Revisiting Quantum Asymmetric Key Cryptography: Enhancing Practical Implementations with a Generalized Grover Search Algorithm

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.