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arxiv: 2403.09322 · v1 · submitted 2024-03-14 · 💻 cs.CR

Privacy Preserving Anomaly Detection on Homomorphic Encrypted Data from IoT Sensors

Anca Hangan , Dragos Lazea , Tudor Cioara This is my paper

Pith reviewed 2026-05-24 02:39 UTC · model grok-4.3

classification 💻 cs.CR
keywords privacy preserving anomaly detectionhomomorphic encryptionTFHEIoT sensorshistogram based detectionencrypted data processinganomaly detection on ciphertexts
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The pith

A histogram anomaly detector identifies faults in IoT sensor data while the readings stay encrypted under TFHE.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper adapts a histogram-based anomaly detection method so it runs directly on data encrypted with the TFHE homomorphic scheme. IoT devices generate sensitive streams that must remain protected, yet operators still need to spot malfunctions or intrusions. Vectorized versions of the required steps—addition, bucket placement, frequency labeling, and range labeling—are built inside TFHE's restricted operations to keep circuit depth manageable. Tests show the encrypted detector flags the same anomalies as the plaintext version and stays reliable when sensor noise, attacks, or device failures occur. This removes the usual requirement to decrypt data before analysis.

Core claim

The authors adapt the histogram-based outlier detection technique to the TFHE homomorphic encryption scheme by creating vectorized support operations for addition, bucket placement, frequency labeling of abnormal buckets, and range labeling of abnormal values. These operations fit within TFHE's constraints on input size and circuit depth. Evaluation on IoT-like data shows the encrypted detector identifies the same anomalies as the plaintext version while keeping all data encrypted.

What carries the argument

Vectorized support operations (addition, bucket placement, frequency labeling, range labeling) implemented inside TFHE to enable histogram anomaly detection on ciphertexts.

If this is right

  • Anomaly detection can be performed on encrypted IoT streams without exposing raw sensor values.
  • The detector continues to work correctly under noisy data, communication failures, and device malfunctions.
  • The same vectorized operations support labeling of both abnormal buckets and individual abnormal values.
  • Computational cost rises but stays within ranges reported for other TFHE applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The vectorization pattern used here could be applied to other lightweight statistical checks on encrypted IoT streams.
  • If the operations remain stable at larger data volumes, the method could support continuous monitoring without periodic decryption.
  • Replacing the histogram step with a different threshold rule would still rely on the same TFHE vector primitives.

Load-bearing premise

The vectorized support operations can be realized inside TFHE without introducing errors that alter the final anomaly decisions compared to plaintext processing.

What would settle it

Run the encrypted detector and the plaintext detector on identical IoT sensor datasets and check whether the sets of flagged anomalous values are exactly the same.

Figures

Figures reproduced from arXiv: 2403.09322 by Anca Hangan, Dragos Lazea, Tudor Cioara.

