Quantum Error Correction for Post-Quantum Cryptographic Algorithms Authors

El Ashmawy, Mohamed Salah

Jiho Jung, Donghwa Ji, Mingyu Lee +1 more

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.

Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi +2 more

Konstantin Nikolaevich Pankov, Михаил Михайлович Глухов

This paper assesses cryptographic security for new, Fourth Industrial Revolution technologies against quantumenabled risks. In this context, the history of successful attacks on post-quantum cryptography algorithms is reviewed and a thorough cryptographic study of these algorithms' resistance to various cryptographic analysis methods is proposed. The paper also describes an effective attack on a post-quantum algorithm proposed by the authors in earlier studies. This description concludes that using the previously proposed parameters is insecure. Modifying these parameters necessitates further investigation into the cryptographic strength of the post-quantum algorithm.

Bikram Paul, Gaurav Trivedi

Jincheng Zhang

This paper presents a novel approach to Quantum Error Correction (QEC) based on topological quantum structures. Traditional QEC methods often rely on measurement, which introduces errors. We propose a new algorithm that leverages the inherent properties of quantum error correction to construct a robust and efficient correction scheme. The core of this approach is the design of a topological structure that protects quantum information from local errors. This structure, when manipulated, effectively mitigates the propagation of quantum information errors, leading to improved performance and resilience. The algorithm's novelty lies in its fundamental shift towards exploiting the quantum properties of the structure itself rather than relying on post-processing measurements. We analyze the algorithm's performance and demonstrate its potential for significantly enhanced error correction capabilities compared to existing techniques.