Tamper-proof FLOP Caps for AI Safety

• Tamper-proof FLOP caps are hardware-embedded mechanisms that use irreversible counters and cryptographic techniques to enforce strict FLOP limits.
• They leverage secure enclaves and physical unclonable functions to provide tamper-evidence and verifiable audit trails for compute operations.
• By constraining compute budgets in AI devices, these caps serve as governance tools to mitigate risks associated with hazardous AI model development.

A tamper-proof FLOP cap is a technical and cryptographic mechanism designed to enforce and evidence an upper limit on the number of floating-point operations (FLOPs) that a hardware device, typically an AI accelerator or compute cluster, can execute. The primary purpose is to ensure that even a physically compromised or maliciously controlled system cannot exceed agreed-upon compute ceilings, thereby directly constraining the development of potentially hazardous AI models at the infrastructure level. Recent scholarship explores FLOP caps both as hardware-anchored governance tools in AI safety and as cryptographically verifiable, tamper-evident constructs for high-assurance systems.

1. Foundational Concepts: From Authentication to One-Way Functions

Tamper-proof FLOP caps are conceptually linked to cryptographically inspired tamper-evidence and authentication strategies for manufactured goods (1512.00351). In these models, tamper-evident packaging acts analogously to encryption, with the breaking of a seal serving as an irreversible, one-way function. Embedding a unique secret or one-time password (OTP) within irreversibly destroyed physical seals assures that unauthorized access or duplication is immediately evident and non-recoverable.

For FLOP caps, this analogy translates to "one-way" hardware or firmware transformations: a register or physical state is irreversibly incremented with every floating-point operation, with no feasible pathway to reset or forge the counter undetectably.

2. Technical Mechanisms for Tamper-Proof FLOP Caps

Implementation of a tamper-proof FLOP cap involves a secure, non-resettable counting and enforcement subsystem embedded in hardware, typically within a chip’s secure enclave or a physically unclonable function (PUF)-fortified board supervisor (2506.20530). The basic mechanism proceeds as follows:

• The supervisor tracks the cumulative number of executed FLOPs, incrementing an internal counter per operation.
• Once the pre-set compute limit $F_{\text{max}}$ is reached:
  • The device disables further computation.
  • Alternatively, the system requires hardware-level reauthorization to continue.
• To maximize tamper resistance, the counting logic and state are implemented in sealed modules with zeroization triggers upon physical intrusion, cryptographic auditability, and secure-boot verification of any firmware controlling the cap logic.

A canonical enforcement formula is:

$$\text{If} \quad \sum_{i=1}^{n} F(i) \geq F_{\text{max}} \implies \text{Cease Execution}$$

where $F(i)$ is the FLOP count of operation $i$.

3. Cryptographic and Information-Theoretic Foundations

The security of tamper-proof FLOP caps rests on the irreversibility and unpredictability under tampering or attack. Core strategies include:

• Physical Unclonable Functions (PUFs): High-assurance devices use on-board PUFs—unique, fabrication-induced physical random functions—to store cryptographic keys or secrets. Tampering irreversibly alters the PUF response, breaking key reconstruction and signaling compromise (2502.03221).
• Zero-Leakage Quantization: Information-theoretic analysis demonstrates how device helper data (needed for reliable PUF key extraction) can be generated and utilized without leaking any information about the key. This is formalized as $P_{S^n|W^n}(s^n|w^n) = P_{S^n}(s^n)$, ensuring helper data and key are statistically independent.
• Wiretap Coding: ECC and quantization schemes are constructed according to wiretap channel secrecy theory, so that the legitimate device can reconstruct keys reliably, but any attacker with less than full access (e.g., because of physical destruction) faces an exponential effort for reconstruction.

For example, to achieve 128 bits of security with 3-bit quantization and an 18% erasure rate (i.e., fraction of destroyed PUF cells), at least 459 PUF cells are required (see Table VIII in (2502.03221)).