Figure 6
Figure 6. Figure 6: Vectorial abnormal value detection in bucket The vectorial approach to label an input value involves iteratively checking if the value is each of the buckets defined by three lists, containing, on the same position the minimum, the maximum and the number of elements already existing in bucket. When the bucket in which the value must be placed was determined, the number of values that it contains is compare… view at source ↗
Figure 7
Figure 7. Figure 7: Vectorial method to detect outliers using equi-width histograms. By using this vectorial approach to label data, the actual binary label associated with the input value can be determined by summing all the elements in the list provided by the vectorial procedure. If the list does not contain any value of 1, the sum is 0 and the value is normal. However, if the list contains a value of 1, the sum of all ele… view at source ↗
Figure 7
Figure 7. Figure 7: Histogram-based anomaly detection. 5. Evaluation Results To evaluate our prototypes, we use the data provided by IoT devices in a city district, specifically an electricity production dataset [22] containing measurements recorded by smart meters on an hourly basis. Since the values measured by the IoT meters are floating point values between 0 and 9.91 kW and our models can operate only on integer data whi… view at source ↗
Figure 8
Figure 8. Figure 8: Preprocessing data flow By applying this technique of data preprocessing which involves data normalization, we aim at converting the data to small sized integers while not disturbing the general distribution of the values [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Results provided by our privacy preserving anomaly detection method on different kinds of variations which simulate various abnormal situations encountered in an IoT system [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Configuration use case for our anomaly detection solution The complexity of our configurations is determined in terms of basic operations, such as clear addition, encrypted addition, encrypted negation, and programmable bootstrap, which is used to reduce the amount of noise within the encrypted representation to allow performing multiple operations on the same encrypted operands. The relative complexity o… view at source ↗
Figure 13
Figure 13. Figure 13: Variation of complexity in configuration UC-1 for different number of buckets and size of input data We evaluate the performance of our prototype by measuring the compile time which is the time needed to train the model using a set of plain input samples, the time taken by the model to generate the keys and the time taken to generate the encrypted labels associated with the input encrypted measurements [… view at source ↗
Figure 14
Figure 14. Figure 14: depicts the variation of all time aspects considered for UC-1 configuration, with the size of inputs. The time needed to generate the keys is significantly lower than both compile time and detection (execution) time, which have a similar way of varying the size of input values [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Correlation of encrypted inputs size with the size of clear inputs for both histogram building and anomaly detection phases in UC-2. A detailed view of the operations-based complexity of the models is presented in table 8, which showsthe number of operations of each type performed by both circuits. As in the case of UC-1, the most frequently performed operation is encrypted addition because the fundamenta… view at source ↗
Figure 16
Figure 16. Figure 16: Variation of complexity in configuration UC-2 for different number of buckets and size of input data The performance of the circuits in UC-2 in terms of compile (training), generating keys and building histogram or detecting anomalies time is synthetically presented in [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Variation of execution time, compile time, and key generation time for both histogram building and anomaly detection phases of UC-2 with the size of the plain input data The third use-case (UC-3 in table 2) aims to increase the security of the process, by computing the histogram and detecting anomalies using the same circuit. However, this results in a higher complexity of the circuit and slower execution… view at source ↗
Figure 20
Figure 20. Figure 20: Execution time, compile time, and key generation time for UC-3 with the size of the plain input data 7. Conclusion In this paper we implemented a self-contained anomaly detection solution for homomorphic encrypted data generated by IoT devices. To overcome constraints such as the limited operations that can be performed on encrypted data, we utilized the TFHE scheme implemented in Concrete. This variant o… view at source ↗
read the original abstract

IoT devices have become indispensable components of our lives, and the advancement of AI technologies will make them even more pervasive, increasing the vulnerability to malfunctions or cyberattacks and raising privacy concerns. Encryption can mitigate these challenges; however, most existing anomaly detection techniques decrypt the data to perform the analysis, potentially undermining the encryption protection provided during transit or storage. Homomorphic encryption schemes are promising solutions as they enable the processing and execution of operations on IoT data while still encrypted, however, these schemes offer only limited operations, which poses challenges to their practical usage. In this paper, we propose a novel privacy-preserving anomaly detection solution designed for homomorphically encrypted data generated by IoT devices that efficiently detects abnormal values without performing decryption. We have adapted the Histogram-based anomaly detection technique for TFHE scheme to address limitations related to the input size and the depth of computation by implementing vectorized support operations. These operations include addition, value placement in buckets, labeling abnormal buckets based on a threshold frequency, labeling abnormal values based on their range, and bucket labels. Evaluation results show that the solution effectively detects anomalies without requiring data decryption and achieves consistent results comparable to the mechanism operating on plain data. Also, it shows robustness and resilience against various challenges commonly encountered in IoT environments, such as noisy sensor data, adversarial attacks, communication failures, and device malfunctions. Moreover, the time and computational overheads determined for several solution configurations, despite being large, are reasonable compared to those reported in existing literature.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes adapting a histogram-based anomaly detection algorithm to the TFHE homomorphic encryption scheme for IoT sensor data. It implements vectorized encrypted operations for addition, bucket placement, frequency-based abnormal bucket labeling, range-based abnormal value labeling, and bucket labeling. The central claim is that these operations enable anomaly detection on encrypted data without decryption while producing results comparable to the plaintext version, with additional claims of robustness to noise, attacks, failures, and malfunctions, and reasonable overhead relative to prior work.

