Security Problems in the Quantum Signature Scheme with a Weak Arbitrator

Very recently, a quantum signature scheme with weak arbitrator was presented (Luo et al. in Int. J. Theor. Phys. 51:2135–2142, 2012). A weak arbitrator is only involved in the disagreement case, which means that the scheme is costless. In this paper, the security of the quantum signature scheme with weak arbitrator is analyzed. We show that attackers can counterfeit a signature for any message, which will pass the verification for the signer. In addition, they can counterfeit a signature for any one of the 4L (L is the length of the intercepted quantum message) messages by employing the known message attack, which will pass the verification for the signed message. In particular, by employing the Z-transform attack, the attackers can forge a signature for any one of the 2L messages, which will pass the verifications for both the signer and the signed message successfully.