Quantum digital signatures (QDS), generating correlated bit strings among three remote parties for signatures through quantum law, can guarantee non-repudiation, authenticity, and integrity of messages. Recently, 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 limited 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.

翻译：量子数字签名（QDS）利用量子定律在三个远程参与方之间生成相关比特串以完成签名，能够保证消息的不可否认性、真实性和完整性。近年来，借助量子非对称加密和通用哈希函数的一次性通用哈希QDS框架被提出，通过直接对长消息的哈希值进行签名，显著提升了签名速率并保证了无条件安全性。然而，与量子密钥分发类似，该框架通过执行隐私放大来使用具有完美保密性的密钥，而隐私放大过程涉及繁琐的矩阵运算，从而耗费大量计算资源，导致延迟增加并提高了失败概率。在此，我们证明：与私人通信不同，在数字签名和认证中可以使用存在有限信息泄露的非完美量子密钥，且安全性不受影响；同时，与传统的单比特方案相比，在签名一兆比特消息时签名速率可提升八个数量级。本研究大幅减少了数据后处理延迟，并兼容任何量子密钥生成协议。在我们的仿真中，以双光子孪生场密钥生成协议为例，QDS可在签名者与接收者之间650公里的光纤距离上实现实际部署。本研究首次提供了具有非完美保密性量子密钥的密码应用，为未来量子网络中数字签名的实用化与灵活化实现铺平了道路。