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Optics Letters

Improved finite-size analysis for measurement-device-independent quantum digital signatures

Jiali Zhu, Chunhui Zhang, Qin Wang

Published Sep 15, 2025• 2 citations
Publisher

Abstract

Quantum digital signatures (QDS), based on the principles of quantum mechanics, provide information-theoretic security, ensuring the integrity, authenticity, and non-repudiation of data transmission. With current QDS protocols, measurement-device-independent QDS (MDI-QDS) can resist all attacks on detections, yet it suffers from finite-size effect. In previous schemes, the SOB-PE model is commonly adopted, in which the main idea is to sign only one bit at one time, resulting in a low signature rate. To solve this problem, we propose two parameter estimation models (SMB1-PE, SMB2-PE) for finite-size analysis to improve the performance. SMB1-PE and SMB2-PE models use X-basis or Z-basis data, respectively, to estimate the single-photon contributions of Z-basis. Simulation results show that SMB1-PE is least affected by the finite-size effect, effectively enhancing the signature rate. Therefore, our present can provide valuable references for practical applications of QDS.

DOI
10.1364/ol.569676

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Quantum digital signatures (QDS), based on the principles of quantum mechanics, provide information-theoretic security, ensuring the integrity, authenticity, and non-repudiation of data transmission. With current QDS protocols, measurement-device-independent QDS (MDI-QDS) can resist all attacks on detections, yet it suffers from finite-size effect. In previous schemes, the SOB-PE model is commonly adopted, in which the main idea is to sign only one bit at one time, resulting in a low signature rate. To solve this problem, we propose two parameter estimation models (SMB1-PE, SMB2-PE) for finite-size analysis to improve the performance. SMB1-PE and SMB2-PE models use X-basis or Z-basis data, respectively, to estimate the single-photon contributions of Z-basis. Simulation results show that SMB1-PE is least affected by the finite-size effect, effectively enhancing the signature rate. Therefore, our present can provide valuable references for practical applications of QDS.
Quantum digital signatures (QDS), based on the principles of quantum mechanics, provide information-theoretic security, ensuring the integrity, authenticity, and non-repudiation of data transmission. With present QDS protocols, measurement-device-independent QDS (MDI-QDS) can resist all attacks on detections, yet it suffers from finite-size effect. In this work, we present and compare three parameter estimation models for finite-size analysis of two-decoy MDI-QDS. The first model is a commonly used model in previous schemes, and we propose two new models to improve the performance. Subsequently, we perform numerical simulations to evaluate the performance of the three models. The results demonstrate that the proposed methods are less affected by finite-size effect, thereby effectively enhancing the signature rate. This work contributes to the practical development of QDS.
Quantum digital signatures (QDSs), which distribute and measure quantum states by key generation protocols and then sign messages via classical data processing, are a key area of interest in quantum cryptography. However, the practical implementation of a QDS network has many challenges, including complex interference technical requirements, linear channel loss of quantum state transmission, and potential side-channel attacks on detectors. Here, we propose an asynchronous measurement-device-independent (MDI) QDS protocol with asynchronous two-photon interference strategy and one-time universal hashing method. The two-photon interference approach protects our protocol against all detector side-channel attacks and relaxes the difficulty of experiment implementation, while the asynchronous strategy effectively reduces the equivalent channel loss to its square root. Compared to previous MDI-QDS schemes, our protocol shows several orders of magnitude performance improvements and doubling of transmission distance when processing multibit messages. Our findings present an efficient and practical MDI-QDS scheme, paving the way for large-scale data processing with nonrepudiation in quantum networks.
Digital signatures play an important role in software distribution, modern communication, and financial transactions, where it is important to detect forgery and tampering. Signatures are a cryptographic technique for validating the authenticity and integrity of messages, software, or digital documents. The security of currently used classical schemes relies on computational assumptions. Quantum digital signatures (QDS), on the other hand, provide information-theoretic security based on the laws of quantum physics. Recent work on QDS Amiri et al., Phys. Rev. A 93, 032325 (2016); Yin, Fu, and Zeng-Bing, Phys. Rev. A 93, 032316 (2016) shows that such schemes do not require trusted quantum channels and are unconditionally secure against general coherent attacks. However, in practical QDS, just as in quantum key distribution (QKD), the detectors can be subjected to side-channel attacks, which can make the actual implementations insecure. Motivated by the idea of measurement-device-independent quantum key distribution (MDI-QKD), we present a measurement-device-independent QDS (MDI-QDS) scheme, which is secure against all detector side-channel attacks. Based on the rapid development of practical MDI-QKD, our MDI-QDS protocol could also be experimentally implemented, since it requires a similar experimental setup.
