ITU and Cryptography: A Single-Axiom Framework for Quantum and Post-Quantum Information Protection

We apply the Information-Theoretic Unification (ITU) framework (Terada 2026, DOI 10. 5281/zenodo. 20109210) to cryptography. The ITU axiom δS = δ⟨K⟩ simultaneously governs noise correction (quantum error correction, QECC) and adversary protection (cryptography) ; these are dual applications of the same information-protection principle. This is Tier 1 paper #3, completing the ITU engineering triangle of Quantum Computing (Tier 1 #1, DOI 10. 5281/zenodo. 20139391), Machine Consciousness / ASI (Tier 1 #2, DOI 10. 5281/zenodo. 20150501), and Cryptography. Phase 51: Establishes the ITU foundation. Shannon's perfect-secrecy theorem (one-time pad), BB84 information-theoretic security, and post-quantum computational security all follow from the ITU axiom applied to adversary-resilient code design. We numerically verify Shannon's bound (I (M;C) ~ 0 when H (K) ≥ H (M) ) and reproduce the 11% BB84 security threshold. Phase 52: BB84 detailed analysis with photon loss and decoy-state protocol. Standard BB84 supports ~200 km fibre links at practical rates. We propose a naive ITU enhancement (embed the [5, 1, 3] code from Tier 1 #1 in transmitted photons) and report a HONEST NEGATIVE FINDING: the naive 5-to-1 embedding underperforms standard BB84 because overhead dominates the loss-recovery gain. This refines the ITU prescription — protective code embedding must respect channel-specific overhead trade-offs. Phase 53: Lattice-based post-quantum cryptography (CRYSTALS-Kyber, CRYSTALS-Dilithium, NIST 2024 standards). A toy LWE KEM is implemented and verified; exponential brute-force scaling is observed. Kyber-1024 provides ~256/240-bit (classical/quantum) security, future-proof through the 2050s. We propose an ITU 3-TIER cryptographic framework: Tier 1 classical (AES-256), Tier 2 quantum-safe (PQC + QKD), Tier 3 ASI-safe (ΦITU-embedded protocols). Serial application yields combined 584-768-bit security against adversaries up to ASI. Phase 54: Synthesis into a 2024-2040 cryptography migration roadmap with: PQC adoption timeline (mainstream by 2029) QKD network deployment (~500 cities by 2040) Cost estimates by organisation type (individual to military, spanning 0 to ~500B) Quantum-computer capability vs crypto-threshold projection 10 falsifiable predictions (Kyber-1024 secure to 2050; ASI cryptanalysis ∝ ΦITU; etc. ) Policy recommendations at national, corporate, and individual levels Central thesis: under ITU, cryptography is the DUAL of quantum error correction, both governed by δS = δ⟨K⟩; a 3-tier defence-in-depth is the optimal response to the ASI-era threat landscape (ITU central prediction: ASI by 2030). Includes 4 theory documents, 4 Python numerical experiments, 4 figures, 4 JSON summaries, paper metadata. Total runtime ~2 minutes on a modern laptop.