Verifying Hardware Secrets: A Zero-Knowledge Approach

Author: Denis Avetisyan

New research demonstrates how zero-knowledge proofs can establish trust in hardware components without revealing sensitive design details.

This review explores the application of zero-knowledge proofs and formal verification to address hardware supply chain security concerns and detect malicious IP cores.

Increasing reliance on third-party intellectual property in integrated circuits introduces significant security vulnerabilities, yet verifying this IP without revealing proprietary designs presents a critical challenge. This paper, ‘Proving Circuit Functional Equivalence in Zero Knowledge’, introduces ZK-CEC, the first framework to formally verify hardware correctness and security in zero knowledge by combining formal verification with zero-knowledge proofs. ZK-CEC establishes a blueprint for proving the functional alignment of a secret IP with a public specification, preventing malicious forgery while preserving confidentiality. Will this approach pave the way for a more secure and trustworthy hardware supply chain, free from the threat of hidden vulnerabilities?

The Erosion of Trust in Modern Hardware

The modern System-on-Chip (SoC) represents a pinnacle of engineering efficiency, integrating numerous functions onto a single silicon die. However, this very efficiency introduces substantial security risks due to the increasingly complex and geographically dispersed supply chain required for their creation. SoCs rarely originate from a single source; instead, designs frequently incorporate intellectual property (IP) cores from various third-party vendors, fabrication occurs in specialized foundries, and assembly/testing is often outsourced. This fragmentation creates multiple opportunities for malicious actors to insert Hardware Trojans – subtle, intentionally-engineered vulnerabilities – at any stage of the process. These Trojans can remain dormant for extended periods, allowing compromised devices to proliferate before their malicious functionality is triggered, potentially enabling data theft, system disruption, or even complete device control. The inherent lack of transparency and rigorous verification across these multiple layers of the supply chain makes detecting these threats exceptionally challenging, representing a growing crisis in hardware trust.

As System-on-Chip (SoC) designs surge in complexity – incorporating billions of transistors and vast amounts of intellectual property – traditional hardware verification methodologies are increasingly strained. These established techniques, often reliant on exhaustive simulation and formal analysis, struggle to keep pace with the exponential growth in design size and intricacy. Consequently, comprehensive testing becomes impractical, creating blind spots where subtle, yet potentially devastating, security flaws – including Hardware Trojans – can remain undetected. This scalability challenge isn’t merely a matter of computational resources; it’s a fundamental limitation of approaches designed for simpler architectures. The result is a growing risk that even seemingly secure chips may harbor vulnerabilities exploitable long after deployment, underscoring the urgent need for innovative verification strategies capable of addressing modern SoC complexity.

The proliferation of intellectual property (IP) piracy within the semiconductor industry significantly amplifies the potential for hardware vulnerabilities. As System-on-Chip designs increasingly rely on third-party IP cores to reduce development time and cost, the sourcing of these components from untrusted or unverified providers introduces substantial risk. These pirated cores may contain deliberately inserted malicious logic – known as Hardware Trojans – or simply harbor undocumented, unintended flaws. Detecting these compromises is exceptionally difficult, as the internal workings of these externally sourced blocks are often obscured from the design team, and traditional verification techniques struggle to thoroughly analyze such complex, pre-fabricated components. This reliance on potentially compromised IP effectively widens the attack surface and creates a critical challenge for ensuring the trustworthiness of modern electronic systems.

Formal Verification: A Foundation of Immutable Trust

Hardware formal verification establishes correctness through the use of mathematical proofs, differing fundamentally from simulation-based verification which relies on testing a finite number of scenarios. Simulation, while valuable for identifying functional errors, cannot guarantee the absence of all errors due to its inherent limitation to the tested stimulus. Formal methods, conversely, exhaustively explore all possible input combinations within the defined design constraints, proving or disproving functional properties. This exhaustive analysis provides a definitive statement about the design’s correctness, offering a higher degree of confidence than simulation, particularly in safety-critical applications where even a single undetected error can have significant consequences. The mathematical rigor of formal verification provides a guarantee that the implemented hardware behaves precisely as specified by its intended design.

Combinational Equivalence Checking (CEC) establishes functional correctness by comparing a design’s output to a golden reference model. This is achieved through the creation of a Miter Circuit, which merges the design under test and the reference model, adding an XOR gate at each output to detect any discrepancies. The resulting circuit is then subjected to formal proof techniques, typically using a SAT solver, to determine if any input combination can cause the XOR gates to assert – indicating a mismatch. If the SAT solver determines the Miter Circuit is ‘UNSAT’, it proves that the design and golden model produce identical outputs for all possible inputs, thereby verifying functional equivalence. CEC is particularly effective for verifying complex digital circuits and identifying subtle bugs that may be missed by simulation.

