What question did this study set out to answer?

This paper aims to explore the developments and implications of post-quantum cryptography using various mathematical models.

May 21, 2026Open Access

ITU Tier 1+ #3: Post-Quantum Cryptography (Kcrypto)

Key Points

This paper aims to explore the developments and implications of post-quantum cryptography using various mathematical models.
Defined K_crypto operator-algebraically for multiple cryptographic problems.
Analyzed numerical results related to lattice complexity and the threat of Shor's algorithm.
Projected costs related to PQC migration and the implementation roadmap.
Kyber and Dilithium demonstrate significant lattice complexities.
Predicted a quantum breach of RSA-2048 by 2035.
Estimated global PQC migration implications by 2030.

Abstract

Tier 1+ Pass-1. 5 paper 3 of 45. ITU-derived post-quantum cryptography on lattice / code / hash / isogeny problems. Defines Kcrypto = -log ρcrypto as the operator-algebraic modular Hamiltonian on Hₗattice ⊗ Hcode ⊗ Hₕash ⊗ Hᵢsogeny. Kcrypto inherits from KQG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Kyber/Dilithium lattice complexity; Shor's algorithm threat timeline; PQC migration cost projection. Topics covered. NIST PQC 2024. 8. 13 finalisation, ML-KEM/ML-DSA/SLH-DSA, Kyber/Dilithium/Falcon/SPHINCS+, Shor 1994, lattice cryptography. 45-vertex polytope #3 top couplings: #3 Kₛemi (0. 85), #13 Kᵣobot (0. 85), #2 AI (0. 85). Ten falsifiable predictions: Pₐvg=0. 65: arXiv 2026 (0. 90 S), Quantum break of RSA-2048 by 2035 (0. 30 W), Global PQC migration 2030 (0. 70 M). Pass-2 roadmap: ~1. 5M: Crypto analytics (500K) + Lean Mathlib (200K) + PQC migration consortium (800K). Copyright © 2026 Munehiro Terada / Roboken. Licensed under CC-BY-4. 0.

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