Silent Threats: How Encrypted Control Systems Remain Vulnerable

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Author: Denis Avetisyan

Despite the widespread adoption of encryption, critical infrastructure controlled by encrypted systems remains susceptible to subtle, yet dangerous, covert attacks.

A covert attack strategy leverages the inherent properties of homomorphisms within an encrypted network communication system (NCS) to compromise security without detection.
A covert attack strategy leverages the inherent properties of homomorphisms within an encrypted network communication system (NCS) to compromise security without detection.

This review details the vulnerabilities of homomorphic encryption in networked control systems and proposes a zero-overhead verifiable computation scheme to enhance security and integrity.

While outsourcing control system evaluation to secure platforms promises confidentiality, it paradoxically introduces vulnerabilities to integrity attacks. This paper, ‘On the (non-)resilience of encrypted controllers to covert attacks’, demonstrates that networked control systems employing homomorphic encryption remain susceptible to covert manipulation, even without knowledge of the underlying system model. Specifically, we show that the inherent malleability of public-key HE schemes enables attackers to exploit the same homomorphisms used for secure computation to launch insidious attacks. Can complementary techniques, such as verifiable computation, effectively bridge this security gap and ensure robust, trustworthy control in the age of networked systems?

The Escalating Vulnerability of Networked Control Systems

The escalating integration of Networked Control Systems (NCS) into critical infrastructure – encompassing power grids, water treatment facilities, and transportation networks – presents an increasingly appealing landscape for malicious actors. These systems, designed for remote monitoring and control, offer unprecedented efficiency and automation, but simultaneously broaden the attack surface for both state-sponsored adversaries and cybercriminals. The allure stems from the potential for widespread disruption; a successful attack isn’t limited to data breaches, but can manifest as physical damage, economic losses, and even threats to public safety. Consequently, sectors once considered isolated are now interconnected and vulnerable, demanding a fundamental shift in security paradigms to address the unique challenges posed by these digitally-dependent systems. The very benefits of NCS – accessibility and interconnectivity – inadvertently create pathways for exploitation, making proactive defense a necessity rather than an option.

Networked Control Systems, while enabling unprecedented automation and efficiency, possess inherent vulnerabilities stemming from their reliance on bidirectional communication channels and intricate operational dynamics. The very networks that facilitate control also create avenues for unauthorized access and malicious interference. Beyond simply stealing information – a breach of confidentiality – attackers can manipulate system settings and data, compromising the integrity of the control process itself. This poses significant risks, as subtle alterations to parameters – unnoticed by standard monitoring – could lead to physical damage, service disruptions, or even safety hazards. The complex interplay of sensors, actuators, and controllers within these systems further exacerbates the problem, making it challenging to detect anomalies and trace the source of an attack. Consequently, safeguarding these critical infrastructures demands a security approach that goes beyond conventional cybersecurity measures, focusing on both data protection and the reliable execution of control functions.

Conventional cybersecurity protocols, designed to detect and prevent unauthorized access, frequently prove inadequate against advanced attacks targeting networked control systems. These systems, governing critical infrastructure like power grids and water treatment facilities, are increasingly susceptible to subtle manipulations that bypass traditional intrusion detection. Sophisticated adversaries employ techniques that alter system parameters or inject false data, creating anomalies that mimic normal operational fluctuations and remain undetected by signature-based security tools. This allows for insidious compromise, where attackers can gradually degrade performance, cause equipment failure, or even trigger cascading system-wide disruptions without raising immediate alarms – a critical vulnerability given the potential for widespread physical and economic consequences.

Experimental results demonstrate successful information leakage via both variants of the homomorphic covert channel, as evidenced by the observed input/output trajectories.
Experimental results demonstrate successful information leakage via both variants of the homomorphic covert channel, as evidenced by the observed input/output trajectories.

The Insidious Nature of Covert Attacks and Integrity Breaches

Covert attacks pose a significant security risk due to their method of operation: the subtle manipulation of Input/Output (I/O) data to alter system behavior without triggering immediate detection. Unlike overt attacks that cause readily apparent disruptions, covert attacks focus on inducing small, incremental changes that are difficult to distinguish from normal operational fluctuations. This is achieved by modifying data transmitted to or from system components – such as sensors, actuators, or memory – in a way that, while statistically significant, does not exceed established thresholds for anomaly detection systems. The attacker effectively operates “under the radar” by staying within the bounds of expected system noise, making these attacks exceptionally difficult to identify and mitigate through traditional security measures.

Additive Bias Injection circumvents traditional anomaly detection systems by introducing subtle, cumulative alterations to system input or processing. Rather than causing abrupt changes that trigger alarms, this technique focuses on incrementally shifting values – for example, consistently adding a small offset to sensor readings or modifying individual bits in data streams. These biases, while individually insignificant, accumulate over time, leading to predictable but disguised system misbehavior. Conventional detectors, often tuned to identify large deviations from established baselines, fail to recognize these gradual shifts as malicious activity, allowing attackers to manipulate system outputs without immediate detection. The effectiveness of this approach stems from its ability to operate within the noise floor of typical system variations, making differentiation between legitimate fluctuations and intentional manipulation exceedingly difficult.

