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arXiv:0806.0854 · Physical Review A

Comment on “Arbitrated quantum-signature scheme”

Marcos Curty, Norbert Lütkenhaus

Published Apr 30, 2008• 94 citations
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Abstract

We investigate the quantum signature scheme proposed by and Zeng and Keitel [Phys. Rev. A 65, 042312 (2002)]. It uses Greenberger-Horne-Zeilinger states and the availability of a trusted arbitrator. However, in our opinion the protocol is not clearly operationally defined and several steps are ambiguous. Moreover, we argue that the security statements claimed by the authors are incorrect.

DOI
10.1103/physreva.77.046301

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We investigate the quantum signature scheme proposed by and Zeng and Keitel [Phys. Rev. A 65, 042312 (2002)]. It uses Greenberger-Horne-Zeilinger states and the availability of a trusted arbitrator. However, in our opinion the protocol is not clearly operationally defined and several steps are ambiguous. Moreover, we argue that the security statements claimed by the authors are incorrect.
Abstract Zeng and Keitel proposed an arbitrated quantum signature scheme In 2002. Recently, Curty and Lütkenhaus pointed out that the protocol is not operationally specified. In a reply, Zeng gave more details of the scheme. The author also claimed that the scheme is suitable for unknown messages. In this letter, we remark that the invented scenario in the original scheme is artificial. This is because its security entirely depends on the presence of a trustworthy arbitrator. Moreover, the claim that the original scheme is suitable for unknown messages is not sound.
Zeng and Keitel proposed an arbitrated quantum signature scheme in 2002. Recently, Curty and Lütkenhaus pointed out that the protocol is not operationally specified. In a reply, Zeng gave more details of the scheme. The author also claimed that the scheme is suitable for unknown messages. In this letter, we remark that the invented scenario in the original scheme is artificial. This is because its security entirely depends on the presence of a trustworthy arbitrator. Moreover, the claim that the original scheme is suitable for unknown messages is not sound.
In an arbitrated quantum signature scheme, the signatory signs the message and the receiver verifies the signature's validity with the assistance of the arbitrator. We present an arbitrated quantum signature scheme using two-particle entangled Bell states similar to the previous scheme using three-particle entangled Greenberger-Horne-Zeilinger states [G. H. Zeng and C. H. Keitel, Phys. Rev. A 65, 042312 (2002)]. The proposed scheme can preserve the merits in the original scheme while providing a higher efficiency in transmission and reducing the complexity of implementation.
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.