Quantum signature with formal security proof

In recent years, the quantum signature protocol has been an important research topic due to its security against quantum adversaries. Although lots of quantum signature protocols have been presented, their security lacks the support of security model and formal security proof. Especially, their security against adaptively chosen-message attack cannot be proved. Some quantum signature protocols have exposed various security vulnerabilities due to their design defects and informal security analysis. In this paper, based on the single particles, a quantum signature protocol with formal security proof is proposed. In this protocol, the signatory signs the message by cloning the particles and encrypting their states with key-controlled unitary operations. Compared with other similar signature protocols, the advantages of this protocol are as follows: (1) The security of this protocol against forgery attack can be proved with formal security proof under the security model. Its security strictly depends on the principle of quantum unclonability. (2) The security proof need not use the assumption of random oracle. (3) The protocol need not prepare decoy particles for eavesdropping detection, thus saving quantum sources and simplifying the protocol. (4) In the protocol, it is unnecessary to prepare entangled quantum particles. (5) The qubit efficiency reaches 50%, even if the decoy particles are counted.