Programmatic Procurement Verification APIs & Zero-Knowledge Attestations for Industrial Machinery

J. McKenney

This paper is part of the WG-10-AN Assurance Network body of work, building a zero-knowledge attestation layer on top of the CycloneDX multi-BOM graph established in WG-10-AN-07-Omnipresent-BOM-CycloneDX-Assurance. It sits alongside WG-10-AN-09-Distributed-ZK-Attestation-Clean-Energy, which applies the same zero-knowledge attestation approach to distributed clean-energy assets rather than centrally procured industrial machinery.

Licence: CC BY 4.0. 17 September 2026.

Executive Abstract#

New regulations require buyers of industrial machinery, such as turbines, substations, and control systems, to see proof that the equipment's supply chain is secure. The manufacturers who build that equipment cannot hand over a full parts list, because it would expose proprietary designs and trade secrets to competitors and hostile states. Regulators want transparency, manufacturers need confidentiality, and until now neither side could get both.

This paper resolves the standoff with zero-knowledge cryptography, which lets one party prove a statement is true without revealing the information behind it. A manufacturer's confidential parts list becomes a cryptographic proof that the equipment meets a specific security requirement, such as having no unpatched vulnerability above a given severity, without disclosing which components are inside. The proof stays valid as new vulnerabilities are discovered later.

It closes with a verification system fast enough to sit inside an automated factory commissioning process, so a buyer's system can check a manufacturer's proof and clear equipment for use in a fraction of a second. Benchmark results come from a real gas turbine governor case study.

Abstract#

Industrial machinery and sovereign infrastructure procurement face a regulatory and security paradox. The EU Cyber Resilience Act (Regulation 2024/2847, Modules B, C, and H), NIS2, and US Executive Order 14028 mandate multi-tier Bills of Materials, yet manufacturers cannot disclose raw software and hardware dependencies without forfeiting intellectual property, firmware topologies, and architectural trade secrets to competitors and state-sponsored adversaries. We present a zero-knowledge supply chain attestation architecture. Arithmetic verification circuits over the BN254 elliptic curve accept an OWASP CycloneDX 1.6+ multi-BOM directed acyclic graph as a private witness W, proving in zero-knowledge that the target machinery satisfies statutory security predicates x, among them zero unmitigated vulnerabilities above a CVSS threshold theta_crit, certified cryptographic suites, and authorized hardware silicon roots of trust, without revealing component names, versions, or dependencies. Poseidon leaf commitments and a Plookup range argument keep circuit costs low. To absorb later vulnerability disclosures and certificate revocations without reissuing proofs, we design an append-only Merkle Mountain Range (MMR) revocation registry with non-membership accumulators. A programmatic procurement API (/api/v1/attestation/verify) delivers sub-12 millisecond proof validation, integrating attestation into automated factory commissioning interlocks and sovereign infrastructure clearance gateways.

1. The Procurement Assurance Paradox in Sovereign Critical Infrastructure#

The architecture below shows how a vendor's confidential multi-BOM graph is compiled into an arithmetic circuit, proved in zero-knowledge, and checked by a sovereign procurement gateway before an automated commissioning interlock releases the equipment.

Procurement of critical industrial control machinery, including gas and steam turbine governors, high-voltage substations, Distributed Control Systems (DCS), and reactor safety interlocks, has historically operated on blind institutional trust and static paperwork certifications. The enactment of the European Union Cyber Resilience Act (Regulation EU 2024/2847) fundamentally dismantles this paradigm. Under CRA Article 32 and Annex VIII, products with digital elements must undergo rigorous third-party or automated conformity assessments. Manufacturers must maintain an exhaustive Software Bill of Materials (SBOM) and Hardware Bill of Materials (HBOM), provide rapid vulnerability remediations, and prove continuous supply chain integrity across all lifecycle phases.