Zero-Dynamics Attacks represent a sophisticated class of integrity breaches that leverage the inherent dynamical properties of a system to achieve stealthy control. Unlike attacks relying on direct manipulation of input or code, these attacks operate by exploiting the system’s natural response to inputs, effectively embedding malicious behavior within legitimate system dynamics. This approach allows attackers to influence system behavior without generating easily detectable anomalies, as the observed outputs remain consistent with the system’s expected operational range. Detection is significantly complicated because traditional anomaly detection methods, focused on deviations from baseline behavior, are less effective when the attack manifests as a subtle modification of existing dynamics rather than an outright deviation. The complexity arises from the need to model and analyze the system’s full state-space to differentiate between legitimate dynamic responses and those induced by the attack.

System integrity, defined as the maintenance of the correctness and completeness of a system, is fundamentally compromised by covert attacks and data manipulation. These attacks bypass traditional security measures by altering system behavior at a low level, without necessarily causing immediate errors or raising alerts. This subversion of expected operation can lead to a gradual erosion of trust in system outputs, potentially resulting in incorrect calculations, flawed decision-making, or the unauthorized execution of malicious code. Catastrophic consequences may range from financial losses and data breaches to physical damage and safety hazards, particularly in critical infrastructure or safety-critical systems where accurate and reliable operation is paramount. The subtle nature of these integrity breaches makes detection and remediation significantly more difficult than conventional attacks, requiring specialized monitoring and analysis techniques.

The homomorphic covert attack space visualizes tradeoffs between resource requirements for different attack variants, with marked points representing those detailed in Sections 3.1 (<span class="katex-eq" data-katex-display="false">∙\bullet</span>) and 3.2 (<span class="katex-eq" data-katex-display="false">◆\blacklozenge</span>), and the dashed line indicating variants with comparable resource needs.
The homomorphic covert attack space visualizes tradeoffs between resource requirements for different attack variants, with marked points representing those detailed in Sections 3.1 (∙\bullet) and 3.2 (◆\blacklozenge), and the dashed line indicating variants with comparable resource needs.

Securing Control Systems Through Cryptographic Verification

Homomorphic Encryption (HE) enables computations to be performed directly on encrypted data without requiring decryption, thereby preserving data confidentiality throughout the entire processing lifecycle. This is achieved through encryption schemes that possess specific algebraic properties allowing operations – such as addition and multiplication – to be conducted on ciphertexts, yielding results that, when decrypted, match the result of the same operations performed on the original plaintext. In the context of control systems, HE allows for secure processing of sensitive data – such as sensor readings or actuator commands – without exposing it to potential attackers, even during remote computation or storage. Different HE schemes offer varying trade-offs between computational complexity, ciphertext expansion, and supported operations; the choice of scheme depends on the specific requirements of the control application and the desired level of security.

The CKKS scheme is a leveled fully homomorphic encryption scheme particularly efficient for computations involving real numbers, a common data type in control systems. Unlike schemes optimized for boolean or integer arithmetic, CKKS represents data as fixed-point numbers, enabling direct application of standard arithmetic operations on encrypted data with controlled approximation errors. Ciphertext Packing, a technique used within CKKS, allows multiple real numbers to be encoded into a single ciphertext, significantly improving computational throughput. This is achieved by performing Single Instruction, Multiple Data (SIMD) operations on packed ciphertexts, effectively vectorizing the computations and reducing communication overhead. The scheme utilizes a noise model that accumulates with each operation, necessitating periodic bootstrapping for long computations, but its efficiency for real-number processing makes it a strong candidate for securing control applications.

Integrating Verifiable Computation (VC) with Homomorphic Encryption (HE) enhances data security by allowing a verifier to confirm the correctness of computations performed on encrypted data without decrypting it. Traditional HE schemes only ensure confidentiality; VC adds a layer of integrity assurance. This is achieved by generating a proof alongside the encrypted computation result. The proof, also encrypted, can be verified by the data owner using a public key, confirming that the computation was performed correctly according to the specified function. This is particularly valuable in scenarios where computations are outsourced to untrusted parties, as it provides a cryptographic guarantee against malicious or erroneous results, mitigating the risk of compromised control system integrity.

The integration of homomorphic encryption and verifiable computation enables secure outsourcing of control tasks while maintaining system integrity and minimizing communication overhead. By performing computations directly on encrypted data, the need to decrypt sensitive information at an untrusted third-party computing node is eliminated. Furthermore, ciphertext packing, utilized within schemes like CKKS, allows for the processing of multiple data points within a single ciphertext. This, coupled with Single Instruction, Multiple Data (SIMD) operations, significantly reduces the amount of data transmitted – achieving effectively zero communication overhead beyond the initial ciphertext transmission, as verification results are embedded within the encrypted result itself.

