Entropic uncertainty in quantum-state cryptography : A mathematical framework for quantum-resilient encryption

Verma, Vivek Kumar; Saini, Bhavna; Jain, Tarun; Dadheech, Pankaj

doi:10.47974/JDMSC-1907

Open Access Research Article

Entropic uncertainty in quantum-state cryptography : A mathematical framework for quantum-resilient encryption

Vivek Kumar Vermavermavivek123@gmail.comDepartment of Information TechnologyManipal University JaipurJaipur, Rajasthan, IndiaView full profile → , Bhavna Sainibhavnasaini10@gmail.comDepartment of Data Science & AnalyticsCentral University of RajasthanRajasthan, IndiaView full profile → , ^*Tarun JainCorresponding authortarunjainjain02@gmail.comDepartment of Computer Science & EngineeringManipal University JaipurJaipur, Rajasthan, IndiaView full profile → , Pankaj Dadheechpankajdadheech777@gmail.comDepartment of Computer Science & EngineeringManagement & GramothanSwami Keshvanand Institute of TechnologyJaipur, Rajasthan, IndiaView full profile →

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pp. 397–407Vol. 27Issue 2-AMarch 2024DOI: 10.47974/JDMSC-1907 Crossmark XML

Published Online:: 06 Apr 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1907
Pages:: 397–407

Abstract

In the escalating race between cryptographic security and quantum computing capabilities, the need for robust encryption methodologies that can withstand the prowess of quantum algorithms is more pressing than ever. This paper introduces a novel cryptographic framework, grounded in the principles of quantum mechanics and the entropic uncertainty principle, to forge a path towards quantum-resilient encryption. At the heart of this approach lies the integration of the entropic uncertainty inherent in quantum states, a fundamental aspect often overlooked in traditional cryptographic strategies. By harnessing this intrinsic uncertainty of quantum mechanics, we propose a mathematical framework that not only challenges the conventional paradigms of encryption but also sets a new benchmark for security in the quantum computing era. The paper delves into the theoretical underpinnings of quantum mechanics relevant to cryptography, with a particular focus on the entropic uncertainty principle. This principle, which posits a natural limit on the precision with which certain pairs of physical properties can be known, serves as the cornerstone of our proposed encryption method. We meticulously develop and outline a mathematical model that leverages this principle, ensuring that the encrypted information remains secure against the formidable computational capabilities of quantum algorithms. We contrast our approach with existing cryptographic methods, highlighting the enhanced security features offered by the entropic uncertainty-based model. The findings underscore the potential of this framework to serve as a resilient encryption mechanism in a landscape increasingly dominated by quantum computing technologies. This research paves the way for a new era of encryption, one that embraces the uncertainty of quantum mechanics as its shield against the threats posed by quantum computing.

Keywords

Quantum-Resilient Encryption Quantum Error Correction Quantum Mechanics in Cryptography Hybrid Cryptographic Systems Entropic Uncertainty Principle

Subject Classifications

81P94

References

[1] X. Li, D. Peng, and J. Cao, ‘Lyapunov Stability for Impulsive Systems via Event-Triggered Impulsive Control,’ IEEE Transactions on Automatic Control, pp. 4908-4913, (2020).
[2] C. Xu, et al., ‘Lyapunov Stability and Wave Analysis of Covid-19 Omicron Variant of Real Data with Fractional Operator,’ Alexandria Engineering Journal, pp. 11787-11802, (2022).
[3] Anil Kumar & Sandeep Kumar Sharma. Information cryptography using cellular automata and digital image processing, Journal of Discrete Mathematical Sciences and Cryptography, 25:4, 1105-1111 (2022), DOI: 10.1080/09720529.2022.2072437.
[4] Sharma, Sandeep Kumar, Kumar, Anil, Ashtagi, Rashmi & Jain, Rekha. OCA: An intelligent model for improving security breach of biometric based authentication systems, Journal of Discrete Mathematical Sciences and Cryptography, 26:5, 1415–1425 (2023), DOI: 10.47974/JDMSC-1765.
[5] Krawec, Walter O. “Quantum sampling and entropic uncertainty.” Quantum Information Processing 18: 1-18, (2019).
[6] Wu, Lin, Liu Ye, and Dong Wang. “Tighter generalized entropic uncertainty relations in multipartite systems.” Physical Review A 106.6: 062219, (2022).
[7] Sharma, S.K., Kumar, A., Digital Image Transformation Using Outer Totality Cellular Automata. Machine Intelligence Techniques for Data Analysis and Signal Processing. Lecture Notes in Electrical Engineering, vol 997. Springer, Singapore (2023). https://doi.org/10.1007/978-981-99-0085-5_69.
[8] Tomamichel, Marco, and Esther Hänggi. “The link between entropic uncertainty and nonlocality.” Journal of Physics A: Mathematical and Theoretical 46.5: 055301, (2013).
[9] Ketterer, Andreas, and Otfried Gühne. “Entropic uncertainty relations from quantum designs.” Physical Review Research 2.2: 023130, (2020).
[10] Wang, Zhao-An, et al. “Generalized multipartite entropic uncertainty relations: theory and experiment.” arXiv preprint arXiv:2207.12693 (2022).
[11] Majenz, Christian. “Entropy in Quantum Information Theory--Communication and Cryptography.” arXiv preprint arXiv:1810.10436 (2018).
[12] Coles, Patrick J., et al. “Entropic energy-time uncertainty relation.” Physical Review Letters 122.10: 100401, (2019).

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