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）通过量子规律在三个远程方之间生成相关比特串以实现签名，能够保障消息的不可否认性、真实性和完整性。近来，借助量子非对称加密与通用哈希函数的一次性通用哈希QDS框架被提出，该框架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确保了无条件安全性。然而，类似于量子密钥分发，该框架通过执行隐私放大来使用具有完美保密性的密钥，但隐私放大引入了繁琐的矩阵运算，从而消耗大量计算资源、造成延迟并增加失败概率。在此，我们证明与私有通信不同，有限信息泄露的非完美量子密钥可在不牺牲安全性的前提下用于数字签名与认证，且相比传统单比特方案，在签署兆比特消息时签名速率提升了八个数量级。本研究大幅降低了数据后处理延迟，并与任何量子密钥生成协议兼容。在仿真中，以双光子孪生场密钥生成协议为例，QDS可在签名方与接收方之间650公里光纤距离上实际实现。本研究首次提供了非完美保密性量子密钥的密码学应用，为未来量子网络中数字签名的实用化与敏捷化实施铺平了道路。