Explainable PQC: A Layered Interpretive Framework for Post-Quantum Cryptographic Security Assumptions

Computer Science > Cryptography and Security [Submitted on 4 Apr 2026] Explainable PQC: A Layered Interpretive Framework for Post-Quantum Cryptographic Security Assumptions Daisuke Ishii, Rizwan Jahangir This paper studies how post-quantum cryptographic (PQC) security assumptions can be represented and communicated through a structured, layered framework that is useful for technical interpretation but does not replace formal cryptographic proofs. We propose ``Explainable PQC,'' an interdisciplinary framework connecting three layers: (1) a complexity-based interpretive model that distinguishes classical security, quantum security, and reduction-backed hardness, drawing on computational complexity classes as supporting language; (2) an exploratory mathematical investigation applying combinatorial Hodge theory and polyhedral geometry to study structural aspects of lattice hardness; and (3)~an empirical experimentation platform, implemented in Julia, for measuring the behavior of lattice basis reduction algorithms (LLL, BKZ) in low-dimensional settings. The motivating case study throughout the paper is lattice-based PQC, including ML-KEM (FIPS 203) and ML-DSA (FIPS 204). The contribution of this paper is conceptual and organizational: it defines a layered interpretive framework, clarifies its scope relative to formal cryptographic proofs and reduction-based security arguments, and identifies mathematical and implementation-level directions through which PQC security claims may be more transparently communicated. This paper does not claim new cryptographic hardness results, new attacks, or concrete security parameter estimates. Comments: 12 pages, 3 figures Subjects: Cryptography and Security (cs.CR); Algebraic Geometry (math.AG) Cite as: arXiv:2604.03665 [cs.CR]   (or arXiv:2604.03665v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2604.03665 Focus to learn more Submission history From: Rizwan Jahangir [view email] [v1] Sat, 4 Apr 2026 09:32:51 UTC (14 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-04 Change to browse by: cs math math.AG References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)