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Confidential FRIT via Homomorphic Encryption

Haruki Hoshino, Jungjin Park, Osamu Kaneko, Kiminao Kogiso

TL;DR

This work tackles confidentiality in data-driven gain tuning for cyber-physical systems by introducing confidential FRIT, a framework that enables gain updates to be computed on encrypted data using homomorphic encryption. It replaces the costly matrix-inversion step with a sum of intermediate matrices $\sum_{k=1}^{(n-1)!}\Phi_k$, allowing exact equivalence to conventional FRIT while outsourcing to an external server. The authors instantiate the framework with ElGamal (partially homomorphic) and CKKS (fully homomorphic) schemes, providing formal setups, numerical examples at $128$-bit security, and a comparison of accuracy and performance. The results show that confidential FRIT can achieve gains nearly identical to standard FRIT, with ElGamal offering much faster server-side performance and CKKS providing post-quantum security, outlining practical guidance for selecting encryption schemes in encrypted CPS control.

Abstract

Edge computing alleviates the computation burden of data-driven control in cyber-physical systems (CPSs) by offloading complex processing to edge servers. However, the increasing sophistication of cyberattacks underscores the need for security measures that go beyond conventional IT protections and address the unique vulnerabilities of CPSs. This study proposes a confidential data-driven gain-tuning framework using homomorphic encryption, such as ElGamal and CKKS encryption schemes, to enhance cybersecurity in gain-tuning processes outsourced to external servers. The idea for realizing confidential FRIT is to replace the matrix inversion operation with a vector summation form, allowing homomorphic operations to be applied. Numerical examples under 128-bit security confirm performance comparable to conventional methods while providing guidelines for selecting suitable encryption schemes for secure CPS.

Confidential FRIT via Homomorphic Encryption

TL;DR

This work tackles confidentiality in data-driven gain tuning for cyber-physical systems by introducing confidential FRIT, a framework that enables gain updates to be computed on encrypted data using homomorphic encryption. It replaces the costly matrix-inversion step with a sum of intermediate matrices , allowing exact equivalence to conventional FRIT while outsourcing to an external server. The authors instantiate the framework with ElGamal (partially homomorphic) and CKKS (fully homomorphic) schemes, providing formal setups, numerical examples at -bit security, and a comparison of accuracy and performance. The results show that confidential FRIT can achieve gains nearly identical to standard FRIT, with ElGamal offering much faster server-side performance and CKKS providing post-quantum security, outlining practical guidance for selecting encryption schemes in encrypted CPS control.

Abstract

Edge computing alleviates the computation burden of data-driven control in cyber-physical systems (CPSs) by offloading complex processing to edge servers. However, the increasing sophistication of cyberattacks underscores the need for security measures that go beyond conventional IT protections and address the unique vulnerabilities of CPSs. This study proposes a confidential data-driven gain-tuning framework using homomorphic encryption, such as ElGamal and CKKS encryption schemes, to enhance cybersecurity in gain-tuning processes outsourced to external servers. The idea for realizing confidential FRIT is to replace the matrix inversion operation with a vector summation form, allowing homomorphic operations to be applied. Numerical examples under 128-bit security confirm performance comparable to conventional methods while providing guidelines for selecting suitable encryption schemes for secure CPS.

Paper Structure

This paper contains 17 sections, 3 theorems, 22 equations, 19 figures, 1 table, 6 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. ElGamal Encryption
  5. CKKS Encryption
  6. Confidential FRIT Problem
  7. Proposed Confidential FRIT
  8. ElGamal-based Confidential FRIT
  9. CKKS-based Confidential FRIT
  10. Numerical Examples
  11. Comparison under Unified Security Level
  12. Example Setups and Tuning Results
  13. Example 1
  14. Example 2
  15. Conclusion
  16. ...and 2 more sections

Key Result

Theorem 4.1

The equation original is expressed as follows: where $\Gamma_i\in\mathbb{R}$ is the $i$-th element of the vector $\Gamma\in\mathbb{R}^{nN}$, $W_{il}\in\mathbb{R}$ is the $(i,l)$-th element of the matrix $W\in\mathbb{R}^{nN\times n}$, $\Phi_{k,l}\in\mathbb{R}^{1\times n}$ is the $l$-th row vector of the intermediate generation matrix $\Phi_k\in\m

Figures (19)

  • Figure 1: Setups of conventional and confidential FRITs, which handle unencrypted and encrypted datasets ($\mathcal{D},\mathcal{F}$), respectively.
  • Figure 2: $x_1(k)$
  • Figure 3: $x_2(k)$
  • Figure 4: $x_1(k;F^*)-x_1(k;\bar{F}^*_\mathcal{E})$
  • Figure 5: $x_2(k;F^*)-x_2(k;\bar{F}^*_\mathcal{E})$
  • ...and 14 more figures

Theorems & Definitions (4)

  • Theorem 4.1
  • Proposition 4.2
  • Remark 1
  • Proposition 4.3