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

TL;DR

This paper introduces 'Explainable PQC,' a layered interpretive framework combining complexity theory, mathematical analysis, and empirical testing to improve communication of post-quantum cryptographic security assumptions.

Contribution

It defines a structured interpretive framework for PQC security, clarifies its scope, and suggests mathematical and experimental directions for transparent security communication.

Findings

Developed a three-layer interpretive model for PQC security

Applied combinatorial Hodge theory and polyhedral geometry to lattice hardness

Created a Julia-based platform for empirical analysis of lattice algorithms

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.