Security analysis and improvement of a quantum multi-signature protocol

Recently, Jiang et al. proposed a novel quantum multi-signature protocol based on locally indistinguishable orthogonal product states. Unfortunately, their protocol cannot resist against the forgery attack and disavowal attack. We investigate the security of Jiang et al.’s quantum multi-signature protocol and demonstrate the signature receiver’s forgery attack. What is more, the signature receiver can extend the forgery attack such that anyone can generate the forgery. On the other hand, their protocol is insecure against the signers’ disavowal attack, too. Then, an improved quantum multi-signature protocol is proposed. In the improved protocol, all the signers share the private keys with the signature receiver and the arbitrator. To generate a quantum multi-signature, all the signers perform the unitary operations controlled by the private keys and the message. The improved protocol overcomes all the security drawbacks of Jiang et al.’s quantum multi-signature. What is more, the arbitrator Trent can be semi-trusted, because he cannot forge any quantum signature of the signers, although Trent shares the private keys with all the signers. At the same time, the new protocol has the same quantum efficiency as that of Jiang et al.’s protocol.