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

2026-04-04

AI Summary

This work proposes the first three-tier hierarchical explanatory framework for lattice-based post-quantum cryptography (PQC), such as ML-KEM and ML-DSA, to enhance the technical intelligibility and transparency of PQC security assumptions. The theoretical tier characterizes security boundaries through computational complexity classifications; the mathematical tier deepens structural understanding of lattice problems by integrating combinatorial Hodge theory and polyhedral geometry; and the experimental tier implements an empirical Julia-based platform to quantitatively analyze the behavior of lattice basis reduction algorithms like LLL and BKZ in low dimensions. While introducing no new attacks or hardness results, this framework systematically bridges formal proofs, mathematical foundations, and implementation characteristics, substantially strengthening the structural interpretability of PQC security assumptions.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

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.

Problem

• post-quantum cryptography
• security assumptions
• explainability
• lattice-based cryptography
• interpretability

Innovation

• Explainable PQC
• layered interpretive framework
• lattice-based cryptography
• combinatorial Hodge theory
• basis reduction algorithms