Tamper-Proof FLOP Caps

• Tamper-proof FLOP caps are security mechanisms that enforce irreversible, tamper-evident state changes using cryptographic and physical methods.
• In compute governance, they constrain FLOP usage via hardware-embedded counters and digital signatures to support AI safety regimes.
• In pharmaceuticals, flip-off caps integrate one-time authentication secrets with physical break-rings to deter counterfeiting and ensure product verification.

A tamper-proof FLOP cap is a term with domain-specific meanings in both advanced computing infrastructure governance and pharmaceutical anti-counterfeiting. In compute governance, a tamper-proof FLOP cap denotes a hardware-embedded mechanism for cryptographically measuring, constraining, and reporting the accumulated floating-point operations (FLOPs) on a compute device, primarily as an enforcement tool for global AI safety regimes (Ramiah et al., 25 Jun 2025). In pharmaceutical supply security, a tamper-proof flip-off (FLOP) cap refers to a tamper-evident physical closure for vials, integrating one-way destruction with embedded one-time authentication secrets to deter counterfeiting and enable public product verification (Kilcullen, 2015). Both uses share core cryptographic analogies: tamper evidence as a physical hash, and embedded secrets mapped to auditable, public verification workflows.

1. Formal Definitions and Domain Contexts

Compute Governance

A tamper-proof FLOP cap in compute governance is a hardware mechanism that:

• Cryptographically measures and constrains total FLOPs performed by a device or device ensemble,
• Enforces a hard stop or forced slowdown upon reaching a defined FLOP budget $B$,
• Produces verifiable, unforgeable digital receipts of FLOP consumption, serving as the technical foundation for enforcement in global regimes aiming to limit training capacity for potentially hazardous AI systems (Ramiah et al., 25 Jun 2025).

Pharmaceutical Security

A tamper-proof flip-off (FLOP) cap is a vial closure with a physically irreversible, tamper-evident ring and an embedded, concealed one-time password (OTP) revealed only upon first opening. The system leverages physical and cryptographic analogies to deliver strong tamper evidence and online authentication of product origin (Kilcullen, 2015).

2. Technical Architecture and Security Properties

Compute: Secure FLOP Accounting and Enforcement

A tamper-proof FLOP cap for compute comprises:

• Monotonic Counter: Each device $i$ maintains a non-volatile, tamper-evident counter $c_i \in \mathbb{N}$, incremented on every floating-point operation.

  $c_i = \sum_{t=1}^T f_{i,t}$

  where $f_{i,t}$ is the FLOPs performed by device $i$ in schedule slice $t$.

• Global FLOP Cap: Training is halted as soon as

  $C_{\text{total}} = \sum_{i=1}^N c_i \geq B$

• Cryptographically Signed Receipts: Each increment is accompanied by a TPM- or enclave-signed receipt:

  $$r_{i,t} = \mathrm{Sign}_{K_i}(\langle \text{device\_id}=i, \Delta c_i, \text{nonce}_{i,t}, \text{prev\_hash}_{i,t-1}\rangle)$$

  where $K_i$ is the device’s isolated signing key, with hash-chained linkages for tamper-evidence.

• Network Aggregation: Aggregators collect receipts and verify that the cumulative sum does not exceed the budget and all cryptographic proofs are valid.
• Optional Zero-Knowledge Proofs: Devices can prove $c_i \leq B_i$ via ZK-SNARKs without leaking exact usage.

Hardware and Firmware Integration

• TPM/Enclave with Monotonic Counter & Crypto Engine: Secure boot ensures FLOP-monitoring logic cannot be overwritten; the TPM zeroizes credentials on tamper detection.
• Firmware Lockdown: Device only runs vendor-signed images and resists all unauthorized updates.
• Remote Attestation at Cluster Startup: Devices sign attestation over firmware and module identity to a cluster controller before connecting to the network.

Pharmaceutical: Tamper-Evident Physical Security Plus Cryptography

• One-Way Physical Function: The break-ring, once fractured, cannot be restored to “intact.” This models a cryptographically irreversible state change.
• Embedded OTP: A high-entropy one-time secret, never visible without destruction, is embedded inside the cap. Example: 128 bits, NIST CSPRNG-generated, mapped to serialization at production.
• Authentication Flow: End user retrieves the OTP only by breaking the cap. They then submit it to a well-known public verification site (e.g., pharma-auth.org), which cross-checks the code against the manufacturer’s secure database.
• Digital Signature Option: Each OTP can be additionally signed (e.g., ECDSA-P256), enabling cryptographic authenticity checks on client devices.