However, full disclosure of machine bills of materials introduces catastrophic operational and intellectual property hazards:

1. Trade Secret and Microarchitecture Exposure: Industrial original equipment manufacturers (OEMs) embed decades of proprietary engineering into firmware routines, register mappings, real-time scheduler optimizations, and custom application-specific integrated circuits (ASICs). Publishing raw CycloneDX bills of materials reveals exact third-party RTOS kernels, memory management wrappers, and bespoke silicon configurations, granting competitors zero-cost architectural blueprints.
2. Asymmetric Reconnaissance for Threat Actors: Disclosing an exhaustive inventory of firmware libraries, compiler build flags, and microcode versions provides advanced persistent threats (APTs) with an optimized attack map. Attackers can cross-reference niche, unpatched subcomponents to orchestrate kinetic disruptions against power grids and chemical processing plants without conducting active network scanning.
3. Multi-Tier Sub-Supplier Resistance: Tier-1 automation integrators aggregate subsystems from hundreds of sub-tier component vendors. These sub-suppliers routinely refuse to share internal component manifests due to non-disclosure agreements, rendering full-chain manual SBOM assembly legally infeasible.

To resolve this conflict, the Eigenia Product Assurance Network formalizes the Zero-Knowledge Procurement Relation $\mathcal{R}$.

Let the private witness $W$ represent the complete, confidential supply chain state held by the manufacturer:

where $G_{\text{BOM}} = (V, E)$ is the directed acyclic graph of all hardware, software, operations, and cryptographic components; $\mathbf{V}_{\text{VEX}}$ is the set of machine-readable vulnerability exploitability assertions; $\mathbf{K}_{\text{keys}}$ is the manufacturer's internal signing key hierarchy; and $\boldsymbol{\sigma}_{\text{sig}}$ represents sub-tier cryptographic signatures.

Let the public statement $x$ represent the buyer's statutory procurement policy:

where $\mathbf{H}_{\text{root}} \in \mathbb{F}_p$ is the public Poseidon root commitment of the top-level machine manifest; $\theta_{\text{crit}} \in \mathbb{R}_{\ge 0}$ is the maximum permissible CVSS severity score for unmitigated flaws; $\mathcal{A}_{\text{crypto}}$ is the set of authorized post-quantum or suite-B cryptographic identifiers; $\mathcal{T}_{\text{timestamp}}$ is the verification epoch; and $\mathbf{R}_{\text{MMR}}$ is the root of the active Merkle Mountain Range revocation registry.

The zero-knowledge attestation system guarantees that the manufacturer generates a succinct cryptographic proof $\pi$ proving knowledge of $W$ satisfying:

The proof $\pi$ achieves zero-knowledge: an auditor, procurement officer, or automated factory gateway learns nothing about $W$ beyond the singular boolean fact that $(x, W) \in \mathcal{R}$.

2. Mathematical Foundation#

zk-SNARK Arithmetic Circuits for Multi-BOM Graphs

To execute zero-knowledge proofs over CycloneDX 1.6+ structures, the dependency graph and associated vulnerability metrics are arithmetized into Rank-1 Constraint Systems (R1CS) and Plonkish gates over a pairing-friendly elliptic curve scalar field $\mathbb{F}_p$. We use the BN254 curve (alt_bn128), defined by:

with prime order:

and base field size $q$ where $q \approx 2^{254}$.

2.1 Algebraic Poseidon Hashing of Component Tuples#

Traditional cryptographic hash functions such as SHA-256 or BLAKE3 incur prohibitive arithmetic circuit costs (approximately 25,000 to 45,000 R1CS constraints per 64-byte block) due to bitwise boolean rotations. In contrast, the Poseidon hash function operates directly over $\mathbb{F}_p$ using full and partial S-box rounds $x^\alpha$ (with $\alpha = 5$), requiring fewer than 240 constraints for a 2-to-1 compression.

Every component $v_i \in V$ within the CycloneDX 1.6+ BOM graph is mapped to an algebraic leaf state vector $\mathbf{s}_i \in \mathbb{F}_p^5$:

where $h_{\text{purl}}$ is the field hash of the package URL string, $h_{\text{version}}$ is the canonical semantic version digest, $s_{\text{CVSS}} \in [0, 100]$ represents the scaled maximum known CVSS score ($10 \times \text{Score}$), $c_{\text{license}}$ is the SPDX numerical license identifier, and $k_{\text{vendor}}$ is the vendor's registered public key scalar.

