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Partial-encryption-decryption-based secure state estimation of singularly perturbed complex networks: A Paillier

Yunjie Chen1, Zidong Wang2, Yurong Liu1

  • 1Department of Mathematics, Yangzhou University, Yangzhou, 225002, China.

Neural Networks : the Official Journal of the International Neural Network Society
|June 29, 2026
PubMed
Summary

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This summary is machine-generated.

This study introduces a secure state estimation method for complex networks using partial encryption-decryption (PED) to balance data security and computational efficiency. The novel approach ensures resilient estimation against perturbations and eavesdropping.

Area of Science:

  • Control Systems Engineering
  • Network Security
  • Information Theory

Background:

  • Secure state estimation is crucial for complex networks transmitting data over open channels.
  • Existing methods face challenges in balancing data security with computational efficiency.
  • Perturbations in estimator gains and measurement quantization can degrade estimation performance.

Purpose of the Study:

  • To develop a secure and resilient state estimation technique for discrete-time singularly perturbed complex networks.
  • To propose a novel Paillier-based partial encryption-decryption (PED) mechanism for enhanced data protection.
  • To design an estimator that robustly handles gain perturbations and quantization errors.

Main Methods:

  • Integration of probabilistic measurement quantization with Paillier homomorphic encryption for partial encryption-decryption (PED).
Keywords:
Mean-square boundednessPaillier encryptionPartial encryption-decryptionResilient estimationSecure state estimationSingularly perturbed complex networks

Related Experiment Videos

  • Development of a group-based round-robin protocol for selecting measurement subsets for encryption.
  • Application of Lyapunov stability theory to derive conditions for estimation error boundedness.
  • Characterization of estimator gains using matrix inequalities for a tractable design.

    • Main Results:

    • The proposed PED mechanism achieves a tradeoff between data security and computational efficiency.
    • Sufficient conditions are derived to guarantee exponential ultimate boundedness of estimation errors in the mean-square sense.
    • A computationally tractable procedure for designing the resilient state estimator is presented.

    Conclusions:

    • The novel secure state estimation scheme effectively enhances data security while maintaining computational efficiency.
    • The designed estimator demonstrates robustness against estimator gain perturbations and quantization errors.
    • Numerical validation confirms the effectiveness and resilience of the proposed approach for complex networks.