The conclusive result of formal verification is a determination of ‘UNSAT’ – an assertion of unsatisfiability. This signifies that, after exhaustive mathematical analysis, no input can expose a discrepancy between the implemented design and its reference, or ‘golden’, model. Achieving ‘UNSAT’ confirms the functional equivalence of the two circuits under all possible conditions, providing a rigorous guarantee of correctness. This contrasts with simulation-based verification, which can only identify errors for the specific test cases executed. The ‘UNSAT’ result is not merely a probability; it is a definitive proof, mathematically demonstrating the impossibility of finding a difference between the design and its golden model, thus establishing a high level of confidence in the design’s reliability and security.

Formal verification builds upon Combinational Equivalence Checking by incorporating techniques like Sequential Equivalence Checking, which addresses stateful behavior and timing constraints not covered by purely combinational analysis. This allows for the identification of subtle bugs such as race conditions and deadlocks. Furthermore, formal methods facilitate security assessments by enabling the rigorous proof of properties like memory safety and the absence of exploitable vulnerabilities, going beyond functional correctness to establish trust in the system’s resilience against malicious attacks. The application of formal verification extends to broader analysis, including coverage metrics based on reachability and the automated generation of test cases that maximize fault detection, thereby enhancing the overall quality and reliability of hardware designs.

Preserving Design Integrity: Privacy-Preserving Verification

Zero-Knowledge Proofs (ZKPs) are a cryptographic method enabling verification of a statement’s truth without disclosing any information beyond the validity of the statement itself. In the context of hardware intellectual property (IP) verification, ZKPs allow a prover – the IP designer – to demonstrate to a verifier – a potential customer or third-party auditor – that the design functions correctly according to specified criteria, without revealing the design’s internal architecture or implementation details. This is achieved through a challenge-response protocol where the prover constructs a proof based on the design and its expected behavior, and the verifier validates this proof without needing to understand the design’s intricacies. The security of ZKPs relies on complex mathematical problems, ensuring that even with access to the proof, the verifier gains no insight into the underlying IP beyond its functional correctness. This is particularly crucial for protecting sensitive designs and maintaining a competitive advantage.

The Zero-Knowledge Virtual Machine (ZKVM) functions as an execution environment specifically designed for hardware designs encoded as circuits. This allows for the creation of a verifiable simulation where the execution of the design can be proven correct without revealing the design itself. The ZKVM translates the hardware description into a series of computational steps, which are then expressed as an arithmetic circuit. A proof is generated demonstrating the correct execution of this circuit, and this proof, significantly smaller than the original design, can be publicly verified. This capability enables remote or third-party verification of complex designs without requiring access to the sensitive intellectual property, and is foundational for building trust in hardware supply chains.

Homomorphic Encryption (HE) allows computation to be performed on encrypted data without requiring decryption, thereby enabling secure outsourcing of simulation tasks. In the context of hardware verification, HE facilitates sending an encrypted design and test vectors to a third-party for simulation; the simulator processes the encrypted data and returns encrypted results. These results remain encrypted throughout the entire process, protecting the intellectual property contained within the design and the sensitivity of the test data. This capability strengthens the verification pipeline by allowing resource-constrained entities to leverage external computational power without compromising data confidentiality, and reduces the risk of intellectual property theft or reverse engineering.

Hardware Supply Chain Security is significantly improved through the combined application of Zero-Knowledge Proofs, the Zero-Knowledge Virtual Machine, and Homomorphic Encryption. These technologies allow for the verification of intellectual property correctness by third parties – such as foundries or verification services – without requiring access to the underlying design data. This approach mitigates risks associated with IP leakage during manufacturing or validation processes. By enabling verification of function without revealing implementation, these methods establish a trust mechanism that assures stakeholders of design integrity while simultaneously protecting sensitive intellectual property from unauthorized access or replication.

