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

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<i>X</i>-basis or <i>Z</i>-basis data, respectively, to estimate the single-photon contributions of <i>Z</i>-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.