Significance. If the homomorphic realizations of bucket placement and labeling are shown to produce anomaly decisions identical to plaintext (i.e., zero decision-bit errors on the evaluated traces), the work would supply a concrete, operation-limited example of privacy-preserving statistical anomaly detection suitable for constrained IoT settings. The explicit vectorization to fit TFHE's supported gates is a constructive step, though the absence of noise-budget verification weakens the empirical support for the comparability claim.

major comments (3)
  1. [Evaluation section] Evaluation section: the manuscript states that results are 'consistent' and 'comparable' to plaintext processing but reports no quantitative agreement metrics (e.g., fraction of identical anomaly decisions, precision/recall deltas, or per-trace decision error rates) between the TFHE and plaintext runs. This metric is required to substantiate the central claim that the encrypted detector 'effectively detects anomalies without requiring data decryption.'
  2. [Implementation / Evaluation] No circuit-depth or noise analysis is provided for the vectorized support operations (bucket placement, frequency labeling, range labeling). TFHE noise grows with each addition and comparison; without parameter selection, bootstrapping schedule, or verification that all intermediate ciphertexts remain below the decryption threshold on the sensor traces, it is impossible to confirm that the homomorphic decisions match the plaintext histogram decisions exactly.
  3. [Evaluation section] The robustness claims (noisy sensor data, adversarial attacks, communication failures) are asserted in the abstract and evaluation summary, yet the text does not describe how these perturbations were injected into the encrypted traces or quantify their effect on the encrypted detector's output relative to plaintext.
minor comments (2)
  1. [Abstract] The abstract refers to 'several solution configurations' and 'reasonable' overheads without defining the configurations (bucket count, threshold values) or providing the concrete timing numbers.
  2. [Method] Notation for the vectorized operations (e.g., how bucket indices and frequency counters are encoded as TFHE ciphertexts) is introduced but not formalized with pseudocode or circuit diagrams.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and will revise the manuscript accordingly to strengthen the evaluation and implementation sections.

read point-by-point responses

  1. Referee: [Evaluation section] Evaluation section: the manuscript states that results are 'consistent' and 'comparable' to plaintext processing but reports no quantitative agreement metrics (e.g., fraction of identical anomaly decisions, precision/recall deltas, or per-trace decision error rates) between the TFHE and plaintext runs. This metric is required to substantiate the central claim that the encrypted detector 'effectively detects anomalies without requiring data decryption.'

    Authors: We agree that quantitative metrics are needed to substantiate the comparability claim. In the revised manuscript we will report the fraction of identical anomaly decisions, decision error rates, and any precision/recall differences between the TFHE and plaintext runs on the evaluated traces. revision: yes

  2. Referee: [Implementation / Evaluation] No circuit-depth or noise analysis is provided for the vectorized support operations (bucket placement, frequency labeling, range labeling). TFHE noise grows with each addition and comparison; without parameter selection, bootstrapping schedule, or verification that all intermediate ciphertexts remain below the decryption threshold on the sensor traces, it is impossible to confirm that the homomorphic decisions match the plaintext histogram decisions exactly.

    Authors: We will add a dedicated subsection on circuit depth and noise analysis, including the TFHE parameter set, bootstrapping schedule, and explicit verification that noise remains below the decryption threshold for all operations on the sensor traces. revision: yes

  3. Referee: [Evaluation section] The robustness claims (noisy sensor data, adversarial attacks, communication failures) are asserted in the abstract and evaluation summary, yet the text does not describe how these perturbations were injected into the encrypted traces or quantify their effect on the encrypted detector's output relative to plaintext.

    Authors: We will revise the evaluation section to describe the exact injection methods for each perturbation type and to report quantitative effects on the encrypted detector's outputs relative to the plaintext baseline. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical comparison is self-contained

full rationale

The paper adapts a standard histogram anomaly detection method to TFHE via vectorized operations and reports empirical results showing comparable anomaly decisions on encrypted vs. plaintext IoT sensor data. No equations, parameters, or claims reduce the reported detection performance to a fitted constant, self-citation chain, or definition internal to the paper. The central result rests on direct experimental runs against external sensor traces rather than any construction that forces equivalence by design.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on the standard semantic security and limited-operation properties of the TFHE scheme plus the correctness of the histogram binning procedure when executed homomorphically. No new physical constants or ad-hoc entities are introduced.

free parameters (1)
  • threshold frequency for abnormal bucket labeling
    Used to decide which buckets count as anomalous; value chosen to match plaintext behavior.
axioms (1)
  • domain assumption TFHE supports addition, comparison, and limited-depth circuits sufficient for the vectorized bucket and labeling steps
    Invoked when the paper states that the operations were implemented within TFHE constraints.

pith-pipeline@v0.9.0 · 5804 in / 1267 out tokens · 18145 ms · 2026-05-24T02:39:30.741230+00:00 · methodology

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