Verifiable computations for dynamic encrypted control

2026-06-16

AI Summary

This work addresses the challenge of verifying the integrity of results returned by cloud servers in dynamic encrypted control systems by proposing a lightweight verification mechanism. It introduces linear dynamical system theory into encrypted control verification for the first time, enabling efficient local validation of computational correctness. The approach operates by injecting artificial challenge signals in parallel at the cloud side and leveraging the inherent input-output system properties of the controller. The proposed scheme incurs negligible additional computational overhead, detects tampering errors with high probability, and effectively mitigates replay attacks. Consequently, it significantly outperforms existing static or computationally expensive verification methods.

Abstract

Encrypted control can preserve the privacy of data and parameters while the necessary computations can be outsourced to a cloud server. To ensure the integrity of the received values from the cloud, i.e., that they have not been changed, however, strong assumptions or verification algorithms are needed. Previous methods require computationally expensive cryptographic protocols or are only applicable to static computations. In this paper, we present a novel type of verification algorithm for linear dynamic encrypted control. We utilize system-theoretic input-output properties of the controller for artificial challenge signals, which are processed in the cloud in parallel with the requested control input, to check the correctness of the results at the plant. This results in almost no additional computational load, wrong computations are revealed with high probability, and no replay attacks are possible.

Problem

• verifiable computation
• encrypted control
• dynamic systems
• integrity verification
• cloud computing

Innovation

• verifiable computation
• encrypted control
• dynamic systems
• input-output properties
• cloud-based control