The leaf commitment $L_i$ is computed via Poseidon hash permutation $\Pi_{\text{pos}}$:

2.2 Arithmetized Graph Traversal and Structural Integrity#

To verify the topology of $G_{\text{BOM}}$ without disclosing sub-assembly relationships, the circuit implements an arithmetized Merkle-DAG proof. Let parent component $P$ possess $m$ child dependencies $\{C_1, C_2, \dots, C_m\}$. The parent node commitment $L_P$ is constrained in R1CS by enforcing:

For every edge $(u, v) \in E$, the circuit verifies non-circularity and topological ordering by assigning an integer topological rank $\tau: V \to \{1, \dots, |V|\}$ proven via strictly positive scalar differences:

where $b_j$ represents the binary bit decomposition enforcing that $\Delta_{\tau} \ge 0$, mathematically preventing recursive cycles or topological spoofing.

2.3 Plookup Range Check for Vulnerability Upper Bounds#

To satisfy the statutory requirement that no unmitigated vulnerability exceeds threshold $\theta_{\text{crit}}$ ($s_{\text{crit}} = 10 \times \theta_{\text{crit}}$), every component leaf must prove that:

Instead of expensive bit-decomposition range proofs across all components, our circuit deploys a Plookup lookup argument. Let table $\mathbf{T}$ be pre-populated with admissible scaled integers:

The circuit proves that the multiset of all component scores $\mathbf{S} = \{ s_{\text{CVSS}, 1}, s_{\text{CVSS}, 2}, \dots, s_{\text{CVSS}, |V|} \}$ is completely contained within $\mathbf{T}$:

Using randomized Grand Product polynomials over evaluation domains $\Omega$, the lookup constraint requires only 2 to 3 constraint rows per component, reducing prover overhead by $84\%$ relative to naive bitwise R1CS comparators.

3. Merkle Mountain Range (MMR) & Append-Only Dynamic Revocation#

Static zero-knowledge attestations suffer from temporal decay: a turbine control module proven compliant on day zero may have a catastrophic critical zero-day vulnerability disclosed on day twelve. Re-executing an end-to-end multi-tier SNARK proof across thousands of components on every vulnerability advisory is computationally unviable for embedded industrial suppliers.

We resolve this operational challenge by pairing static circuit proofs with an Append-Only Merkle Mountain Range (MMR) Revocation Registry.

3.1 MMR Structural Properties#

An MMR is an append-only binary tree collection characterized by strictly logarithmic peaks. Let $N$ be the total number of leaves representing revoked component digests or invalidated certificate serials. The binary representation of $N$:

uniquely defines the active peaks. The global MMR commitment $R_{\text{MMR}}$ is defined by hashing the active peak array:

Appending a new revocation leaf requires exactly $\nu(N)$ hash evaluations, where $\nu(N)$ is the number of trailing ones in the binary representation of $N$. The append operation exhibits an amortized computational complexity of $\mathcal{O}(1)$ and worst-case complexity of $\mathcal{O}(\log N)$.

3.2 Cryptographic Non-Membership Proofs#

During the procurement gateway check, the vendor provides an attestation proof $\pi_{\text{static}}$ generated against BOM commitment $\mathbf{H}_{\text{root}}$. To verify that no component $v_i \in V$ has been revoked in the active MMR accumulator $R_{\text{MMR}}$, the vendor issues a lightweight non-membership proof $\pi_{\text{fresh}}$.

Let the revocation registry maintain a sorted sparse array of revoked leaf hashes $\mathbf{R} = \{ r_1, r_2, \dots, r_K \}$ such that $r_1 < r_2 < \dots < r_K$. To prove that a valid component hash $h_i \notin \mathbf{R}$, the prover demonstrates the existence of two adjacent entries $(r_j, r_{j+1})$ within the MMR satisfying:

The non-membership circuit verifies:

1. Inclusion of $r_j$ and $r_{j+1}$ in the MMR root $R_{\text{MMR}}$ via standard $\mathcal{O}(\log N)$ Merkle authentication paths.
2. The strict monotonic range check $r_{j+1} - r_j - 1 \ge 0$.
3. The lower bound $h_i - r_j - 1 \ge 0$.
4. The upper bound $r_{j+1} - h_i - 1 \ge 0$.

By bundling these non-membership verifications into a succinct recursive SNARK (using the Nova folding scheme or Groth16 aggregation), the operational gateway validates dynamic supply chain freshness in less than $2.4\text{ ms}$, entirely offline and decoupled from cloud telemetry.

4. Programmatic API Specification & Verification Pipeline#

The interface between industrial machinery vendors and sovereign procurement entities is codified via programmatic REST and JSON-RPC APIs. The procurement gateway runs as a high-integrity, air-gappable daemon deployed at Purdue Model Levels 3 and 4, directly fronting physical plant commissioning networks.

4.1 REST Endpoint: /api/v1/attestation/verify#

The primary ingestion endpoint receives the cryptographic proof, public inputs, and metadata assertions.

Request Schema (POST /api/v1/attestation/verify)#

{
  "$schema": "https://eigenia.org/schemas/v1/attestation-verify-request.json",
  "procurementContext": {
    "assetId": "UR-GT-GOV-0402",
    "contractRef": "EU-TEN-E-2026-8812",
    "requiredPolicy": {
      "maxCvssThreshold": 0.0,
      "allowedCryptoSuites": ["ML-KEM-768", "ML-DSA-65", "AES-256-GCM"],
      "enforceHardwareRootOfTrust": true,
      "targetCraAnnex": "MODULE_H"
    }
  },
  "publicInputs": {
    "rootManifestCommitment": "0x19a4e872c3d5269bb0d176ea39f50e827183e294b05781a7b036982041865758",
    "mmrRoot": "0x0df294b81c4e126a87bb51f22e89d6174a817b3901bcf52e468201739f40821e",
    "verificationEpoch": 1789344000,
    "maxCvssScaled": 0
  },
  "proof": {
    "protocol": "groth16",
    "curve": "bn254",
    "pi_a": [
      "0x24d29b15809ef812e9b0849204859a8c7b8493012847d92847c92847d92847c9",
      "0x1847c82947192847d92847192847d92847c82947192847d92847192847d92847"
    ],
    "pi_b": [
      [
        "0x0948c82947192847d92847192847d92847c82947192847d92847192847d92847",
        "0x1847d92847c92847d92847c92847d92847c92847d92847c92847d92847c92847"
      ],
      [
        "0x2947c82947192847d92847192847d92847c82947192847d92847192847d92847",
        "0x3847d92847c92847d92847c92847d92847c92847d92847c92847d92847c92847"
      ]
    ],
    "pi_c": [
      "0x1f48c82947192847d92847192847d92847c82947192847d92847192847d92847",
      "0x0a47d92847c92847d92847c92847d92847c92847d92847c92847d92847c92847"
    ]
  }
}

Response Schema (200 OK)#

{
  "verificationResult": "PASS",
  "receipt": {
    "attestationId": "ATT-BN254-20260914-88419",
    "verifiedAt": "2026-09-14T03:12:44.821Z",
    "executionTimeMs": 3.48,
    "pairingEvaluations": 3,
    "constraintsVerified": 248912,
    "revocationCheck": {
      "registry": "MMR_SOVEREIGN_ROOT_08",
      "status": "CLEAR",
      "revokedEntriesEvaluated": 18490
    },
    "clearanceAuthorization": {
      "status": "APPROVED",
      "token": "eyJhbGciOiJFUzM4NCIsInR5cCI6IkpXVCJ9.e30.signature_blob",
      "gooseInterlockRelease": true,
      "validUntilEpoch": 1789430400
    }
  }
}

4.2 Mathematical Pairing Verification Implementation#

The Groth16 verifier checks the fundamental pairing equation over BN254:

where $e: G_1 \times G_2 \to G_T$ is the optimal Ate pairing, $\alpha, \beta, \gamma, \delta$ are toxic-waste points from the trusted setup (or universal powers-of-tau ceremony), and $x_i \in \mathbb{F}_p$ are the public inputs.

