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Secure parameter identification of ARX systems with CKKS cryptosystem

Jialong Chen, Jimin Wang, Ji-Feng Zhang

TL;DR

This paper focuses on the cloud-based parameter identification problem of ARX systems while protecting the system input and output and proposes a CKKS-cryptosystem-based parameter identification algorithm that has the same security level as the standard CKKS cryptosystem.

Abstract

This paper focuses on the cloud-based parameter identification problem of ARX systems while protecting the system input and output. To do so, a CKKS-cryptosystem-based parameter identification algorithm is proposed. By rigorously proving that the statistical distance between the Gaussian distribution and the truncated discrete one is negligible, the algorithm has the same security level as the standard CKKS cryptosystem. By utilizing the projection mapping on the estimates, the conditions for correct encryption and decryption are given. Based on these conditions, the stochastic approximation method is further employed to achieve the almost sure and mean square convergence of the algorithm. The effectiveness is demonstrated through a numerical example.

Secure parameter identification of ARX systems with CKKS cryptosystem

TL;DR

This paper focuses on the cloud-based parameter identification problem of ARX systems while protecting the system input and output and proposes a CKKS-cryptosystem-based parameter identification algorithm that has the same security level as the standard CKKS cryptosystem.

Abstract

This paper focuses on the cloud-based parameter identification problem of ARX systems while protecting the system input and output. To do so, a CKKS-cryptosystem-based parameter identification algorithm is proposed. By rigorously proving that the statistical distance between the Gaussian distribution and the truncated discrete one is negligible, the algorithm has the same security level as the standard CKKS cryptosystem. By utilizing the projection mapping on the estimates, the conditions for correct encryption and decryption are given. Based on these conditions, the stochastic approximation method is further employed to achieve the almost sure and mean square convergence of the algorithm. The effectiveness is demonstrated through a numerical example.

Paper Structure

This paper contains 11 sections, 5 theorems, 95 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and problem formulation
  3. CKKS Cryptosystem
  4. Problem Formulation
  5. Main results
  6. CKKS-Cryptosystem-Based Parameter Identification Algorithm
  7. Security Analysis
  8. Conditions for Correct Encryption and Decryption
  9. Convergence Analysis
  10. Numerical example
  11. Conclusion

Key Result

Lemma 1

Let $\mathcal{L}\subset\mathbb{R}^N$ be a lattice, $\mathbf{v}_0\in\mathbb{R}^N$, and $\sigma,\tau,r,\Gamma>0$. If the following holds: then $\textsf{dist}(\mathcal{D}\!\textit{G}_{\Gamma,\mathcal{L}+\mathbf{v}_0}(\sigma^2)+\mathcal{N}(0,\tau^2),\mathcal{N}(0,r^2))\leq 3\exp(-N)$.

Figures (2)

  • Figure 1: The configuration of the problem
  • Figure 2: Trajectories of estimation errors

Theorems & Definitions (5)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • Theorem 3