The quantum digital signature (QDS) has attracted much attention as it ensures the nonrepudiation, unforgeability, and transferability of signature messages based on information-theoretic security. Amiri et al. ( Phys. Rev. A 93 032325 ) proposed the first practical QDS protocol based on orthogonal coding, which has realized information-theoretic security and become the mainstream paradigm in QDS research. The procedure of QDS involves two essential stages, the one is the distribution stage, in which Alice-Bob and Alice-Charlie individually utilize the three-intensity decoy-state quantum key distribution protocol but without error correction or privacy amplification, namely, key-generation protocol, to generate correlated bit strings, the other is the messaging stage, in which Alice transmits signature messages to the two recipients. However, previous theoretical and experimental studies both overlooked the modulation errors that may be introduced in the state preparation process due to the imperfections in modulator devices. Under the traditional framework of GLLP analysis method, these errors will significantly reduce the actual signature rates. Therefore, we propose a state-preparation-error tolerant QDS and use parameter analysis to characterize the state preparation error to make the simulation analysis more realistic. In addition, we analyze the signature rates of the present scheme by using the three-intensity decoy-state method. Compared with previous QDS protocols, our protocol almost shows no performance degradation under practical state preparation errors and exhibits a maximum transmission distance around 180 km. Furthermore, state preparation errors do not have a significant influence on the bit error rate induced by normal communication between the legitimate users or the one produced by an eavesdropper. These results prove that the method proposed in this paper has excellent robustness against state preparation errors and it can achieve much higher signature rates and signature distances than other standard methods. Besides, signature rates are basically unchanged under different total pulse numbers, which shows that our protocol also has good robustness against the finite-size effect. Additionally, in the key generation process, our method is only required to prepare three quantum states, which will reduce the difficulty of experiment realizations. Furthermore, the proposed method can also be combined with the measurement-device-independent QDS protocol and the twin-field QDS protocol to further increase the security level of QDS protocol. Therefore, our work will provide an important reference value for realizing the practical application of QDS in the future.
The quantum digital signature (QDS) has attracted much attention as it ensures the nonrepudiation, unforgeability, and transferability of signature messages based on information-theoretic security. Amiri et al. ( Phys. Rev. A 93 032325 ) proposed the first practical QDS protocol based on orthogonal coding, which has realized information-theoretic security and become the mainstream paradigm in QDS research. The procedure of QDS involves two essential stages, the one is the distribution stage, in which Alice-Bob and Alice-Charlie individually utilize the three-intensity decoy-state quantum key distribution protocol but without error correction or privacy amplification, namely, key-generation protocol, to generate correlated bit strings, the other is the messaging stage, in which Alice transmits signature messages to the two recipients. However, previous theoretical and experimental studies both overlooked the modulation errors that may be introduced in the state preparation process due to the imperfections in modulator devices. Under the traditional framework of GLLP analysis method, these errors will significantly reduce the actual signature rates. Therefore, we propose a state-preparation-error tolerant QDS and use parameter analysis to characterize the state preparation error to make the simulation analysis more realistic. In addition, we analyze the signature rates of the present scheme by using the three-intensity decoy-state method. Compared with previous QDS protocols, our protocol almost shows no performance degradation under practical state preparation errors and exhibits a maximum transmission distance around 180 km. Furthermore, state preparation errors do not have a significant influence on the bit error rate induced by normal communication between the legitimate users or the one produced by an eavesdropper. These results prove that the method proposed in this paper has excellent robustness against state preparation errors and it can achieve much higher signature rates and signature distances than other standard methods. Besides, signature rates are basically unchanged under different total pulse numbers, which shows that our protocol also has good robustness against the finite-size effect. Additionally, in the key generation process, our method is only required to prepare three quantum states, which will reduce the difficulty of experiment realizations. Furthermore, the proposed method can also be combined with the measurement-device-independent QDS protocol and the twin-field QDS protocol to further increase the security level of QDS protocol. Therefore, our work will provide an important reference value for realizing the practical application of QDS in the future.
