Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Thermodynamic Entropy Bounds Integrated into Security Reductions (Vol-IX)

Syed Muntasir Mamun

Published Jan 1, 2026• 0 citations

Abstract

This ninth volume closes a critical gap in post-quantum cryptography (PQC) by deriving hybrid, thermodynamic-augmented security reductions for lattice-based architectures. The work shifts the definition of cryptographic resilience from model-relative computational assumptions (Tier-1) to a physically conserved resource strictly bounded by the irreversible laws of thermodynamics and fractal phase-space geometry (Tier-2). The proposed construction, Thermodynamic-LWE (T-LWE), mandates noise generation via physically irreducible Enclave-Oracle Physical Unclonable Functions (PUFs) and utilizes heavy-tailed Lévy/Cauchy distributions to enforce physical interaction limits. By integrating Landauer's principle for the cost of quantum Mamun, SM (2026) …………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Thermodynamic Entropy Bounds Integrated into Security Reductions (Vol-IX) K S C state preparation and the Fannes-Audenaert inequality for von Neumann entropy continuity, the analysis proves that any quantum adversary attempting sophisticated extraction algorithms incurs a non-bypassable information-theoretic penalty. This penalty is exponentially amplified by the multifractal topology ($D_f$) of the noise distribution. The resulting framework furnishes the global cryptographic community with deployable, entropy-augmented security proofs, anchoring quantum resilience to immutable physical laws. Also available on Academia.edu: https://www.academia.edu/attachments/132780724/download_file?s=portfolio

DOI: 10.5281/zenodo.22991690

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Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Thermodynamic Entropy Bounds Integrated into Security Reductions (Vol-IX)

Syed Muntasir Mamun

Published Jan 1, 2026• 0 citations

Publisher

Abstract

D_f

) of the noise distribution. The resulting framework furnishes the global cryptographic community with deployable, entropy-augmented security proofs, anchoring quantum resilience to immutable physical laws. Also available on Academia.edu: https://www.academia.edu/attachments/132780724/download_file?s=portfolio

DOI: 10.5281/zenodo.22991690

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Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of QRAM-Hardness Primitives and Thermodynamic Security (Vol-III)

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This third volume advances QRAM-hardness cryptography, arguing that the ultimate quantum resilience of lattice-based primitives must be grounded in the thermodynamic lower bounds governing coherent state preparation, rather than transient algorithmic assumptions. While Learning with Errors (LWE) is mathematically susceptible to the Gottesman-Kitaev-Preskill (GKZ) quantum learning algorithm, this paper definitively proves that the index-erasure problem and the construction of a necessary Quantum Random Access Memory (QRAM) oracle impose insurmountable physical barriers. The necessity of reversing classical computation paths to maintain quantum coherence is subject to Landauer's Principle, dissipating a minimum energy of $k_B T \ln 2$ per erased bit. For cryptographically relevant dimensions, the total dissipated energy scales to macroscopic limits, instantly vaporizing cryogenic cooling systems and physically preventing the required Mamun, SM (2026) …………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of QRAM-Hardness Primitives and Thermodynamic Security (Vol-III) $\left|\psi_{s, e}\right\rangle$ superposition state preparation. Furthermore, this heat manifests as non-Gaussian thermodynamic noise, pushing continuous-variable GKP error-correction codes beyond their critical correctable threshold and inducing catastrophic logical failure. Also available on Academia.edu: https://www.academia.edu/attachments/132761250/download_file?s=portfolioThis third volume advances QRAM-hardness cryptography, arguing that the ultimate quantum resilience of lattice-based primitives must be grounded in the thermodynamic lower bounds governing coherent state preparation, rather than transient algorithmic assumptions. While Learning with Errors (LWE) is mathematically susceptible to the Gottesman-Kitaev-Preskill (GKZ) quantum learning algorithm, this paper definitively proves that the index-erasure problem and the construction of a necessary Quantum Random Access Memory (QRAM) oracle impose insurmountable physical barriers. The necessity of reversing classical computation paths to maintain quantum coherence is subject to Landauer's Principle, dissipating a minimum energy of $k_B T \ln 2$ per erased bit. For cryptographically relevant dimensions, the total dissipated energy scales to macroscopic limits, instantly vaporizing cryogenic cooling systems and physically preventing the required Mamun, SM (2026) …………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of QRAM-Hardness Primitives and Thermodynamic Security (Vol-III) $\left|\psi_{s, e}\right\rangle$ superposition state preparation. Furthermore, this heat manifests as non-Gaussian thermodynamic noise, pushing continuous-variable GKP error-correction codes beyond their critical correctable threshold and inducing catastrophic logical failure. Also available on Academia.edu: https://www.academia.edu/attachments/132761250/download_file?s=portfolio

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D_f

k_B T \ln 2

per erased bit. For cryptographically relevant dimensions, the total dissipated energy scales to macroscopic limits, instantly vaporizing cryogenic cooling systems and physically preventing the required Mamun, SM (2026) …………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of QRAM-Hardness Primitives and Thermodynamic Security (Vol-III)

\left|\psi_{s, e}\right\rangle

superposition state preparation. Furthermore, this heat manifests as non-Gaussian thermodynamic noise, pushing continuous-variable GKP error-correction codes beyond their critical correctable threshold and inducing catastrophic logical failure. Also available on Academia.edu: https://www.academia.edu/attachments/132761250/download_file?s=portfolio