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International Journal of Advanced Trends in Computer Science and Engineering

An overview of Quantum Cryptography and Shor’s Algorithm

Published Oct 15, 2020• 30 citations
Publisher

Abstract

The paper aims to examine the mechanisms of quantum cryptography and review the relationship between quantum and classical encryption schemes.A brief introduction of quantum computation is provided, with a simplified explanation of Shor's Algorithm showcasing the potentials of quantum computation.Related literature such as books, journals, proceedings, lecture notes and webpages on quantum cryptography were reviewed and were sourced from prominent databases like IEEE Xplore, ScienceDirect, and JSTOR.This gave a clearer picture on the mechanisms of quantum cryptography and Shor's algorithm.The authors were able to succinctly describe quantum cryptography, show how encryption is achieved by exploiting the properties of quantum particles, and demonstrated with examples the intricacies with Shor's algorithm.It is expected that interested researchers will be more informed on current research in quantum cryptography and influence potential cryptography scholars to explore further the mechanisms of quantum cryptography, quantum computation, and other principles of the quantum theory.

DOI
10.30534/ijatcse/2020/82952020

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The paper aims to examine the mechanisms of quantum cryptography and review the relationship between quantum and classical encryption schemes.A brief introduction of quantum computation is provided, with a simplified explanation of Shor's Algorithm showcasing the potentials of quantum computation.Related literature such as books, journals, proceedings, lecture notes and webpages on quantum cryptography were reviewed and were sourced from prominent databases like IEEE Xplore, ScienceDirect, and JSTOR.This gave a clearer picture on the mechanisms of quantum cryptography and Shor's algorithm.The authors were able to succinctly describe quantum cryptography, show how encryption is achieved by exploiting the properties of quantum particles, and demonstrated with examples the intricacies with Shor's algorithm.It is expected that interested researchers will be more informed on current research in quantum cryptography and influence potential cryptography scholars to explore further the mechanisms of quantum cryptography, quantum computation, and other principles of the quantum theory.
The paper aims to examine the mechanisms of quantum cryptography and review the relationship between quantum and classical encryption schemes.A brief introduction of quantum computation is provided, with a simplified explanation of Shor's Algorithm showcasing the potentials of quantum computation.Related literature such as books, journals, proceedings, lecture notes and webpages on quantum cryptography were reviewed and were sourced from prominent databases like IEEE Xplore, ScienceDirect, and JSTOR.This gave a clearer picture on the mechanisms of quantum cryptography and Shor's algorithm.The authors were able to succinctly describe quantum cryptography, show how encryption is achieved by exploiting the properties of quantum particles, and demonstrated with examples the intricacies with Shor's algorithm.It is expected that interested researchers will be more informed on current research in quantum cryptography and influence potential cryptography scholars to explore further the mechanisms of quantum cryptography, quantum computation, and other principles of the quantum theory.
Quantum Information and Quantum Computation are rapidly evolving domains in their theoretical foundations, implementations and applications. The main scope of the present book is to give the basic ideas of this field to undergraduate students in Physics. A rigorous approach is used to provide the key concepts and methods. Many examples are discussed. To be self-contained, the principles of Quantum Mechanics are reviewed. The discussion is aimed to the specific, but paradigmatic, factorization problem of integers, dealt by the Quantum Shor’s Algorithm. Thus, notions of the Number Theory are given in the first Chapter, while the exposition of the algorithm and its implementation is reserved to the last Section.
Quantum cryptography is a significant development in secure communication that uses quantum mechanics concepts to improve data security against developing attacks. By utilizing phenomena such as quantum superposition and entanglement, it provides robust methods such as quantum key distribution (QKD) that provide key security against eavesdropping. This review begins with the underlying concepts of quantum computing, which support quantum cryptography techniques. This research study provides a brief comparison of classical computing with quantum computing and technological developments through various research and possible consequences. Then it investigates fundamental principles of quantum mechanics such as, Heisenberg uncertainty principle and photon polarization. The chapter then explores the main quantum cryptography concepts such as QKD, emphasizing its theoretical foundations, Shor’s and Grover’s algorithm effects on traditional algorithms, and programming tools which can be used in real-world applications.
Abstract This chapter gives a brief introduction to quantum computing, which is the discipline of studying algorithms based on the principles of quantum theory. It outlines the two fundamental quantum algorithms, which are known as Grover’s and Shor’s algorithm, which are able to solve number-theoretical problems that are intractable for present conventional computers. Thus, this chapter also shows the impact of these quantum algorithms on present cryptography under the assumption of the existence of a large-scale quantum computer, concluding that quantum computing poses a serious threat to public-key cryptosystems, because their underlying mathematical problems can be solved efficiently by using Shor’s algorithm.
Abstract Quantum computing exploits superposition and entanglement to process information in an exponentially large state space, enabling algorithms such as Shor’s to factor large integers efficiently and thereby undermining RSA and elliptic curve cryptography. Quantum cryptography, here encompassing post quantum cryptographic (PQC) algorithms and quantum key distribution (QKD), is a leading candidate for protecting data against quantum capable adversaries. PQC designs classical schemes conjectured to be secure against both quantum and classical attacks, whereas QKD uses quantum mechanics to detect eavesdropping and establish information theoretically secure keys. Existing literature and limitations. Recent surveys summarise PQC families and the standardisation process led by the U.S. National Institute of Standards and Technology (NIST), and reviews outline QKD protocols and their challenges. However, most prior work either addresses narrow subtopics or does not systematically synthesise empirical evidence across technical and application domains. As a result, there is still limited integrated understanding of key issues, technologies, mathematical foun dations, algorithms, programming tools and real world deployments. Objective and contributions of this review. This study systematically analyses 61 peer reviewed journal articles published within the last five years that focus on quantum cryptography. Using Covidence to manage study identification, selection, quality assessment, data extraction and narrative synthesis, it (a) characterises current issues and challenges; (b) surveys recent technological advancements and implementations; (c) evaluates algorithmic approaches and their effectiveness; (d) examines the underlying mathematical models; (e) maps the programming languages and tools used to implement quantum schemes; and (f) synthesises evidence on practical applications and future research directions. The review integrates findings on PQC and QKD, highlights gaps in the current evidence base, and offers practitioners, scholars and policymakers guidance for developing quantum secure communication systems. Keywords Quantum cryptography, Post quantum cryptography, Quantum key distribution, Systematic literature review, Quantum secure communication
This review paper provides an in-depth exploration of quantum computing and the algorithms that drive its potential. It begins by introducing quantum computers and explores various types of quantum computers, focusing on the most prominent architectures. This paper also explains the concept of qubits, highlighting their unique properties such as superposition and entanglement, which differentiate quantum systems from classical computing. It discusses the specific properties of quantum computers that make them particularly suited to solving certain classes of problems, such as optimization, cryptography, and simulation. Additionally, the paper provides a detailed overview of key quantum algorithms, including Shor’s algorithm for integer factorization, Grover’s algorithm for unstructured search, and the use of quantum simulation in modelling complex physical systems. Through this review, we aim to showcase the evolving landscape of quantum computing, its capabilities, and the algorithms driving its future impact across various fields.