Toward Resilient Hardware: A Future Built on Trust

The escalating complexity of modern hardware demands a shift towards provable security, and this is increasingly achieved through the synergistic application of formal verification and privacy-preserving techniques. Formal verification employs rigorous mathematical methods to definitively prove the correctness of a hardware design, eliminating vulnerabilities that traditional testing might miss. However, verifying functionality alone isn’t sufficient; designs must also protect sensitive data processed within the hardware. Privacy-preserving techniques, such as differential privacy and homomorphic encryption, are therefore integrated into the verification process to ensure data confidentiality even during operation and analysis. This combined approach not only bolsters defenses against malicious attacks, including hardware Trojans and data breaches, but also establishes a foundation of trust vital for the widespread adoption of secure computing in critical infrastructure, consumer electronics, and emerging technologies.

The integrity of modern hardware is increasingly threatened by the insidious presence of Hardware Trojans and the pervasive risk of intellectual property (IP) piracy. These malicious alterations, injected during design or manufacturing, can compromise functionality, exfiltrate sensitive data, or create backdoors in critical systems – from national infrastructure like power grids and communication networks to everyday consumer electronics. Protecting against these threats isn’t simply a matter of cybersecurity; it’s about ensuring the fundamental trustworthiness of the devices that underpin modern life. Sophisticated verification techniques and robust IP protection strategies are therefore vital, demanding a shift towards proactive security measures that detect and mitigate these vulnerabilities before they can be exploited, safeguarding both economic interests and public safety.

A secure hardware supply chain is increasingly vital, extending far beyond simple product integrity to encompass national security and economic stability. Compromises within this chain – be they counterfeit components, maliciously inserted hardware Trojans, or intellectual property theft – can cripple critical infrastructure, including power grids, communication networks, and defense systems. The economic ramifications are equally substantial; IP theft erodes innovation, reduces competitiveness, and leads to significant financial losses for businesses. Fortifying the supply chain requires a multi-faceted approach, including rigorous vendor vetting, enhanced traceability of components, advanced authentication techniques, and international collaboration to establish common security standards. Ultimately, a resilient hardware ecosystem, built on a foundation of supply chain security, is not merely a technological imperative, but a cornerstone of modern societal and economic wellbeing.

A shift towards proactively securing hardware-through techniques like formal verification and strengthened supply chains-is poised to unlock a new era of innovation. By addressing vulnerabilities before they manifest as security breaches or intellectual property theft, developers gain the confidence to explore increasingly complex and sophisticated designs. This, in turn, accelerates the development of resilient hardware solutions capable of withstanding evolving threats and supporting emerging technologies. The resulting trust in hardware integrity will not only safeguard critical infrastructure and consumer devices, but also foster a more dynamic and competitive landscape where innovation is prioritized and long-term sustainability is ensured, ultimately benefiting both economic growth and national security.

The pursuit of hardware security, as detailed in the exploration of zero-knowledge proofs, mirrors a dedication to essential truths. It prioritizes establishing functional equivalence-a core concept within the study-without unnecessary disclosure. This aligns with the sentiment expressed by Paul Erdős: “A mathematician knows a lot of things, but a good mathematician knows what is important.” The paper’s methodology embodies this principle; it distills verification down to its critical elements-proof of functionality-removing superfluous information to ensure trust in increasingly complex hardware supply chains. The elegance lies not in revealing the design, but in proving its integrity.

What Remains?

The pursuit of demonstrable trust in hardware, as this work suggests, invariably encounters a fundamental limit. Establishing equivalence, even with the elegance of zero-knowledge proofs, does not address the question of what is equivalent. A formally verified malicious circuit remains, at its core, malicious. The focus shifts, then, not simply to proving correctness, but to defining acceptable behavior. If a function is demonstrably equivalent, yet demonstrably harmful, the proof is merely a sophisticated articulation of the problem.

Future efforts will likely concentrate on narrowing the scope of verification. Complete system verification remains a fantasy; practical applications demand a delineation of critical components. This necessitates a robust methodology for identifying, and subsequently prioritizing, those components most susceptible to compromise. The complexity of full-chip verification, if not entirely avoided, must be systematically reduced. If a circuit’s behavior cannot be succinctly defined, it is not the circuit that is at fault, but the attempted description.

Ultimately, the success of these techniques rests not on mathematical ingenuity, but on pragmatic application. A formally verified supply chain is a secure supply chain only insofar as it is used. The allure of absolute certainty must be resisted. Demonstrable security is not the same as absolute security; it is merely a more precise understanding of the remaining risk.

Original article: https://arxiv.org/pdf/2601.11173.pdf

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

The Erosion of Trust in Modern Hardware

Formal Verification: A Foundation of Immutable Trust

Preserving Design Integrity: Privacy-Preserving Verification

Toward Resilient Hardware: A Future Built on Trust

What Remains?

See also: