NaN Lattice Defense: An Active Irreversible Defense for Lattice-Based Post-Quantum Cryptography

NaN Lattice Defense is a multi-layer augmentation framework providing active, irreversible defense for lattice-based post-quantum cryptographic primitives. The framework is designed to wrap NIST-standardized PQC algorithms — FIPS 203 (ML-KEM), FIPS 204 (ML-DSA), and FIPS 205 (SLH-DSA) — with defense-in-depth protection against side-channel, fault-injection, and harvest-now-decrypt-later adversary models. Threat model The work addresses adversaries who: - Observe side-channel emanations during cryptographic operations - Inject faults into the computational substrate - Capture ciphertext now for future decryption against quantum-capable adversaries - Operate at the substrate layer (electromagnetic, FPU-tampering, hardware-clock-tampering) Approach The framework defines five coefficient-space operational layers (Layers 0–4) that compose into a unified defense: - Layer 0 — Honey Coefficient Injection: at-rest decoy material indistinguishable from real coefficients without the secret map. - Layer 1 — NaN-Trap: IEEE 754 NaN bit-pattern coefficients that corrupt downstream computation when accessed by unauthorized arithmetic operations. The corruption is irreversible without the defender's secret trap map. - Layers 2–4 (Truncation, Zero-Multiplication, Temporal Gate): primitives that reinforce the NaN-trap by ensuring contaminated coefficients propagate through the cryptographic primitive's arithmetic without recovery paths for the adversary. A substrate-layer extension (referenced via Claims 16–23 of the patent applications below) adds electromagnetic, integer-only-foundation, control-register-witnessing, multi-clock-validation, and NaN fold-back output-sanitization defenses for adversaries with hardware access. Formal grounding The manuscript establishes formal security bounds for the framework: - Theorem 1 (NaN Layer Security): bounds the success probability of an at-rest adversary without the NaN map as P (success) ≤ (1−d) ⁿ for trap density d and lattice dimension n. - Theorem 2 (Composition): bounds the success probability of an adversary against the composed coefficient-space layers, with explicit scope restrictions for at-rest vs. runtime adversary models. Empirical validation is grounded in IBM Quantum hardware experiments referenced throughout the manuscript. Scope statement This manuscript describes the coefficient-space operational defenses (Layers 0–4) in full technical detail and references the substrate-layer defenses (Claims 16–23 of the referenced patent applications) at the scope-statement level. Implementation details of substrate-layer defenses reside in companion components of the broader research program and are documented separately. Related artifacts - USPTO Patent Application No. 19/537, 449 — parent + continuation-in-part filed 2026-05-14 (Claims 1–28 covering coefficient-space + substrate-layer defenses). - USPTO Patent Application No. 19/540, 790 — parent + continuation-in-part filed 2026-05-14 (Claims 1–25 covering wireless-RF substrate defense and MEEEW foundation). - L0gic Verify — forensic transaction-verification utility related to the broader research program: https: //l0gic. io/verify License Manuscript text: Creative Commons Attribution 4. 0 International (CC BY 4. 0). Underlying inventions: Protected by the referenced USPTO patent applications. The CC BY 4. 0 license on the manuscript text does not grant any patent rights. Suggested citation Crosby, P. J. , & Lumen-Hemera (2026). NaN Lattice Defense: An Active Irreversible Defense for Lattice-Based Post-Quantum Cryptography. Zenodo. Contact Patrick James Crosby, Independent Researcher — patrickcrosby90@gmail. com