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Physics Letters A

Optimal eavesdropping in semi-quantum key distribution

Hasnaa Hajji, M. El Baz, Walter O. Krawec

Published Dec 3, 2025• 2 citations
Publisher
DOI
10.1016/j.physleta.2025.131174

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Quantum key distribution cannot satisfy some users without quantum capability, so semi-quantum key distribution emerges as the times required. Semi-quantum key distribution protocol is described as Alice has quantum ability to prepare and measure qubits with an arbitrary basis, while Bob only measures qubits with the computational basis or reflects qubits to Alice. However, most existing semi-quantum key distribution protocols have been performed with low eavesdropping detection probability. In this paper, we present an innovative semi-quantum key distribution protocol with high efficiency based on EPR and single-particle hybridization, in which the specific contents of {\scriptsize CTRL} or {\scriptsize SIFT} operations have been newly defined. Then, the security analysis indicates the proposed protocol is asymptotically secure with more high eavesdropping detection probability against individual eavesdropping attacks. Moreover, the efficiency analysis shows that the presented protocol is more efficient than similar literatures.
Summary Quantum Key Distribution (QKD) is a secure key sharing technology with unconditional security. Certain well-known protocols for QKD have been presented, which claim their security by means of higher eavesdropping error-rates. A generalized quantum key distribution protocol that can be optimized for arbitrary number of bases and dimensions of photon states is presented in this paper. The protocol can provide higher eavesdropping error-rates than the well-known existing QKD protocols like BB-84 [4] and B-92 [5]. The higher error-rate makes it possible for Alice and Bob to share secure keys on relatively large distances.
Research on optimal eavesdropping models under practical conditions will help to evaluate realistic risk when employing quantum key distribution (QKD) system for secure information transmission. Intuitively, fiber loss will lead to the optical energy leaking to the environment, rather than harvested by the eavesdropper, which also limits the eavesdropping ability while improving the QKD system performance in practical use. However, defining the optimal eavesdropping model in the presence of lossy fiber is difficult because the channel is beyond the control of legitimate partners and the leaked signal is undetectable. Here we investigate how the fiber loss influences the eavesdropping ability based on a teleportation-based collective attack model which requires two distant stations and a shared entanglement source. We find that if the distributed entanglement is limited due to the practical loss, the optimal attack occurs when the two teleportation stations are merged to one and placed close to the transmitter site, which performs similar to the entangling-cloning attack but with a reduced wiretapping ratio. Assuming Eve uses the best available hollow-core fiber, the secret key rate in the practical environment can be 20%~40% higher than that under ideal eavesdropping. While if the entanglement distillation technology is mature enough to provide high quality of distributed entanglement, the two teleportation stations should be distantly separated for better eavesdropping performance, where the eavesdropping can even approach the optimal collective attack. Under the current level of entanglement purification technology, the unavoidable fiber loss can still greatly limit the eavesdropping ability as well as enhance the secret key rate and transmission distance of the realistic system, which promotes the development of QKD systems in practical application scenarios.