4. Tamper-Proof FLOP Caps in AI Compute Governance

In AI governance frameworks, tamper-proof FLOP caps are proposed as critical technical levers to prevent the development of AI systems with catastrophic risk potential (2506.20530). Within the Governance–Enforcement–Verification (GEV) architecture, FLOP caps are positioned as the foundational enforcement mechanism:

• Governance: Multilateral authorities define the maximum safe FLOP budgets ($F_{\text{max}}$), updated in response to advances in algorithmic efficiency.
• Enforcement: Device-level logic blocks execution in hardware on exceeding $F_{\text{max}}$, operating independently of user compliance or supervision.
• Verification: Devices issue cryptographically signed audit receipts for all intermediate and final results ($R_{j} = \sum_{k=1}^{m_j} F_{j,k}$), enabling post hoc tracing and audit of actual compute usage.

Integration with traceability (unique IDs, supply chain records) and regulatory controls (licensing, export caps) is necessary to maximize effectiveness and limit circumvention through aggregation or gray-market hardware.

Mechanism	Primary purpose	Tamper-resistance	Implementation difficulty	Downsides
Tamper-proof FLOP Caps	Enforce compute ceilings in hardware	High	Difficult (chip/board redesign)	Task splitting, gray/legacy hardware

5. Tamper-Evident FLOP Caps: Quantum and Advanced Approaches

Beyond classical hardware, research explores information-theoretic tamper evidence using quantum properties and short keys (2006.02476). In these schemes:

• Data or device state is encoded into quantum states interspersed with "trap" qubits.
• Any measurement or disturbance by an adversary trying to read or reset the state is likely to be detected, by virtue of the entropic uncertainty relation $$H_{\min}^\varepsilon(X|E) + H_{\max}^\varepsilon(X'|B) \geq n$$.
• The efficiency of such tamper-evidence is subject to the device’s entropy/randomisability; when secrets or device states cannot be adequately randomised, the tamper-evidence weakens for a fixed key length.

A plausible implication is that future FLOP caps for the highest-assurance domains may combine PUFs and quantum tamper-evidence, with trade-offs in cost, environmental robustness, and system integration.

6. Limitations, Challenges, and Interactions

Tamper-proof FLOP cap deployment faces several technical, practical, and governance challenges:

• Technical Complexity: Retrofitting existing hardware with robust FLOP caps is difficult; chip/board redesign and industry-scale production adaptation may require years.
• Bypass Risks: Distributed task splitting and aggregation of many capped modules can bypass per-chip caps. Mitigation requires integration with networking controls and global device traceability.
• Global Buy-In: The system relies on universal adoption and regulatory enforcement; otherwise, uncapped or legacy hardware may concentrate in unregulated markets.
• Physical Coverage: PUF-based mechanisms only secure the interfaces or circuits physically covered—gaps in hardware design or analog probing capacity may create attack surface for highly capable adversaries.

7. Extensions and Analogies: From Drug Packaging to Compute Governance

Tamper-proof FLOP caps share foundational principles with tamper-evident packaging in pharmaceuticals and anti-counterfeiting measures in currency and luxury goods (1512.00351). In all such systems:

• Security is derived from the irreversibility of a one-way function (breaking a seal, consuming a PUF, incrementing an irreversible counter).
• Authentication leverages secrets revealed only by irreversible physical or cryptographic action, checked via public authentication resources.
• The generalization to compute governance entails embedding such "one-way," auditable limits into hardware, providing game-theoretic deterrence: the cost of circumvention far exceeds the value of unauthorized compute.

In summary, tamper-proof FLOP caps operationalize hardware-based, cryptographically evidenced ceilings on fundamental computational capability. They represent a convergence of physical, cryptographic, and information-theoretic tamper-resistance, serving both as practical anti-counterfeiting mechanisms and as core governance tools for AI safety and secure infrastructure. The ongoing evolution of their technical and policy implementation is central to emerging debates on high-assurance system design and the governance of advanced computation.