In this paper, based on multi-arbitrators and the product states, a new quantum signature scheme (QSS) is proposed. In our scheme, two arbitrators are used to share private keys with the signer. The signer encodes the bit message into orthogonal product states, which are locally indistinguishable. Then, to produce the signature, the signer signs the product states with the key-controlled Hadamard operator and Y operator. Our scheme has the good virtues as follows. First, our signature not only has the security property of unforgeability, but also has the property of strong non-repudiation. Second, when signing a message and verifying a signature, the partners do not need to prepare or transmit any entangled particle. Third, the partners do not need to perform the state comparison algorithm. Fourth, the signer does not need to share any private key with the signature verifier. For our scheme, the signer only shares two private keys with the arbitrators. At last, in our scheme, the repudiation can be flexibly solved. Compared with the other schemes with semi-trusted arbitrator, ours has better performances in security, practicability and efficiency.
