Security of the arbitrated quantum signature protocols revisited

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Recently, much attention has been paid to the study of arbitrated quantum signature (AQS). Among these studies, the cryptanalysis of some AQS protocols and a series of improved ideas have been proposed. Compared with the previous analysis, we present a security criterion, which can judge whether an AQS protocol is able to prevent the receiver (i.e. one participant in the signature protocol) from forging a legal signature. According to our results, it can be seen that most AQS protocols which are based on the Zeng and Keitel (ZK) model are susceptible to a forgery attack. Furthermore, we present an improved idea of the ZK protocol. Finally, some supplement discussions and several interesting topics are provided.