Theoretical Vulnerabilities of Post-Quantum Cryptography to (Bio)Physics Beyond the Standard Model

Trevor Nestor

Kunal Das, Arindam Sadhu

Syed Muntasir Mamun

The transition to post-quantum cryptography (PQC) based on the Learning with Errors (LWE) problem suffers from a critical epistemological gap: its security is predicated on transient computational bottlenecks, not information-theoretic permanence, making it vulnerable to mature quantum algorithms like Gottesman-Kitaev-Preskill (GKP) error correction. This critique argues that absolute quantum resilience requires a pivot to inherently hybrid architectures that systematically combine LWE's computational efficiency with the absolute, physics-bound security of Quantum Key Distribution (QKD) and Physical Random Oracles (PROs), such as Physical Unclonable Functions (PUFs). This volume details these hybrid primitives, addressing structural vulnerabilities in standard PQC and QKD. Key architectural syntheses include the Lattice PUF, which provably binds ML-modeling resistance to the LWE problem hardness using PAC theory, and Quantum-Locked Physical Mamun, SM (2026) …………………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Hybrid Info-Theoretic and Computational Primitives (Vol-II) K S C Primitives (HLPUF, HEPUF), which utilize conjugate coding and entanglement to provide authentication guarantees independent of algorithmic hardness. Also available on Academia.edu: https://www.academia.edu/attachments/132761055/download_file?s=portfolio

Antonia Wachter-Zeh

Anas Hlayhel

Syed Muntasir Mamun

The foundational security of lattice-based post-quantum cryptography (PQC), underpinned by the Learning with Errors (LWE) problem, faces a critical physical vulnerability: the structural isomorphism between its standard discrete Gaussian noise and the continuous-variable displacement errors correctable by Gottesman-Kitaev-Preskill (GKP) bosonic codes. This vulnerability suggests that a fault-tolerant quantum adversary could physically extract the secret by neutralizing the LWE noise via advanced quantum error correction (QEC) protocols. This final volume of the analytical series addresses this loophole by designing and formalizing a suite of GKP-resistant Mamun, SM (2026) …………………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of GKP-Lattice Crypto Countermeasures (Vol-V) K S C LWE countermeasures. These variants engineer non-Gaussian physical noise distributions—specifically heavy-tailed Cauchy and Lévy-stable noise, structured long-range correlated noise, and multi-modal lattice-modulated errors—that deliberately violate the bounded-distance thresholds and local Markovian assumptions of concatenated surface-GKP architectures. The analysis demonstrates that these engineered noise profiles retain highly efficient classical decryption while forcing quantum syndrome extraction into an information-theoretically lossy and computationally intractable (NP-hard) regime. Also available on Academia.edu: https://www.academia.edu/attachments/132771487/download_file?s=portfolio