Design And Analysis Of Quantum Proxy Blind Multi-signature Protocol

As an important branch of cryptography,the digital signature has been widely applied in providing safe electronic communications.The digital signature has such characteristics as identity authentication,non-repudiation and data integrity,which is suitable for the security of some tasks,such as secure payment in electronic trading system,secure signing of electronic contract and so on.Most of the current digital signature schemes are based on public key cryptography,in which the security is based on the computational complexity of some mathematical problems:discrete logarithm,large integer prime factorization and so on.With the improvement of computing power,especially the advent of quantum computers,all digital signature schemes based on computational complexity will become insecure.Obviously,it needs new digital signature which can provide information security,instead of the computational security.Quantum signature is different from traditional digital signature.It is a new signature scheme that can realize digital signature method by using the idea of quantum physics,and its security is guaranteed by the basic principle of quantum mechanics which has been proved to be unconditionally secure.Therefore,more and more attention has been paid to quantum signature.In current quantum proxy blind signature protocols,one proxy signer can only represent one original signer.In this paper,we mainly study quantum proxy blind multi-signature protocols.Based on quantum entanglement and quantum teleportation,two quantum proxy blind multi-signature protocols are proposed,respectively,and we analyze their security and efficiency in detail.The main research results are listed as follows:(1)A quantum proxy blind multi-signature protocol with public verifiability was proposed.Based on the GHZ states,the proposed protocol employs secret sharing to realize the authorization of the proxy signer from multiple original signers,and utilizes the classic encoding methods to implement the signature and verification of quantum bit string.Without using the verifier's key in the generation of the signature,everyone can verify whether the signature is effective or not by the features of quantum one-way function and the unitary operation,so there is a better prospect of its applications.The security of the proposed protocol depends on quantum key distribution and one-time pad,which can ensure the unconditional security.(2)A quantum proxy blind multi-signature protocol based on quantum teleportation was presented.According to good advantages of phase rotation operation,this protocol can not only achieve the multi-signature(i.e.,a proxy represents multiple signers to generate the multi-signature),but can also ensure that the operator complexity of the proxy is independent of the number of the original signers.In this protocol,the owner of messages first sends two particle sequences in Bell states to the original signers and the verifier,respectively.Furthermore,one by one,all original signers perform a phase rotation operator on each particle in the sequence received from the previous one by their shared key,and the last original signer sends the sequence to the proxy signer.According to the certificates authorized by the original signers,the proxy signer performs the inverse operators to restore Bell states shared between the proxy signer and the verifier.Then it makes Bell measurements on each pair of particles in his hands,where one is in the sequence selected from Bell states and the other is in the blind-message sequence,and then generates the signatures by encrypting the measurement results.Finally,the verifier performs the corresponding operators on the other particles in Bell states by the public information to get the verification sequence,and further determinates whether the signature is valid by the comparisons of the verification sequence and the blind-message sequence.This protocol has good performances,such as higher security and relatively-simple technical requirements.The theoretical analysis shows that the two proposed schemes cannot only meet signature's properties of non-repudiation,forgery and blindness in security,but can also have better efficiency in the signing phase compared with previous schemes.