Quantum key distribution (QKD) enables the establishment of shared keys between two distant users, Alice and Bob, based on the fundamental principles of quantum mechanics, and it has proven to possess information-theoretic security. In most of QKD systems, Alice and Bob require a shared reference frame, and real-time calibration of the reference frame increases system costs and reduces its performance. Fortunately, the reference-frame-independent QKD protocol has been proposed, overcoming reference-frame drift issues and receiving widespread attention. However, in practical QKD systems, the non-ideal characteristics of realistic devices introduce certain inconsistency between the theory and the practice. In real-world quantum key distribution systems, device imperfections can lead to security vulnerabilities, thereby reducing system security. For example, imperfections in the encoding apparatus at the source end may result in errors in the quantum states. The inherent defects in the detection part may cause after-pulse effects and dead-time effects, thus reducing the key rate. Therefore, in this work, we propose a practical state-preparation error tolerant reference-frame-independent quantum key distribution protocol by taking imperfections in both the source and the detectors into account. Moreover, a three-intensity decoy-state scheme for modeling analysis and numerical simulations is employed. In this protocol, we reduce the influence of state-preparation errors on the key rate by utilizing virtual state methods to precisely estimate the phase-error rate. Furthermore, by characterizing the effects of after-pulses and dead-time on the key rate, our protocol exhibits higher robustness and can effectively address issues related to detector imperfections. This approach can also be extended to other quantum key distribution protocols with higher security levels, such as measurement-device-independent quantum key distribution protocol and twin-field quantum key distribution, further mitigating the influence of device imperfections on practical implementation of QKD system. Therefore, our present work provide important reference value for putting the quantum key distributions into practical application.
Quantum digital signatures (QDSs), generating correlated bit strings among three remote parties for signatures through quantum law, can guarantee nonrepudiation, authenticity, and integrity of messages. Recently, a one-time universal-hashing QDS framework, exploiting the quantum asymmetric encryption and universal hash functions, has been proposed to significantly improve the signature rate and ensure unconditional security by directly signing the hash value of long messages. However, similar to quantum key distribution, this framework utilizes keys with perfect secrecy by performing privacy amplification that introduces cumbersome matrix operations, thereby consuming large computational resources, causing delays, and increasing failure probability. Here, we prove that, different from private communication, imperfect quantum keys with partial information leakage can be used for digital signatures and authentication without compromising the security while having eight orders of magnitude improvement on signature rate for signing a megabit message compared with conventional single-bit schemes. This study significantly reduces the delay for data postprocessing and is compatible with any quantum key generation protocols. In our simulation, taking two-photon twin-field key generation protocol as an example, QDS can be practically implemented over a fiber distance of 650 km between the signer and receiver. For the first time, this study offers a cryptographic application of quantum keys with imperfect secrecy and paves a way for the practical and agile implementation of digital signatures in a future quantum network.
In practical quantum key distribution systems, there inevitably exist errors in the quantum state preparation process due to imperfections in realistic equipment and devices. Those errors would lead to some security loopholes in the quantum key distribution systems. According to the work of Tamaki et al. ( Phys. Rev. A 90 052314 ), here in this work we propose a state preparation error tolerant quantum key distribution protocol through using heralded single-photon sources. In this protocol, we characterize the size of the error in the preparation state of Alice and bring it into the security analysis, thereby avoiding possible security loopholes and improving the security of the system. Moreover, we take the three-intensity decoy-state method for example to introduce the method of constructing the model and estimating the parameters, and carry out corresponding numerical simulations. We make a comparison between the loss tolerant protocol with weak coherent source (WCS) and our present protocol using heralded single-photon source (HSPS). Simulation results show that under the same state preparation error, the key generation rate of the protocol based on WCS is higher than that of protocol based on HSPS at short transmission distances (e.g. less than 150 km). The main reason is that the detection efficiency of the local detector used in the latter scheme is low. However, in the case of long transmission distances (e.g. greater than 200 km), the key generation rate of scheme with WCS drops deeply, while the decline of the key generation rate of the present scheme is much flatter. As a result, the former can no longer generate keys after 211 km, while the latter can transmit a maximum distance of 228 km. Moreover, we also make a comparison between the present scheme and the GLLP protocol with HSPS. The simulation results show that the GLLP protocol with HSPS is very sensitive to the state preparation error and its key generation rate will rapidly decrease with the increase of the state preparation error. On the contrary, our present protocol shows almost no performance degradation under practical state preparation errors. It thus verify the robustness against the state preparation errors of our present work. In addition, in principle, the method can also be combined with the measurement-device-independent quantum key distribution protocol and the twin-field quantum key distribution protocol to further increase the secure communication transmission distance that the present system can reach. Therefore, this work may provide an important reference value for the practical application of long-distance quantum secure communication in the near future.
