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This paper analyzes the fundamental limitations of lattice-based post-quantum cryptography (PQC) across computational complexity, thermodynamics, quantum error correction, and quantum learning theory. It argues that the security of these schemes relies on provisional complexity-theoretic assumptions and transient physical bottlenecks rather than unbreakable theoretical boundaries. The analysis demonstrates that injected Gaussian noise doesn't permanently erase information, leaving the underlying cryptographic secret vulnerable to advanced quantum error correction and learning techniques.
Lattice-based cryptography's reliance on injected noise for security is more akin to hiding secrets under a rug than truly erasing them, leaving them vulnerable to future quantum attacks.
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.