Using projective coordinate arithmetic and precomputed Miller loops, this check is executed in exactly 3 Ate pairings and $\ell$ scalar multiplications in $G_1$, yielding a deterministic execution latency under $4.0\text{ ms}$ on standard server x86-64 hardware without hardware acceleration.

5. Empirical Benchmarks & Industrial Case Study#

To quantify the performance, scalability, and physical feasibility of zero-knowledge procurement verification, the Eigenia Product Assurance Network conducted comprehensive empirical benchmarking on a full-scale industrial control target: a Combined-Cycle Gas Turbine Governor Controller (Mark VIe / ABB 800xA class).

5.1 System Profile#

The target system comprises:

• HBOM: 128 discrete silicon elements (Host CPU, BMC, FPGA coprocessors, secure enclave, PHY transceivers, isolated I/O modules).
• SBOM: 1,424 software packages, real-time operating system kernel modules, networking stacks (lwIP, OPC UA stack, Modbus/TCP), and control logic binaries across 4 supply tiers.
• CBOM: 68 cryptographic algorithms, certificate chains, and key agreements.
• OBOM: 222 network conduits, Purdue level firewall parameters, and container configuration manifests.
• Total Graph Size: $|V| = 1{,}842$ nodes, $|E| = 3{,}914$ dependency edges.
• Vulnerability Baseline: 8 known historic vulnerabilities evaluated against VEX mitigation status (all mitigated or compensated via network isolation).

5.2 Comparative Prover and Verifier Metrics#

We benchmarked three zero-knowledge proof architectures: Groth16 (BN254), Plonk with KZG commitments (BN254), and a transparent STARK baseline (using Winterfell / Blake3). Benchmarks were executed on an AMD EPYC 9654 (96 cores, 3.7 GHz) for the vendor prover, and an Intel Xeon E-2388G (8 cores, 3.2 GHz) representing the on-premise industrial gateway verification proxy.

As demonstrated in the empirical results, Groth16 over BN254 achieves superior operational performance for real-time factory procurement gates: a minuscule 128-byte proof payload and a deterministic $3.48\text{ ms}$ verification time, well within the $15\text{ ms}$ industrial interlock SLA. While STARKs offer post-quantum security, their $142.6\text{ kB}$ proof size and $24.8\text{ ms}$ verification latency introduce friction on bandwidth-constrained substation conduits. Consequently, the Eigenia architecture deploys Groth16 for immediate 2026 to 2032 CRA enforcement, while maintaining recursive STARK-to-SNARK wrappers as an updatable cryptographic roadmap.

5.3 Automated SCADA Commissioning Interlock Integration#

The verification gateway interfaces directly with substation automation over IEC 61850 Generic Object Oriented Substation Events (GOOSE) and OPC Unified Architecture (OPC UA).

When a new turbine control module is connected to the commissioning bay:

1. The management switch isolates the unit on Quarantine VLAN 666.
2. The module presents its hardware identity (TPM 2.0 DICE quote) and zero-knowledge attestation payload to the local procurement proxy.
3. The proxy verifies the Groth16 proof against the active MMR revocation registry in $3.48\text{ ms}$.
4. Upon successful verification, the proxy issues an authenticated IEC 61850 GOOSE multicast message (InterlockRelease = TRUE) signed with the gateway's localized private key.
5. The programmable managed switch dynamically shifts the port to Operational Bus VLAN 100, enabling turbine synchronization.

If the proof fails, or if an unmitigated vulnerability exceeding $\theta_{\text{crit}}$ exists, the switch preserves the quarantine state, triggers an emergency supervisory alarm, and logs the cryptographic failure to the tamper-evident audit ledger.