Quantum digital signatures (QDS) are able to verify the authenticity and integrity of a message in modern communication. However, the current QDS protocols are restricted by the fundamental rate-loss bound and the secure signature distance cannot be further improved. We propose a twin-field quantum digital signature (TF-QDS) protocol with fully discrete phase randomization and investigate its performance under the two-intensity decoy-state setting. For better performance, we optimize intensities of the signal state and the decoy state for each given distance. Numerical simulation results show that our TF-QDS with as few as six discrete random phases can give a higher signature rate and a longer secure transmission distance compared with current quantum digital signatures (QDSs), such as BB84-QDS and measurement-device-independent QDS (MDI-QDS). Moreover, we provide a clear comparison among some possible TF-QDSs constructed by different twin-field key generation protocols (TF-KGPs) and find that the proposed TF-QDS exhibits the best performance. Conclusively, the advantages of the proposed TF-QDS protocol in signature rate and secure transmission distance are mainly due to the single-photon interference applied in the measurement module and precise matching of discrete phases. Besides, our TF-QDS shows the feasibility of experimental implementation with current devices in practical QDS system.
A quantum digital signature (QDS) guarantees the unforgeability, nonrepudiation, and transferability of signature messages with information-theoretic security, and hence has attracted much attention recently. However, most previous implementations of QDS showed relatively low signature rates and/or short transmission distance. In this Letter, we report a proof-of-principle phase-encoding QDS demonstration using only one decoy state. First, such a method avoids the modulation of the vacuum state, thus reducing experimental complexity and random number consumption. Moreover, incorporated with low-loss asymmetric Mach-Zehnder interferometers and a real-time polarization calibration technique, we have successfully achieved a higher signature rate, e.g., 0.98 bit/s at 103 km, and to date, a record-breaking, to the best of our knowledge, transmission distance of over 280-km installed fibers. Our work represents a significant step towards real-world applications of QDS.
Digital signatures can guarantee the unforgeability and transferability of the message. Differently from classical digital signatures, whose security depends on computational complexity, quantum digital signatures (QDSs) can provide information-theoretic security. We propose a general method of random-pairing QDS, which can drastically increase QDS efficiency. In a way, our random-pairing method provides a tightened result for the security level of QDS. In the method, the parity value of each pair is used for the outcome-bit value. We present general formulas for the fraction of untagged bits and error rates of the outcome bits. Random pairing can be applied as a fundamental method to increase the QDS efficiency for all existing quantum key distribution (QKD) protocols. We take the QDS with sending-or-not-sending protocol and the QDS with side-channel-free protocol as examples to demonstrate the advantage of random pairing through numerical simulation. A similar advantage with random pairing is also found with decoy-state measurement-device-independent QKD and also the decoy-state BB84 protocol. We study the random-pairing QDS with sending-or-not-sending protocol considering effects of finite data size through optimization. The numerical simulation results show that the signature rate can be increased by more than $100\mathrm{%}$ under a noisy channel using our random-pairing method.