Control-theoretic Approach to Malleability Cancellation by Attacked Signal Normalization

Teranishi, Kaoru; Kogiso, Kiminao

doi:10.1016/j.ifacol.2019.12.171

Cited by 10 publications

(6 citation statements)

References 24 publications

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“…In the first step of Definition 3.1, the malicious inputs a t can be injected properly even though control inputs are encrypted by updatable homomorphic encryption because, in general, an encryption scheme and a public key are public information. Furthermore, even if an adversary does not know a public key, the adversary can falsify ciphertexts using malleability [17][18][19][20].…”

Section: Threat Modelmentioning

confidence: 99%

Optimal Security Parameter for Encrypted Control Systems Against Eavesdropper and Malicious Server

Teranishi¹,

Kogiso²

2023

Preprint

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A sample identifying complexity and a sample deciphering time have been introduced in a previous study to capture an estimation error and a computation time of system identification by adversaries. The quantities play a crucial role in defining the security of encrypted control systems and designing a security parameter. This study proposes an optimal security parameter for an encrypted control system under a network eavesdropper and a malicious controller server who attempt to identify system parameters using a least squares method. The security parameter design is achieved based on a modification of conventional homomorphic encryption for improving a sample deciphering time and a novel sample identifying complexity, characterized by controllability Gramians and the variance ratio of identification input to system noise. The effectiveness of the proposed design method for a security parameter is demonstrated through numerical simulations.

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Section: Threat Modelmentioning

confidence: 99%

Optimal Security Parameter for Encrypted Control Systems Against Eavesdropper and Malicious Server

Teranishi¹,

Kogiso²

2023

Preprint

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“…Although eavesdropping attacks can be prevented, the direct manipulation of signals or controller parameters enables the degradation of control performance or compromises it to break in the worst case. Encrypted control systems are vulnerable to attacks that use the malleability of the homomorphic encryption scheme [25], which means an attacker can manipulate encrypted signals and parameters to adjust controlled outputs without decrypting them. To reduce the vulnerability to attacks, there are related studies that consider countermeasures such as homomorphic authentication [26], obfuscation of controller parameters [25], and cancellation and detection by a modified somewhat homomorphic encryption [27], [28], which uses the malleability of a homomorphic encryption scheme.…”

Section: Related Workmentioning

confidence: 99%

“…Encrypted control systems are vulnerable to attacks that use the malleability of the homomorphic encryption scheme [25], which means an attacker can manipulate encrypted signals and parameters to adjust controlled outputs without decrypting them. To reduce the vulnerability to attacks, there are related studies that consider countermeasures such as homomorphic authentication [26], obfuscation of controller parameters [25], and cancellation and detection by a modified somewhat homomorphic encryption [27], [28], which uses the malleability of a homomorphic encryption scheme. However, these studies could hardly identify an attacked component within signals and control parameters.…”

Section: Related Workmentioning

confidence: 99%

“…An attacker does not know the homomorphic operation key sk h for Eval; therefore, they tamper with the third element of the ciphertext using a constant factor. Because the homomorphic encryption scheme yields malleability, the attacker can obtain the desired decryption result by falsifying the ciphertext [25]. In KH-PKE, the last element of the Dec algorithm is m = ϵ/π mod p, which means, if the third element e of the ciphertext is multiplied by λ ∈ G, the decryption result is λ-fold.…”

Section: Attack Detectionmentioning

confidence: 99%

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Cybersecurity-Enhanced Encrypted Control System Using Keyed-Homomorphic Public Key Encryption

et al. 2023

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Encrypted control systems are secure control methods that use the cryptographic properties of a specific homomorphic encryption scheme. This study proposes a cyberattack-detectable encrypted control system and validates its effectiveness using a proportional integration derivative (PID) positioncontrol system for an industrial motor. The proposed encrypted control system uses a keyed-homomorphic public-key encryption scheme for real-time detection of cyberattacks, such as signal and control parameter falsification. Additionally, a novel quantizer is presented to reduce the computation cost and quantizationerror effects on control performance. The quantizer demonstrated a significant improvement, reducing the computation time by 47.3 % compared to using our previous quantizer, and decreasing the quantization-error effect by 30.6 % compared to a widely-used gain-multiplying quantizer. Moreover, this study establishes conditions through a theorem to avoid an overflow in the proposed control system. Experimental validation confirms that the proposed control system effectively conceals the control operation, and the presented theorem aids in designing the quantization gains to prevent overflows. Notably, the results of falsification attack tests highlight that the proposed control system enables real-time detection of attacked components within control parameters and signals, representing a significant advantage of this study.

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“…1. In particular, we ignore the malleability risks [22] inherent to the considered HE scheme, which is beyond the scope of this paper. In our context, Syn(Enc(•)) can be thought of as a ciphertext domain implementation of RL algorithms.…”

Section: Encrypted Learning Over the Cloud A Cloud-based Reinforcemen...mentioning

confidence: 99%

Encrypted Value Iteration and Temporal Difference Learning over Leveled Homomorphic Encryption

Suh

Tanaka

2021

Preprint

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We consider an architecture of confidential cloudbased control synthesis based on Homomorphic Encryption (HE). Our study is motivated by the recent surge of data-driven control such as deep reinforcement learning, whose heavy computational requirements often necessitate an outsourcing to the third party server. To achieve more flexibility than Partially Homomorphic Encryption (PHE) and less computational overhead than Fully Homomorphic Encryption (FHE), we consider a Reinforcement Learning (RL) architecture over Leveled Homomorphic Encryption (LHE). We first show that the impact of the encryption noise under the Cheon-Kim-Kim-Song (CKKS) encryption scheme on the convergence of the model-based tabular Value Iteration (VI) can be analytically bounded. We also consider secure implementations of TD(0), SARSA(0) and Z-learning algorithms over the CKKS scheme, where we numerically demonstrate that the effects of the encryption noise on these algorithms are also minimal.

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Control-theoretic Approach to Malleability Cancellation by Attacked Signal Normalization

Cited by 10 publications

References 24 publications

Optimal Security Parameter for Encrypted Control Systems Against Eavesdropper and Malicious Server

Optimal Security Parameter for Encrypted Control Systems Against Eavesdropper and Malicious Server

Cybersecurity-Enhanced Encrypted Control System Using Keyed-Homomorphic Public Key Encryption

Encrypted Value Iteration and Temporal Difference Learning over Leveled Homomorphic Encryption

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