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A quantum proxy signature scheme makes the proxy signer can generate a quantum signature on behalf of the original signer. Although many quantum proxy signature schemes have been proposed, none of them can be formally proved to be secure. There is not even security model for the quantum proxy signatures. Some quantum proxy signature schemes have been proved to be insecure against forgery attacks. In this paper, first, the formal definition and the corresponding security model for the quantum proxy signatures are proposed. Second, based on the Hadamard operator and the controlled NOT operation, a new quantum proxy signature scheme is proposed. The security of our quantum proxy signature scheme can be formally proved under security model. The security model of the quantum proxy signatures is helpful for analyzing and improving the security of the quantum proxy signature schemes. On the other hand, compared with the other quantum proxy signatures, the new one proposed in this paper is the first that can be formally proved to be secure under security model.

Based on the Hadamard operator and Bell states, an identity-based public-key quantum signature scheme is proposed. In our scheme, the signer’s identity is used as her public key. Her private keys are generated by the trusted private key generator (PKG). Given a quantum signature, the verifier can verify the validity of the quantum signature by the signer’s identity information without any public-key certificate. So, our quantum signature has the advantages of the identity-based signature system. On the other hand, in our scheme, it need not use the long-term quantum memory. The verifier need not perform any quantum swap test or state comparison algorithm. What is more, our quantum signature is secure against PKG’s forgery attack. And the disputation of losing quantum signature can be arbitrated by PKG. Therefore, our scheme is relatively more practical and efficient than the similar schemes.

Certificateless public key cryptography is an attractive paradigm which combines advantages of both traditional public key cryptography and identity-based cryptography because it avoids using certificates and does not suffer from key escrow. In this paper, the author proposed a certificateless signature (CLS) scheme built upon bilinear pairings and proved its security in the standard model. The schemeturns out to be more efficient than other proposed CLS schemes in the standard model, and the signin algorithm needs no pairing operation while the reverse operation requires only three pairing computations.