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arxiv: 2511.14267 · v2 · pith:JWHMLPO3new · submitted 2025-11-18 · 📡 eess.SY · cs.SY

Secure Parameter Identification for Multi-Participant ARX Systems via CKKS Cryptosystem-Based Proxy Re-Encryption

Jialong Chen , Ji-Feng Zhang This is my paper

Pith reviewed 2026-05-21 19:19 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords secure parameter identificationARX systemsCKKS cryptosystemproxy re-encryptiontruncated Gaussian noiseRLWEIND-CPA securitymulti-participant systems
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The pith

Replacing discrete Gaussian noise with a truncated version in CKKS enables IND-CPA secure proxy re-encryption for multi-participant ARX parameter identification.

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

The paper develops a secure method for identifying parameters in autoregressive exogenous input systems shared among multiple participants without exposing private inputs or outputs. It modifies the CKKS homomorphic encryption scheme by using truncated discrete Gaussian noise instead of the standard version and proves their statistical distance is negligible. This negligible distance supports a polynomial-time reduction from the standard Ring-Learning with Errors problem, which establishes indistinguishability under chosen-plaintext attacks for the resulting algorithm. Key-switching is incorporated to build a proxy re-encryption scheme that supports the multi-party identification task. The work also supplies a lower bound on plaintext space size to avoid overflow and derives the mean-square convergence rate together with the explicit trade-off between security level and convergence speed.

Core claim

By rigorously proving that the statistical distance between the discrete Gaussian noise and the truncated one is negligible, the polynomial-time reduction between the standard Ring-Learning with Errors problem and the RLWE problem with the truncated discrete Gaussian noise is established. This result ensures the IND-CPA security of the secure parameter identification algorithm built on a CKKS-based proxy re-encryption scheme for multi-participant ARX systems. A lower bound condition on the size of the plaintext space avoids computational overflow, after which the mean square convergence and convergence rate of the algorithm are given along with the trade-off between security level and the (s

What carries the argument

CKKS cryptosystem with truncated discrete Gaussian noise plus key-switching to realize proxy re-encryption, which allows encrypted data sharing and joint parameter estimation while preserving input-output privacy.

If this is right

  • The algorithm converges in the mean-square sense at an explicit rate once the plaintext-space lower bound is met.
  • Increasing the security parameter widens the gap between security level and convergence speed.
  • Both system inputs and outputs remain protected throughout the multi-participant identification process.
  • Computational overflow during encryption is avoided when the plaintext space satisfies the derived lower bound.

Where Pith is reading between the lines

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

  • The same truncation-plus-reduction technique could be applied to other privacy-preserving system identification tasks in networked control.
  • Lower computational cost from truncation may improve practicality of homomorphic encryption in real-time control loops.
  • The convergence-security trade-off suggests tuning guidelines for choosing truncation width in different operating regimes.

Load-bearing premise

The statistical distance between standard discrete Gaussian noise and the truncated version remains negligible for the chosen truncation parameters, allowing the security reduction to the standard RLWE problem to hold.

What would settle it

An efficient algorithm that distinguishes RLWE samples generated with the truncated noise from those generated with standard discrete Gaussian noise at a non-negligible advantage, or a chosen-plaintext attack that recovers a participant's private input or output data from the encrypted identification transcripts.

Figures

Figures reproduced from arXiv: 2511.14267 by Jialong Chen, Ji-Feng Zhang.

Figure 1
Figure 1. Figure 1: The configuration of the problem 3. MAIN RESULTS 3.1 CKKS-Cryptosystem-Based Parameter Identification Algorithm We propose the following CKKS-cryptosystem-based pa￾rameter identification algorithm. Algorithm 2 CKKS-cryptosystem-based parameter iden￾tification algorithm Input: The step-size parameter α, and the initial estimate ˆθ0 ∈ X . for k = 0, 1, . . . , do 1: Sensor S encodes the regressor φk, the sys… view at source ↗
Figure 2
Figure 2. Figure 2: Trajectories of estimation errors 5. CONCLUSION In this paper, we proposed a CKKS-cryptosystem-based parameter identification algorithm for the cloud-based parameter identification problem of ARX systems. By giving a lower bound of the truncation value of the truncated discrete Gaussian distribution, the negligible statistical distance between the Gaussian distribution and the truncated discrete one is pro… view at source ↗
read the original abstract

This paper investigates the parameter identification for multi-participant autoregressive exogenous input (ARX) systems while protecting the system input and output. To do so, the discrete Gaussian noise in the standard Cheon-Kim-Kim-Song (CKKS) cryptosystem is replaced with a truncated one. By using the CKKS cryptosystem with the truncated discrete Gaussian noise and the key-switching technique, a proxy re-encryption scheme is developed. Based on this scheme, a secure parameter identification algorithm is proposed for multi-participant ARX systems. By rigorously proving that the statistical distance between the discrete Gaussian noise and the truncated one is negligible, the polynomial-time reduction between the standard Ring-Learning with Errors (RLWE) problem and the RLWE problem with the truncated discrete Gaussian noise is established. This result ensures the indistinguishability under chosen-plaintext attacks (IND-CPA) security of the algorithm. By giving a lower bound condition on the size of the plaintext space, the computational overflow in encryption is avoided. Based on this condition, the mean square convergence and convergence rate of the algorithm are given. The trade-off between the security level and the convergence of the algorithm is presented. Finally, a numerical example is given to verify the effectiveness of the algorithm.