Secure computation pipelines enable evaluation of <span class="katex-eq" data-katex-display="false">hh</span> with and without verification, utilizing server-side operations highlighted by double-outlined boxes.
Secure computation pipelines enable evaluation of hh with and without verification, utilizing server-side operations highlighted by double-outlined boxes.

Harmonizing Cryptography with System Dynamics for Robust Control

The successful implementation of cryptographic security within a networked control system fundamentally depends on a precise and comprehensive understanding of the underlying system’s behavior. This necessitates detailed modeling of the system’s dynamics, particularly focusing on its linear characteristics to predict responses to various inputs and disturbances. Without this foundational knowledge, security measures risk introducing unintended consequences, such as instability or performance degradation. A robust system model allows for the careful selection and tuning of cryptographic algorithms and control strategies, ensuring that security enhancements do not compromise the system’s primary function. Furthermore, analyzing the system’s dynamics facilitates the identification of potential vulnerabilities and attack surfaces, enabling proactive security design and mitigating the risk of successful exploits. The interplay between system understanding and cryptographic implementation is therefore critical for building resilient and secure networked control systems.

Traditional control methodologies, such as Static Output Feedback Controllers, rely heavily on efficient matrix-vector multiplication for real-time system adjustments. However, integrating these techniques into cryptographically secured Networked Control Systems demands careful adaptation. The computational intensity of cryptographic operations-encryption, decryption, and key management-introduces latency and resource constraints that can destabilize a control loop if not addressed. Researchers are exploring methods to perform these matrix operations directly within the encrypted domain, or to optimize the control algorithms to minimize the number of computations required while maintaining stability. This often involves redesigning the controller to utilize lightweight cryptographic primitives and tailoring the control law to the specific characteristics of the cryptographic scheme. The goal is to ensure that security measures do not introduce unacceptable performance degradation, and that the system remains controllable and stable despite the added computational burden.

The core innovation lies in a security framework that doesn’t demand a trade-off between privacy and performance within networked control systems. Traditional cryptographic approaches often introduce latency or operational overhead, potentially destabilizing sensitive control loops. However, by strategically integrating cryptographic principles into the system dynamics – rather than layering them on top – this method achieves confidentiality without hindering real-time responsiveness. This is accomplished through carefully designed control algorithms that inherently mask sensitive data during transmission and processing, ensuring that the system continues to operate predictably and reliably even under adversarial conditions. The result is a robust architecture where security becomes an integral, seamless component of the control process itself, rather than an impediment to it.

The fusion of cryptography and system dynamics yields a notably robust defense against a spectrum of cyber threats, encompassing both disruptive active attacks and stealthy passive reconnaissance. Rigorous testing demonstrates this integrated strategy achieves exceptionally high accuracy in attack detection; specifically, simulations reveal over 99.99% accuracy is attainable when employing a parameter setting of λ = 16. Even under more conservative conditions, with λ = 4, the system consistently surpasses 99% accuracy, signifying a substantial improvement in system security and operational stability. This heightened resilience isn’t merely preventative; the system’s capacity to swiftly and reliably identify malicious activity minimizes potential damage and ensures continued, trustworthy operation of the networked control system.

The pursuit of secure control systems, as detailed in this work regarding encrypted controllers and covert attacks, demands more than simply ‘making it work.’ The paper’s innovative verifiable computation scheme, offering zero-overhead integrity verification, resonates with a sentiment expressed by Brian Kernighan: “Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it.” This applies directly to security protocols; complex encryption, while appearing robust, can mask underlying vulnerabilities. true resilience, as the study demonstrates, comes not from obfuscation, but from provable correctness and transparent integrity – revealing the invariant, rather than relying on the illusion of security.

Future Directions

The demonstrated susceptibility of homomorphically encrypted control systems to even subtly crafted covert attacks casts a long shadow. It is not sufficient to merely encrypt a control loop; integrity, the demonstrable correctness of computation, remains paramount. The presented zero-overhead verifiable computation scheme offers a potential, if preliminary, solution. However, its scalability to truly complex, high-dimensional control systems-those beyond the illustrative examples-remains an open question, and a rigorous asymptotic analysis is demanded.

Future work must address the inherent trade-offs between computational burden and demonstrable security. The current focus on purely additive noise models within homomorphic encryption feels… optimistic. Real-world actuators and sensors are plagued by non-Gaussian disturbances, and a robust solution will necessitate a deeper engagement with stochastic control theory and the limits of verifiable computation in noisy environments. A truly elegant solution will not simply detect attacks, but mathematically preclude their possibility.

Ultimately, the pursuit of secure control systems is not an engineering problem alone. It is a question of mathematical certainty. The field must move beyond empirical validation and embrace formal methods, striving for provably secure control algorithms. Only then can one confidently claim a system is not merely ‘working on tests’, but fundamentally resistant to malicious manipulation.

Original article: https://arxiv.org/pdf/2605.14230.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-05-16 06:18