The quantum asymmetric key (QAE) cryptography scheme, originally proposed using the Grover quantum search algorithm and demonstrating significant advancements in theoretical generalization, is revisited. To enhance its practical implementation, the authors evaluate the protocol's performance under real-world conditions. This includes analyzing the impact of hardware limitations and the one-iteration Grover search algorithm (GSA) on QAE accuracy, with tests conducted on IBM Quantum simulators and devices. To address these challenges, the paper focuses on extending the GSA to support non-standard initial states. This is achieved by designing a tailored diffusion operator, resulting in the generalized GSA. The study marks the first practical implementation of QAE on IBM Quantum devices, introducing generalized GSA and providing empirical performance insights. Empirical results reveal scalability challenges, with success probabilities decreasing significantly as qubit count increases. For instance, the 2-qubit system achieves near-perfect accuracy, while the 4-qubit system shows notable degradation, especially on quantum hardware. These findings underscore the need for improved hardware fidelity and algorithmic optimization to advance quantum cryptography.
The quantum asymmetric key (QAE) cryptography scheme, originally proposed using the Grover quantum search algorithm and demonstrating significant advancements in theoretical generalization, is revisited. To enhance its practical implementation, the authors evaluate the protocol's performance under real-world conditions. This includes analyzing the impact of hardware limitations and the one-iteration Grover search algorithm (GSA) on QAE accuracy, with tests conducted on IBM Quantum simulators and devices. To address these challenges, the paper focuses on extending the GSA to support non-standard initial states. This is achieved by designing a tailored diffusion operator, resulting in the generalized GSA. The study marks the first practical implementation of QAE on IBM Quantum devices, introducing generalized GSA and providing empirical performance insights. Empirical results reveal scalability challenges, with success probabilities decreasing significantly as qubit count increases. For instance, the 2-qubit system achieves near-perfect accuracy, while the 4-qubit system shows notable degradation, especially on quantum hardware. These findings underscore the need for improved hardware fidelity and algorithmic optimization to advance quantum cryptography.
The emergence of quantum computing poses significant threats to conventional public-key cryptography, driving the urgent need for quantum-resistant cryptographic solutions. While quantum key distribution addresses secure key exchange, its dependency on symmetric keys and point-to-point limitations present scalability constraints. Quantum Asymmetric Encryption (QAE) offers a promising alternative by leveraging quantum mechanical principles for security. This paper presents the first practical implementation of a QAE protocol on IBM Quantum devices, building upon the theoretical framework originally proposed by Yoon et al. We develop a generalized Grover Search Algorithm (GSA) framework that supports non-standard initial quantum states through novel diffusion operator designs, extending its applicability beyond idealized conditions. The complete QAE protocol, including key generation, encryption, and decryption stages, is translated into executable quantum circuits and evaluated on both IBM Quantum simulators and real quantum hardware. Experimental results demonstrate significant scalability challenges, with success probabilities deteriorating considerably for larger systems. The 2-qubit implementation achieves near-perfect accuracy (100% on the simulator, and 93.88% on the hardware), while performance degrades to 78.15% (simulator) and 45.84% (hardware) for 3 qubits, and declines critically to 48.08% (simulator) and 7.63% (hardware) for 4 qubits. This degradation is primarily attributed to noise and decoherence effects in current Noisy Intermediate-Scale Quantum (NISQ) devices, highlighting the limitations of single-iteration GSA approaches. Our findings underscore the critical need for enhanced hardware fidelity and algorithmic optimization to advance the practical viability of quantum cryptographic systems, providing valuable insights for bridging the gap between theoretical quantum cryptography and real-world implementations.
A coming great revolution in technology is quantum computing, which opens new attacks on most of the developed cryptographic algorithms, including AES. These emerging quantum capabilities risk weakening cryptographic techniques, which safeguard a vast amount of data across the globe. This research uses Grover's algorithm to explore the vulnerabilities of the Advanced Encryption Standard to quantum attacks. By implementing quantum cryptographic algorithms and Quantum Error Correction on simulators and quantum hardware, the study evaluates the effectiveness of these techniques in mitigating noise and improving the reliability of quantum computations. The study shows that while AES is theoretically at risk due to Grover’s algorithm, which demonstrates a theoretical reduction in AES key search complexity, current hardware limitations and noise levels encountered in today’s quantum computers reduce the immediate threat and limit practical exploitation. The research also examines NTRU encryption, a quantum-resistant alternative, highlighting its robustness in quantum environments. The findings emphasize the need for further development in QEC and quantum-resistant cryptography to secure digital communications against future quantum threats. Future work will focus on advancing QEC techniques and refining quantum algorithms, addressing both hardware and theoretical advancements, including the potential use of high-capacity processors like Jiuzhang 3.0. These improvements will ensure the scalability of quantum-resistant systems to practical key sizes and usage scenarios.