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

1 major / 2 minor

Summary. The paper proposes a secure parameter identification algorithm for multi-participant ARX systems. It replaces the discrete Gaussian noise in the CKKS cryptosystem with a truncated version, develops a proxy re-encryption scheme using key-switching, and claims IND-CPA security via a polynomial-time reduction to the standard RLWE problem. This reduction is based on proving that the statistical distance between standard and truncated discrete Gaussian noise is negligible. The authors also derive a lower bound on plaintext space size to avoid encryption overflow, establish mean-square convergence and rate under this condition, analyze the security-convergence trade-off, and include a numerical example for validation.

Significance. If the security reduction holds tightly for the concrete parameters and the convergence analysis is rigorous, the work could provide a useful bridge between homomorphic encryption techniques and distributed system identification, with the explicit trade-off discussion and convergence guarantees as notable strengths.

major comments (1)
  1. The central security claim (abstract and security analysis section) asserts a polynomial-time reduction to standard RLWE based on negligible statistical distance between discrete Gaussian and truncated noise. However, this requires an explicit check that the chosen truncation bound B (relative to sigma) yields total variation distance below 2^{-lambda} for the ring dimension, modulus q, and security parameter lambda used in the numerical example and convergence bounds. Without this verification, the reduction tightness and IND-CPA guarantee may not hold for the paper's parameters.
minor comments (2)
  1. In the numerical example, explicitly state the values of B, sigma, n, and q and confirm they satisfy the plaintext space lower bound to prevent overflow.
  2. Clarify the multi-participant extension in the convergence proof: how the proxy re-encryption affects the mean-square error bound derivation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying this important point on the concrete security parameters. We address the comment below and will revise the manuscript to incorporate the requested verification.

read point-by-point responses

  1. Referee: The central security claim (abstract and security analysis section) asserts a polynomial-time reduction to standard RLWE based on negligible statistical distance between discrete Gaussian and truncated noise. However, this requires an explicit check that the chosen truncation bound B (relative to sigma) yields total variation distance below 2^{-lambda} for the ring dimension, modulus q, and security parameter lambda used in the numerical example and convergence bounds. Without this verification, the reduction tightness and IND-CPA guarantee may not hold for the paper's parameters.

    Authors: We appreciate the referee pointing out the value of an explicit numerical check for the concrete parameters. The manuscript provides a general proof that the statistical distance between the discrete Gaussian and its truncated version is negligible for truncation bounds B that are sufficiently large relative to the standard deviation sigma. To directly address the concern and confirm that the polynomial-time reduction to standard RLWE (and thus the IND-CPA security) holds tightly for the specific ring dimension, modulus q, and security parameter lambda appearing in the numerical example and convergence bounds, we will add an explicit computation of the total variation distance in the revised security analysis section. This will verify that the distance falls below 2^{-lambda} for the chosen B and sigma values used in the paper. revision: yes

Circularity Check

0 steps flagged

Security reduction to external RLWE and convergence bounds are self-contained

full rationale

The paper establishes IND-CPA security by proving the statistical distance between standard and truncated discrete Gaussian noise is negligible, yielding a polynomial-time reduction to the standard RLWE problem (an external hardness assumption independent of the paper's fitted values or internal parameters). Convergence rate and mean-square bounds follow directly from the algorithm steps plus the stated plaintext-space lower bound condition that prevents overflow. No load-bearing step reduces by construction to a self-fit, self-citation chain, or renamed input; the derivation therefore remains independent of the quantities it analyzes.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on the standard hardness of the RLWE problem and on the negligibility of the statistical distance after truncation; a lower bound on plaintext space size is introduced to prevent overflow but is not fitted to data.

free parameters (1)
  • plaintext space size lower bound
    Condition given to avoid computational overflow during encryption; its specific value is chosen to satisfy the algorithm's numerical stability.
axioms (1)
  • domain assumption The Ring-Learning with Errors problem is computationally hard for appropriate parameters
    Invoked to transfer security from the standard CKKS setting to the truncated-noise variant via the statistical-distance argument.

pith-pipeline@v0.9.0 · 5760 in / 1303 out tokens · 59587 ms · 2026-05-21T19:19:40.172687+00:00 · methodology

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Reference graph

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