6. Harmonised Standards, CRA Compliance Auditing & Future Trajectory#

The zero-knowledge procurement verification architecture aligns directly with emerging international cybersecurity mandates and technical harmonization bodies:

1. EU Cyber Resilience Act (Regulation 2024/2847):
   • Article 13(8); Annex I Part II (1): Continuous vulnerability handling and SBOM maintenance. By attesting zero-knowledge adherence to CycloneDX 1.6+ multi-BOM invariants, vendors satisfy compliance without forfeiting trade secrets.
   • Module B (EU-Type Examination) & Module H (Full Quality Assurance): Notified Bodies inspect the public arithmetic circuit specifications and trusted setup ceremonies, approving the circuit as a certified conformity mechanism.
2. CEN/CENELEC JTC 13 & ETSI EN 303 645:
   • Technical standards under development for CRA harmonization recognize mathematical zero-knowledge proofs as valid technical documentation under protective confidentiality provisions.
3. Purdue Model & IEC 62443 Part 4-1 / 4-2:
   • The air-gappable architecture allows utilities to operate procurement verification nodes inside Level 3 operations control networks without outbound internet connectivity, validating MMR revocation increments across unidirectional hardware data diodes.

Conclusion#

The programmatic procurement verification API and zero-knowledge attestation architecture developed by J. McKenney and the Eigenia Product Assurance Network proves that supply chain transparency and commercial confidentiality are not mutually exclusive. By encoding CycloneDX 1.6+ multi-BOM invariants into arithmetic circuits over BN254, industrial asset owners obtain mathematical certainty of safety, regulatory compliance, and vulnerability hygiene, while manufacturers preserve their hard-won intellectual property. This methodology establishes a scalable, automated foundation for sovereign infrastructure integrity across the next generation of industrial cyber-physical systems.

7. References#

1. Ben-Sasson, E., Chiesa, A., Tromer, E., & Virza, M. (2014). Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture. Proceedings of the 23rd USENIX Security Symposium, 781-796.
2. Groth, J. (2016). On the Size of Pairing-Based Non-interactive Arguments. Advances in Cryptology: EUROCRYPT 2016, Lecture Notes in Computer Science, 9666, 305-326.
3. Gabizon, A., Williamson, Z. J., & Ciobotaru, O. (2019). PLONK: Permutations over Lagrange-bases for Oecumenical Non-interactive arguments of Knowledge. IACR Cryptology ePrint Archive, Report 2019/953.
4. Crosby, S. A., & Wallach, D. S. (2009). Efficient Data Structures for Tamper-Evident Logging. Proceedings of the 18th USENIX Security Symposium, 317-334.
5. European Parliament and Council of the European Union. (2024). Regulation (EU) 2024/2847 on Horizontal Cybersecurity Requirements for Products with Digital Elements (Cyber Resilience Act). Official Journal of the European Union, L series.
6. Open Web Application Security Project (OWASP). (2024). CycloneDX Specification Version 1.6. OWASP Foundation.
7. Grassi, L., Khovratovich, D., Rechberger, C., Roy, P., & Schofnegger, M. (2021). Poseidon: A New Hash Function for Zero-Knowledge Proof Systems. 30th USENIX Security Symposium, 519-535.
8. Bowe, S., Gabizon, A., & Miers, I. (2017). Scalable Multi-party Computation for zk-SNARK Parameters in the Random Beacon Model. IACR Cryptology ePrint Archive, Report 2017/1050.
9. International Electrotechnical Commission. (2018). IEC 62443-4-2: Security for industrial automation and control systems - Technical security requirements for IACS components. IEC.
10. International Electrotechnical Commission. (2020). IEC 61850-7-2: Communication networks and systems for power utility automation. IEC.
11. Todd, P. (2016). Merkle Mountain Ranges: Compact, Append-Only Commitments for Scalable Blockchains. GitHub Technical Specification.
12. Boneh, D., Drake, J., Fisch, B., & Gabizon, A. (2020). Halo Infinite: Recursive Zero-Knowledge Arguments from Additive Polynomial Commitments. IACR Cryptology ePrint Archive, Report 2020/1536.