Extending device-independent (DI) quantum cryptography to composably support all fundamental information security objectives is crucial for secure quantum networks. Achieving this goal requires composable quantum digital signatures (QDSs), which support integrity, authenticity, and nonrepudiation when integrated into quantum networks. Yet existing QDS protocols generally rely on assumptions about the underlying quantum devices, while their security analyses remain largely restricted to stand-alone settings, leaving related-key attacks on the underlying linear feedback shift register (LFSR)-based Toeplitz authentication unaddressed. Here, we establish the first composable security framework for QDS within constructive cryptography, and realize the corresponding ideal QDS resource by developing a DI-QDS protocol employing one-time universal hashing and multi-channel multiplexing. We further derive a related-key security bound for the underlying LFSR-based Toeplitz authentication, thereby establishing unforgeability while extending the forgery boundary considered in previous QDS security analyses. We also demonstrate the practical feasibility of our DI-QDS protocol under realistic quantum network conditions in the finite-size regime, with numerical simulations showing that it enables efficient signing of multibit documents over metropolitan-scale distances. Our results establish QDS as a composable cryptographic primitive and extend DI quantum cryptography to support the full range of information security objectives with composable security guarantees in future quantum networks.
The development of quantum networks will be paramount towards practical and secure telecommunications. These networks will need to sign and distribute information between many parties with information-theoretic security, requiring both quantum digital signatures (QDS) and quantum key distribution (QKD). Here, we introduce and experimentally realise a quantum network architecture, where the nodes are fully connected using a minimum amount of physical links. The central node of the network can act either as a totally untrusted relay, connecting the end users via the recently introduced measurement-device-independent (MDI)-QKD, or as a trusted recipient directly communicating with the end users via QKD. Using this network, we perform a proof-of-principle demonstration of QDS mediated by MDI-QKD. For that, we devised an efficient protocol to distil multiple signatures from the same block of data, thus reducing the statistical fluctuations in the sample and greatly enhancing the final QDS rate in the finite-size scenario.
Measurement-device-independent quantum key distribution (MDI-QKD) protocol can effectively resist all possible attacks targeting the measurement devices in a quantum key distribution (QKD) system, thus exhibiting high security. However, due to the protocol’s high sensitivity to channel attenuation, its key generation rate and transmission distance are significantly limited in practical applications. To improve the performance of MDI-QKD, researchers have proposed quantum-memory (QM)-assisted MDI-QKD protocol, which has enhanced the protocol's performance to a certain extent. Nevertheless, under finite-size conditions where the total number of transmitted pulses is limited, accurately estimating the relevant statistical parameters is still a challenge. As a result, existing QM-assisted MDI-QKD schemes still encounters issues such as low key rates and limited secure transmission distances. To solve these problems, this work proposes a novel improved finite-size QM-assisted MDI-QKD protocol. By utilizing quantum memories to temporarily store early-arriving pulses and release them synchronously, the protocol effectively reduces the influence caused by channel asymmetry. Additionally, the protocol introduces a four-intensity decoy-state method to improve the estimation accuracy of single-photon components. Meanwhile, to mitigate the influence of finite-length effects on QM schemes, the proposed protocol combines a collective constraint model and a double-scanning algorithm to jointly estimate scanning error counts and vacuum-related counts. This approach enhances the estimation accuracy of the single-photon detection rate and phase error rate under finite-size conditions, thereby significantly improving the secure key rate of the MDI-QKD system. Simulation results show that under the same experimental conditions, compared with the existing QM-assisted three-intensity decoy-state MDI-QKD protocol and the four-intensity decoy-state MDI-QKD protocol based on Heralded Single-photon Source (HSPS), the proposed protocol extends the secure transmission distance by more than 30 km and 100 km, respectively. This proves that under the same parameter settings, the proposed scheme exhibits significant advantages in both key rate and secure transmission distance. Therefore, this research provides important theoretical references and valuable benchmarks for developing long-distance, high-security quantum communication networks.