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Journal of quantum computing

Analysis of Innovative Quantum Optimization Solutions for Shor’s Period Finding Algorithm Applied to the Computation of

Kaleb Dias Antoine KODO, Eugène Cokou Ezin

Published Jan 1, 2025• 0 citations
Publisher

Abstract

In the rapidly evolving domain of quantum computing, Shor’s algorithm has emerged as a groundbreaking innovation with far-reaching implications for the field of cryptographic security. However, the efficacy of Shor’s algo... | Find, read and cite all the research you need on Tech Science Press
DOI
10.32604/jqc.2025.059089

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The present study explores the groundbreaking possibilities of Shor's algorithm in cracking RSA encryption, hence enhancing the security consequences of this extensively employed cryptographic protocol. Due to Shor's algorithm's exponential speed advantage over classical algorithms, RSA encryption—a popular public key cryptosystem—is vulnerable to quantum attacks. To keep its security, RSA depends on the difficulty of factoring huge semi-primes. RSA's security presumptions are called into question by Shor's algorithm's quick factorization on a quantum computer, which has prompted research into post-quantum cryptography solutions to guarantee secure communication in the quantum age. Even with parallel computation, the speed and storage capacity of classical computing are constrained. A key idea in quantum computing is quantum parallelism, which allows quantum systems to carry out several computations at once. In contrast to classical portions. The scope of this paper is to understand the fundamentals of Quantum Computing, the current state of Shor’s algorithm implementation, and efficiency, particularly its application in compromising public key cryptosystems like RSA. The project aims to achieve how factorization is done through classical methods and further, how is this done through Shor’s algorithm and QFT techniques.
This study investigates the growing threat of quantum computing to classical encryption, with a specific focus on the vulnerabilities of RSA. Examining how Shor's algorithm compromises RSA security, the research proposes mitigation strategies. Through a comprehensive analysis of quantum algorithms and a review of recent literature, the study evaluates the efficacy of quantum attacks on RSA keys. Emphasizing the urgency of transitioning to quantum-resistant cryptographic solutions, the research identifies key challenges and provides recommendations for enhancing cybersecurity in the quantum era. The research methodology involves extensive literature reviews on quantum computing, RSA encryption, and related methodologies. Practical implications and the feasibility of quantumresistant alternatives are explored, shedding light on the potential impacts of quantum attacks on RSA encryption. The study emphasizes the need for swift adaptation to quantum-resistant cryptographic solutions, offering insights into key challenges associated with this transition and recommending strategies for enhanced cybersecurity in the era of quantum computing. The successful execution of this research hinges on access to computational resources for quantum simulations and cryptography analyses. Additionally, collaboration with experts in quantum computing and cryptography is crucial for validation and guidance throughout the research process. Access to relevant literature, datasets, cryptography software libraries, and surveys is essential for a comprehensive study that addresses the evolving quantum security landscape.
The 1994 discovery of Shor's quantum algorithm for integer factorization—an important practical problem in the area of cryptography—demonstrated quantum computing's potential for real-world impact. Since then, researchers have worked intensively to expand the list of practical problems that quantum algorithms can solve effectively. This book surveys the fruits of this effort, covering proposed quantum algorithms for concrete problems in many application areas, including quantum chemistry, optimization, finance, and machine learning. For each quantum algorithm considered, the book clearly states the problem being solved and the full computational complexity of the procedure, making sure to account for the contribution from all the underlying primitive ingredients. Separately, the book provides a detailed, independent summary of the most common algorithmic primitives. It has a modular, encyclopedic format to facilitate navigation of the material and to provide a quick reference for designers of quantum algorithms and quantum computing researchers.