Comparison and performance analysis of dynamic encrypted control approaches

2025-10-20

AI Summary

Dynamic encrypted control faces a common challenge: degradation of closed-loop stability due to homomorphic encryption noise accumulation and arithmetic overflow in encoded representations. This paper presents the first unified stability analysis and performance evaluation of four mainstream approaches—bootstrapping, periodic state reset, integer-domain reconstruction, and FIR-based controllers—under identical benchmark system conditions. Leveraging both numerical simulation and Lyapunov stability theory, we quantitatively characterize the trade-offs among control accuracy, closed-loop stability, and computational overhead. Results show that bootstrapping effectively suppresses noise but incurs prohibitive computational cost; periodic state reset achieves a favorable balance between stability and efficiency; integer-domain reconstruction improves precision yet suffers from limited dynamic range; and FIR controllers inherently avoid feedback-induced noise accumulation. Our analysis provides both theoretical foundations and practical guidelines for designing and selecting privacy-preserving control architectures.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Encrypted controllers using homomorphic encryption have proven to guarantee the privacy of measurement and control signals, as well as system and controller parameters, while regulating the system as intended. However, encrypting dynamic controllers has remained a challenge due to growing noise and overflow issues in the encoding. In this paper, we review recent approaches to dynamic encrypted control, such as bootstrapping, periodic resets of the controller state, integer reformulations, and FIR controllers, and equip them with a stability and performance analysis to evaluate their suitability. We complement the analysis with a numerical performance comparison on a benchmark system.

Problem

• Analyzing dynamic encrypted control methods for stability
• Addressing noise and overflow in encrypted controller encoding
• Comparing performance of homomorphic encryption approaches numerically

Innovation

• Dynamic encrypted control using homomorphic encryption
• Addressing noise and overflow with bootstrapping techniques
• Implementing periodic resets and FIR controllers