3. Threat Model and Security Analysis

Compute Domain

Threat	Mechanism	Mitigation
Physical Tampering	Bypass secure counter	Tamper mesh zeroizes keys; epoxy potting; side-channel detectors
Counter Rollback/Reflash	Reset monotonic counter	TPM monotonic counters; anti-rollback fuses; OTP memory
Task Splitting/Fragmentation	Split jobs under caps	Cluster-level aggregation of receipts; cross-device flow logs
Side-Channel Leakage	Extract keys or counters	Electromagnetic shielding; constant-time cryptography; noise injection
License Forgery	Fake license tokens	Asymmetric crypto tokens; short-lived challenge-response tokens

Enforcement relies on both physical (tamper detection) and cryptographic (receipt signatures/attestations) primitives. Full security is contingent on uncompromised hardware root-of-trust and protocol adherence.

Pharmaceutical Domain

Threat	Vector	Mitigation
Cap Resealing	Remove, read, re-glue	Visual inspection, glue residue, micro-text, matte/gloss mismatch
Non-Invasive Code Extraction	X-ray, micro-drilling	Opaque foil liners; physical failure of liner destroys code
OTP Guessing	Brute-force inputs	128-bit code space; lockout after three attempts
Fraudulent Websites	Fake verification URLs	Only a single public URL; signatures prevent off-path validation
Database Exfiltration	OTP list breach	OTPs stored as salted hashes (SHA256)

The design ensures attacks require substantial cost, are easily detected, or are computationally infeasible.

4. Governance, Attestation, and Operation in Compute Infrastructure

GEV Integration (Governance–Enforcement–Verification)

• Governance: International or regional authority sets FLOP budgets $B$, certification norms, and device export rules (e.g., via OECD or G7 AI Council).
• Enforcement: Hardware-level cap activation (auto-shutdown/throttle), licensing with cryptographically bound sub-budgets $B_i$, offline tokens for air-gapped facilities, and restrictiveness via export control.
• Verification: Streamed or batch-signed receipt logs for audit. Challenge on-site inspections of hardware identity, firmware, and receipt chains; Merkle tree or ZK proof options for scalable auditability.

Example Scenarios

• Lab Deployment: Each GPU/TPU, capped at $B=10^{23}$ FLOPs, regularly emits signed receipts. Sub-budgets are allocated via offline tokens tied to device/lab identity. Receipts are aggregated and can be audited externally.
• Export Control: Chips are registered per serial with a compute supply registry. Exported lots are scanned at border; firmware modifications are detectable/fail activation.
• Emergency Pause: A global council decrements all active FLOP caps by a fixed percentage, enforcing a “pause” without software-level intervention.

5. Performance, Scalability, and Deployment Considerations

• Overhead: Additional logic for FLOP counting and cryptographic signing is minimal; <1% cost if receipts are pipelined. Receipts can be batched, reducing bandwidth/incidental latency in HPC contexts.
• Large-Scale Cluster Support: Per-device Merkle trees and hierarchical aggregation allow $O(\log N)$ verification steps; signatures verified in batches.
• Compatibility: Hardware counter integration at instruction decode layer is minimal for new hardware. Existing GPUs/TPUs can be partially secured through firmware updates with software-level counters and signatures, though with weaker tamper-resistance.
• Impact on Training: Memory and key storage footprint is minor. Primary resource constraint arises from cryptographic operation throughput—amortized by batching/epoch alignment.

6. Regulatory and Supply-Chain Integration

• Traceability: Compute supply registry catalogs device serials, firmware hashes, and cryptographic fingerprints. Receipts can be mapped to origin for forensics.
• Licensing: Devices receive sub-budgets, cryptographically bound to verified entities (e.g., KYC-compliant labs). Policy changes, such as a “pause,” are propagated through signed tokens enforceable by hardware on reboot or at relicensing intervals.
• Export Controls: Only certified, FLOP-cap–enabled chips are legally exportable. Production mandates ensure all new compute modules are compliant.
• Model Locking: Once the budget is spent, model weights remain sealed in enclave-attached ciphertext until regulatory release, preventing unauthorized deployment even post-training.

7. Comparative Analogues and Broader Significance

In both compute and pharmaceutical domains, tamper-proof FLOP caps instantiate a physical or logical one-way function (irreversible state transition) paired with an embedded, auditable secret (cryptographically signed receipt/OTP). They effectuate material-layer governance, shifting oversight from post-hoc detection to built-in, independently verifiable controls. This model parallels frameworks from nuclear non-proliferation (irreversible sealing, audit trails) and high-assurance supply chains, reinforcing the thesis that cryptographically enforced tamper-proofing at the substrate layer is essential for scalable, enforceable global safety regimes (Ramiah et al., 25 Jun 2025, Kilcullen, 2015). The efficacy of such a system is bounded by the strength of hardware root-of-trust, enforcement of a shared verification ecosystem, and integration with multi-layer regulatory instruments.