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AggFT: Low-Cost Fault-Tolerant Smart Meter Aggregation with Proven Termination and Privacy

Günther Eibl, Sanaz Taheri-Boshrooyeh, Alptekin Küpçü

TL;DR

This paper revisits an existing error-resilient privacy-preserving aggregation protocol based on masking and improves it, and provides a formal proof of the privacy guarantee under failure.

Abstract

Smart meter data aggregation protocols have been developed to address rising privacy threats against customers' consumption data. However, these protocols do not work satisfactorily in the presence of failures of smart meters or network communication links. In this paper, we propose a lightweight and fault-tolerant aggregation algorithm that can serve as a solid foundation for further research. We revisit an existing error-resilient privacy-preserving aggregation protocol based on masking and improve it by: (i) performing changes in the cryptographic parts that lead to a reduction of computational costs, (ii) simplifying the behaviour of the protocol in the presence of faults, and showing a proof of proper termination under a well-defined failure model, (iii) decoupling the computation part from the data flow so that the algorithm can also be used with homomorphic encryption as a basis for privacy-preservation. To best of our knowledge, this is the first algorithm that is formulated for both, masking and homomorphic encryption. (iv) Finally, we provide a formal proof of the privacy guarantee under failure. The systematic treatment with strict proofs and the established connection to graph theory may also serve as a starting point for possible generalizations and improvements with respect to increased resilience.

AggFT: Low-Cost Fault-Tolerant Smart Meter Aggregation with Proven Termination and Privacy

TL;DR

This paper revisits an existing error-resilient privacy-preserving aggregation protocol based on masking and improves it, and provides a formal proof of the privacy guarantee under failure.

Abstract

Smart meter data aggregation protocols have been developed to address rising privacy threats against customers' consumption data. However, these protocols do not work satisfactorily in the presence of failures of smart meters or network communication links. In this paper, we propose a lightweight and fault-tolerant aggregation algorithm that can serve as a solid foundation for further research. We revisit an existing error-resilient privacy-preserving aggregation protocol based on masking and improve it by: (i) performing changes in the cryptographic parts that lead to a reduction of computational costs, (ii) simplifying the behaviour of the protocol in the presence of faults, and showing a proof of proper termination under a well-defined failure model, (iii) decoupling the computation part from the data flow so that the algorithm can also be used with homomorphic encryption as a basis for privacy-preservation. To best of our knowledge, this is the first algorithm that is formulated for both, masking and homomorphic encryption. (iv) Finally, we provide a formal proof of the privacy guarantee under failure. The systematic treatment with strict proofs and the established connection to graph theory may also serve as a starting point for possible generalizations and improvements with respect to increased resilience.

Paper Structure

This paper contains 13 sections, 1 theorem, 4 equations, 7 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Existing Aggregation Algorithms
  4. Error-Resilient Masking Algorithm from Knirsch16a
  5. AggFT
  6. Assumptions
  7. Failure Resistance and Simplifying the Flow
  8. Security and Costs
  9. Enabling Homomorphic Encryption
  10. Guaranteed Termination and Correctness
  11. Computational and Network Costs
  12. Privacy Guarantee and Proof
  13. Assumptions and Game-Based Privacy Definition

Key Result

Theorem 1

Assuming that during a single aggregation round communication channels and smart meters are either on or off and that the $\mathcal{DC}$ always works, the aggregation scheme shown in Algorithm fig: algoGeneralV02 terminates properly despite these errors. More precisely:

Figures (7)

  • Figure 1: Illustration of the information flow of the masking protocol: it starts at the $\mathcal{DC}$, proceeds along the ring of smart meters and ends at the $\mathcal{DC}$. The sum of shares $S$ is computed along the ring. When a smart meter gets active it sends its masked value $\tilde{m}$ directly to the $\mathcal{DC}$ (gray arrows). In practice, the arrows point in both directions because each message is directly answered by a corresponding ACK-message.
  • Figure 2: Example network consisting of 4 smart meters and the data concentrator used to demonstrate arising problems. Connections that are on and off at round $t$ are solid and dashed, respectively.
  • Figure 3: Example network consisting of 5 smart meters and the $\mathcal{DC}$ used to demonstrate assumptions, algorithms and arising problems. Connections that are on and off at round $t$ are solid and dashed, respectively. Smart meters that will get active are filled, used links are green, unused links are black.
  • Figure 4: Demonstration of the simplified information flow: $\mathcal{SM}_2$ is removed, since only the smart meters that successfully send the masked measurements to the $\mathcal{DC}$ in step 1 can act later on. Dashed arrows are ack-signals that notify a successful reception of a message.
  • Figure 5: An alternative way to try fixing some issues of Algorithm \ref{['fig: algoExisting']}. Red nodes are failing ones, only green nodes can contribute, black messages get through, red messages do not reach its recipient. Ack-messages are dashed.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 1: Termination, Resilience and Correctness
  • Definition 1: Data Unlinkability