A quantum digital signature (QDS) is utilized to authenticate classical messages and offers information theoretical security guaranteed by the laws of quantum mechanics. Focusing on signing a one-bit message, previous continuous-variable quantum digital signature (CV-QDS) protocols that shared secret keys are generated by quantum key distribution, and it is only mentioned to suitably iterate the one-bit protocol for a multibit message. Although the CV-QDS protocol is unconditionally secure while sending single-bit messages, iterating the one-bit protocol in a naive way will allow some forgery attacks. In this paper, for signing one-bit and multibit messages, a CV-QDS protocol is proposed, on the condition that nonrepudiation and no forging are guaranteed. For one-bit and multibit schemes, we compare the difference in the distribution stage and messaging stage, analyzing the security as well as summarizing some formulas for calculation. We hope the protocol with continuous variables could further improve the performance of QDS.

• Received 8 July 2020
• Accepted 24 December 2020

DOI:https://doi.org/10.1103/PhysRevA.103.012410