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Secure Change-Point Detection for Time Series under Homomorphic Encryption

Federico Mazzone, Giorgio Micali, Massimiliano Pronesti

TL;DR

This work introduces the first method for change-point detection on encrypted time series that employs the CKKS homomorphic encryption scheme to detect shifts in statistical properties without ever decrypting the data.

Abstract

We introduce the first method for change-point detection on encrypted time series. Our approach employs the CKKS homomorphic encryption scheme to detect shifts in statistical properties (e.g., mean, variance, frequency) without ever decrypting the data. Unlike solutions based on differential privacy, which degrade accuracy through noise injection, our solution preserves utility comparable to plaintext baselines. We assess its performance through experiments on both synthetic datasets and real-world time series from healthcare and network monitoring. Notably, our approach can process one million points within 3 minutes.

Secure Change-Point Detection for Time Series under Homomorphic Encryption

TL;DR

This work introduces the first method for change-point detection on encrypted time series that employs the CKKS homomorphic encryption scheme to detect shifts in statistical properties without ever decrypting the data.

Abstract

We introduce the first method for change-point detection on encrypted time series. Our approach employs the CKKS homomorphic encryption scheme to detect shifts in statistical properties (e.g., mean, variance, frequency) without ever decrypting the data. Unlike solutions based on differential privacy, which degrade accuracy through noise injection, our solution preserves utility comparable to plaintext baselines. We assess its performance through experiments on both synthetic datasets and real-world time series from healthcare and network monitoring. Notably, our approach can process one million points within 3 minutes.
Paper Structure (30 sections, 4 theorems, 51 equations, 8 figures, 4 tables, 14 algorithms)

This paper contains 30 sections, 4 theorems, 51 equations, 8 figures, 4 tables, 14 algorithms.

Table of Contents

  1. Introduction
  2. Our Approach and Contributions
  3. Background
  4. System and Threat Model
  5. Threat Model
  6. Time Series and the CPD Problem
  7. Ordinal Patterns Representation
  8. Example
  9. Turning Rates and CPD Algorithm
  10. FHE and CKKS
  11. Secure CPD
  12. Block-Based Matrix Encoding
  13. Summarization Functions
  14. CUSUM Statistic
  15. CPD Algorithms
  16. ...and 15 more sections

Key Result

proposition 1

Let $\beta>1$ and $P = \mathcal{N}(\mu_1,\sigma^2)$, $Q = \mathcal{N}(\mu_2,\sigma^2)$. Then

Figures (8)

  • Figure 1: Three common types of change points in time series.
  • Figure 2: The six ordinal patterns of order $2$ (figure from betken2025ordinal).
  • Figure 3: Schematic representation of our secure CPD pipeline. Here $n = 9$, $m = 3$, and the change point is detected at the second block.
  • Figure 4: Runtime of our approach for increasing time series length.
  • Figure 5: Relative error of the local-DP approach on four AR(1) series. The shaded areas show $\pm 2\,\mathrm{SEM}$ around the mean relative error. The horizontal dashed lines indicate the relative error of our approach as a baseline.
  • ...and 3 more figures

Theorems & Definitions (8)

  • definition 1
  • definition 2
  • definition 3
  • definition 4: Additive Gaussian mechanism
  • proposition 1: Gaussian RDP, equal variances
  • corollary 1: RDP of $\mathcal{A}$
  • theorem 1: $(\varepsilon,\delta)$-DP guarantee
  • corollary 2