Quantum computing poses a significant threat to classical cryptographic algorithms, particularly the Advanced Encryption Standard (AES). This study investigates the impact of Grover's algorithm on the AES S-box, a fundamental component of the AES encryption process. By leveraging quantum mechanics, Grover's algorithm can potentially reduce the time required to break AES encryption from 2128operations to 264operations, thus presenting a substantial security risk. This research aims to evaluate the feasibility of such quantum attacks on AES S-box by conducting experiments using virtual quantum simulators. The study examines the resource requirements, including the number of gates and qubits, and assesses the scalability of Grover's algorithm across different data sizes and types. The findings indicate that, while theoretically effective, the practical implementation of Grover's algorithm is currently hindered by significant resource constraints on existing quantum hardware. These results underscore the need for continued advancements in quantum technology and the development of quantum-resistant cryptographic methods to ensure data security in the quantum era. This research contributes to the understanding of quantum vulnerabilities in classical cryptography and supports the development of robust encryption strategies that can withstand future quantum attacks.
With the growth of quantum computing hardware technology, more developers are becoming involved in the design and development of quantum algorithms, leading to the creation of practical applications that align with real-world needs through the combination of quantum hardware and software. Among quantum algorithms, the most well-known include Grover’s algorithm and Shor’s algorithm. Grover’s algorithm can quickly provide search results, making it highly valuable for search-related applications. In light of this, this study primarily examines the theoretical usability of Grover’s algorithm and explores its limitations. Additionally, on the practical side, this research implements Grover’s algorithm using IBM Quantum Computing and the IBM Qiskit package. By comparing simulation results with those obtained from execution on real quantum computers, the study discusses the current limitations of quantum computing hardware technology.
Quantum search is one of the most important algorithmic developments in quantum computing because it demonstrates how quantum principles can improve the efficiency of solving unstructured search problems. Grover’s algorithm provides a quadratic speed-up over classical linear search by reducing query complexity from O(N) to O(√N), where N represents the size of the search space. This review examines the principles, performance, and applications of Grover’s algorithm, with emphasis on its theoretical foundation and practical relevance. The discussion covers the roles of superposition, quantum interference, oracle operations, diffusion operators, and amplitude amplification in increasing the probability of measuring a desired solution. The manuscript also reviews the computational performance of quantum search in comparison with classical search methods and considers its relevance to database searching, combinatorial optimisation, cryptography, machine learning, bioinformatics, quantum chemistry, and materials science. The review highlights that Grover’s algorithm is not limited to database retrieval, as many computationally intensive problems can be reformulated as search or optimisation tasks. However, practical implementation remains constrained by current quantum hardware limitations, including decoherence, quantum noise, limited qubit availability, circuit depth, and the difficulty of designing efficient oracles. Despite these challenges, continuing progress in quantum hardware, error correction, cloud-based quantum platforms, and hybrid quantum-classical architectures suggests that quantum search will remain an important area of research. Overall, Grover’s algorithm represents a foundational quantum algorithm with significant theoretical value and potential long-term application in computational domains involving large and unstructured search spaces.
The K-SAT problem is a fundamental challenge in computational theory, widely used in artificial intelligence, cryptography, and optimization. Classical algorithms struggle with exponential time complexity, making them inefficient for large-scale instances. In this research, we propose an efficient quantum computing approach based on Grover’s algorithm to enhance the search process for satisfiable solutions in K-SAT problems. Our implementation leverages quantum superposition and amplitude amplification to explore multiple possible solutions simultaneously, reducing the search complexity from O (2ⁿ) in classical methods to O(√2ⁿ) in quantum computing. We design a quantum oracle that encodes the K-SAT clauses and integrates it into Grover’s iterative search framework. The performance is evaluated through Qiskit simulations, demonstrating a significant improvement in search efficiency compared to classical brute-force techniques. The results highlight the potential of quantum algorithms in solving complex combinatorial problems with enhanced speed and accuracy. This study contributes to the development of quantum-accelerated optimization methods, paving the way for real-world applications in machine learning, cryptanalysis, and large-scale data processing.