Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography An Anatomical Critique of Noise-Reliant Security in the Quantum Era (Vol-I)
This review provides a detailed anatomical dissection of Jung et al. (2026), a recent preprint that challenges the prevailing classification of lattice-based cryptography—particularly the Learning with Errors (LWE) paradigm—as unconditionally "post-quantum." The paper systematically interrogates LWE across computational complexity, information-theoretic thermodynamics, quantum error correction (QEC), and quantum learning theory, arguing that its security rests on transient physical and engineering bottlenecks rather than fundamental theoretical barriers. We evaluate the paper's structure, strengths, and limitations; situate its claims within at least ten competing models and theories in post-quantum cryptography (PQC); examine the ontological (nature of cryptographic security) and epistemological (justification KSCCN Mamun, SM (2026)…………………………………1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Noise-Reliant Security in the Quantum Era (Vol-I) of security claims) dimensions of its central themes; and propose extensions and ideation pathways. While the work offers a provocative interdisciplinary synthesis, its conclusions remain largely speculative and do not constitute a practical break of standardized schemes. Nonetheless, it underscores critical gaps in the long-term robustness of noise-dependent PQC. Also available on Academia.edu: https://www.academia.edu/attachments/132758388/download_file?s=portfolio
This review provides a detailed anatomical dissection of Jung et al. (2026), a recent preprint that challenges the prevailing classification of lattice-based cryptography—particularly the Learning with Errors (LWE) paradigm—as unconditionally "post-quantum." The paper systematically interrogates LWE across computational complexity, information-theoretic thermodynamics, quantum error correction (QEC), and quantum learning theory, arguing that its security rests on transient physical and engineering bottlenecks rather than fundamental theoretical barriers. We evaluate the paper's structure, strengths, and limitations; situate its claims within at least ten competing models and theories in post-quantum cryptography (PQC); examine the ontological (nature of cryptographic security) and epistemological (justification KSCCN Mamun, SM (2026)…………………………………1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Noise-Reliant Security in the Quantum Era (Vol-I) of security claims) dimensions of its central themes; and propose extensions and ideation pathways. While the work offers a provocative interdisciplinary synthesis, its conclusions remain largely speculative and do not constitute a practical break of standardized schemes. Nonetheless, it underscores critical gaps in the long-term robustness of noise-dependent PQC. Also available on Academia.edu: https://www.academia.edu/attachments/132758388/download_file?s=portfolio
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
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
This sixth volume of the anatomical critique systematically deconstructs the purely mathematical paradigm of lattice-based post-quantum cryptography (PQC), proposing that cryptographic security in the quantum era is fundamentally a thermodynamic property of information systems. The work validates this 'transient bottleneck thesis' through comprehensive empirical quantum simulations of Learning with Errors (LWE) extraction on 2026-era Mamun, SM (2026) ………………………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Empirical Quantum Simulation on NISQ and Analog Devices (Vol-VI) K S C Noisy Intermediate-Scale Quantum (NISQ) gate-based processors (IBM, IonQ, Rigetti), neutral-atom analog platforms (QuEra), and photonic continuous-variable systems. Empirical results confirm that standard Gaussian LWE is protected against heuristic Variational Quantum Algorithm (VQA) attacks by the exponential thermodynamic overhead required for deep circuit transpilation and error mitigation. However, experiments on analog and photonic hardware physically prove the structural equivalence between LWE noise and continuous-variable displacement errors, confirming that Gottesman-Kitaev-Preskill (GKP) error correction can function as a physical decryption mechanism. Also available on Academia.edu: https://www.academia.edu/attachments/132771797/download_file?s=portfolio
This seventh volume of the series establishes the first formal post-post-quantum taxonomy—a three-tier ontological and epistemological hierarchy that reclassifies all post-quantum cryptographic schemes according to the fundamental nature and justification of their security. The hierarchy progresses from computational (algorithmic hardness assumptions) through physical (thermodynamic, noise-engineered, and hardware-constrained irreversibility) to device-independent (information-theoretic guarantees independent of device implementation). Building directly upon the anatomical critiques, hybrid primitives (Vol II), QRAM-hardness (Vol III), parameterized adversary models (Vol IV), GKP-resistant countermeasures (Vol V), and NISQ empirical validation (Vol VI), we provide a complete reclassification of NIST PQC standards, hybrid protocols, and the novel primitives introduced across the series. Dedicated Mamun, SM (2026) ……………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Post-Post-Quantum Taxonomy (Vol-VII) sections dissect the ontology (what security is) and epistemology (how security claims are known and justified) of each tier. K S C The taxonomy reveals that current lattice-based schemes remain anchored in the provisional computational tier, while the countermeasures developed in Vols III–VI elevate them into the physical tier. True device-independent security remains an aspirational frontier. Also available on Academia.edu: https://www.academia.edu/attachments/132771868/download_file?s=portfolio
This culminating tenth volume systematically establishes the profound LWE-QML Duality: the mathematical architecture securing lattice-based post-quantum cryptography (Learning with Errors, LWE) is structurally and functionally isomorphic to the mechanism conferring adversarial certified robustness upon Quantum Machine Learning (QML) systems. Formal bidirectional reductions, supported by the Choi-Jamiolkowski isomorphism, Mamun, SM (2026) …………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Learning-with-Errors Analogs in Quantum Machine Learning Robustness (Vol-X) demonstrate that cryptographic hardness inherently begets algorithmic robustness. The noise distributions engineered to obfuscate the LWE secret vector operate identically to the quantum noise mechanisms that shield quantum neural networks (QNNs) from malicious perturbation. This synthesis fundamentally alters the epistemological standing of LWE, transitioning it from a computational assumption to a physical boundary. C The paper refutes the structural vulnerabilities suggested by quantum-sample attacks (Grilo, Zeng) and the assertion of transient hardware bottlenecks (Jung et al.). This neutralization is achieved by implementing QML-inspired adversarial training and non-Gaussian, GKP-resistant noise topographies (e.g., Cauchy-LWE) that induce a multi-fractal phase-space fragmentation. Also available on Academia.edu: https://www.academia.edu/attachments/132780875/download_file?s=portfolio
Modern lattice-based cryptography, particularly the learning with errors paradigm, relies on injecting artificial noise to secure data against quantum adversaries. This study systematically examines the theoretical and physical boundaries of this noise-reliant model across four interconnected domains: computational complexity, information-theoretic thermodynamics, quantum error correction, and quantum learning theory. Starting from the algorithmic foundation, our analysis notes that these frameworks rely on provisional complexity-theoretic assumptions that remain vulnerable to future quantum algorithmic advancements. Furthermore, by translating this cryptographic mechanism into physical thermodynamics, we illustrate that intentionally injected discrete Gaussian noise does not equate to the permanent erasure of information. Because the structural integrity of the cryptographic secret remains preserved within the ciphertext, advanced quantum error correction protocols and quantum learning models can efficiently extract the underlying mathematical kernel. Ultimately, we suggest that while lattice-based cryptography provides a robust transitional alternative, definitively classifying these frameworks as unconditionally post-quantum represents a premature classification relying on transient physical bottlenecks rather than impenetrable theoretical boundaries.