This paper presents the generalized implementation of the quantum circuit utilized in Shor’s algorithm, which was simulated using the quantum simulator offered by IBM. Shor’s Algorithm is a ground-breaking Quantum Algorithm that works on Integer Factorization; for a classical computer, the following task would require an exponential amount of time, whereas a Quantum Computer running Shor’s Algorithm would only require Polynomial-time. Using the principles of Quantum Superposition and Quantum Entanglement, the algorithm demonstrates the potential of quantum computing to solve complex mathematical problems efficiently. Experimental results show the effectiveness of the implemented algorithm in Integer Factorization and discrete logarithm, disturbing the safety of major encryption algorithms. This paper contributes to advancing the understanding and practical application of quantum algorithms in real-world scenarios.
This paper presents the generalized implementation of the quantum circuit utilized in Shor’s algorithm, which was simulated using the quantum simulator offered by IBM. Shor’s Algorithm is a ground-breaking Quantum Algorithm that works on Integer Factorization; for a classical computer, the following task would require an exponential amount of time, whereas a Quantum Computer running Shor’s Algorithm would only require Polynomial-time. Using the principles of Quantum Superposition and Quantum Entanglement, the algorithm demonstrates the potential of quantum computing to solve complex mathematical problems efficiently. Experimental results show the effectiveness of the implemented algorithm in Integer Factorization and discrete logarithm, disturbing the safety of major encryption algorithms. This paper contributes to advancing the understanding and practical application of quantum algorithms in real-world scenarios.
In this research, we investigate the relationships between classical and quantum computing, and the superior time complexity and memory allocation proposed theoretically for quantum algorithms. This is accomplished by building quantum circuits to represent algorithms and test in a quantum computer simulation. Classical circuit components have been continually reducing in size to the point where they are now being impacted by quantum properties, resulting in the need to investigate quantum computing. The inherent parallelism of quantum computing also allows us to solve problems for which classical computers are inept. The class of intractable problems in computing where the solution can only be found through exhaustive search is where we observe quantum computing supremacy. It is important to explore and advance our knowledge of quantum computing so we are prepared for when it becomes a reality, and so that in the future our understanding of encryption is deepened and new quantum-proof methods can be developed. Although Google and IBM have developed physical quantum computers, there is still a large deficit in knowledge of how they may be utilized. There is also a gap between proposed superior quantum solutions and problems demonstrably solved using quantum algorithms. Among the problems classically considered intractable is one extremely relevant to cybersecurity, known as Shor’s algorithm, that being an efficient algorithm for integer factorization, breaks down our well-established methods of cryptography. The aim of this research is to show the differences and advantages of quantum computing, and to specifically demonstrate how we can use Shor’s algorithm in a quantum system.
Nowadays, quantum computing is an important topic since it allows computations to be completed in a small amount of the time. The goal of using quantum computers (QC) is to solve an increasing number of problems that were previously intractable to address with traditional computing. The classical approaches work with bits, which are made up of 0s and 1s, whereas QC uses qubits. Classical computing is limited by storage capacity and speed of calculations, even when parallel computation is conducted on it. Compared to traditional methods, quantum parallelism allows the storage to be reduced exponentially with the potential of a shorter amount of time. Besides, Peter Shor's algorithm can solve the factorization problem used in RSA in polynomial time, whereas in a classical computer, factoring any big integer is intractable. The purpose of this research is to explore and implement quantum computing schemes and how Shor's algorithm can break RSA algorithms.
Ever since the realisation of the potential computational power of quantum-natured circuits, multiple quantum algorithms have been proposed, exploiting quantum superposition or quantum entanglement features to simulate quantum systems that classical computers cannot efficiently probe. The most notable among these strategies is Shor’s algorithm, which takes advantage of the quantum Fourier transform and has been shown capable of solving integer factorisation problems within polynomial time. This article’s focus is on one type of quantum algorithm based on amplitude amplification, namely Grover’s algorithm. This algorithm’s working principle is explained, and a discussion of its recent developments and possible direction of future reach is provided. In addition, implementations of Grover’s algorithm have been performed using the IBM Quantum Lab, followed by a reference to its connection to life sciences.
This paper explores the potential of quantum computing to revolutionize cryptanalysis. It proposes a novel algorithm leveraging the principles of quantum computation, specifically utilizing variants of Shor's algorithm, to analyze and ultimately break currently prevalent cryptographic systems. The core claim centers on the disruptive capability of quantum computation, potentially rendering existing encryption methods obsolete. The algorithm is designed to exploit the exponential speedup offered by quantum computers in solving specific mathematical problems, such as integer factorization and discrete logarithms, which are the foundations of many widely used encryption schemes, including RSA and ECC. This work outlines the theoretical framework, detailing the mathematical underpinnings of the proposed analysis and highlighting the significant implications for cybersecurity. The focus remains on the algorithmic design and theoretical considerations, omitting experimental validation due to the current limitations of quantum computing hardware.
Abstract Shor’s algorithm represents a landmark advancement in quantum computing, offering an efficient method for integer factorization, a problem that is computationally hard for classical computers. A core component of the algorithm is the Quantum Fourier Transform (QFT), which enables fast Fourier analysis on quantum hardware. This study focuses on the implementation and analysis of Shor’s algorithm on a 5-qubit IBM quantum computer, exploring both the theoretical principles and practical execution on a limited quantum device. By examining this implementation, we highlight the potential impact of quantum computing on classical cryptographic schemes, assess risks to information security, and discuss the algorithm’s efficiency, scalability, and applicability in real-world computational environments.
Shor’s algorithm stands as a breakthrough in quantum computing due to its potential to factor large integers exponentially quicker than classical algorithms. However, implementing and evaluating this algorithm on real quantum computer hardware remains exciting due to qubit limitations, gate noise, and hardware constraints. This research presents a comprehensive performance evaluation of Shor’s algorithm using simulated quantum backends provided by Qiskit. A flexible and generic implementation is proposed, allowing dynamic input of integers to be factored, with randomized co-prime selection and automated circuit generation. The algorithm is tested on various semiprime numbers, such as 15, 21, and 35, using IBM’s Aer simulator. A major contribution of this work is the circuit-level analysis conducted both before and after transpilation. Metrics such as gate counts, circuit depth, and simulator runtime are extracted to assess scalability and resource requirements. High-resolution plots of the pre-transpiled circuits are saved to visualize algorithmic complexity, while post-transpilation metrics inform future quantum hardware feasibility. The output measurement distributions are analyzed to estimate periodicity and derive correct factors. The proposed implementation is compared with existing fixed-instance Shor demonstrations to highlight its flexibility and extensibility. Experimental results show consistent success in factor retrieval and provide valuable insight into circuit growth and complexity under realistic constraints. This analysis lays the groundwork for future adaptation to NISQ hardware and contributes to understanding Shor’s algorithm from both computational and architectural perspectives.