has access to all the messages. We first establish that a differentially private consensus algorithm cannot guarantee convergence of the agents' states to the exact average in distribution, which in turn implies the same impossibility for other stronger notions of convergence. This result motivates our design of a novel differentially private Laplacian consensus algorithm in which agents linearly perturb their state-transition and message-generating functions with exponentially decaying Laplace noise. We prove that our algorithm converges almost surely to an unbiased estimate of the average of agents' initial states, compute the exponential mean-square rate of convergence, and formally characterize its differential privacy properties. We show that the optimal choice of our design parameters (with respect to the variance of the convergence point around the exact average) corresponds to a one-shot perturbation of initial states and compare our design with various counterparts from the literature. Simulations illustrate our results.

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Secure consensus averaging in sensor networks using random offsets

Cited by 55 publications

References 5 publications

Privacy preservation in a continuous-time static average consensus algorithm over directed graphs

Privacy preservation in a continuous-time static average consensus algorithm over directed graphs

Consensus with preserved privacy against neighbor collusion

Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design

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