Quantum Secure Multi-party Computation Based On Quantum Fourier Transform

With the expansion of the quantum information in the pratical application,quantum cryptography has developed rapidly.As a research branch of the quantum cryptography,quantum secure multi-party computation(QSMC)is a new research area which is combined with secure multi-party computation and quantum information.It overcomes the difficulty of classical secure multi-party computation relying on computational complexity.QSMC has the advantages in terms of efficiency and security of computation and has the properties of unconditional security and detectability of eavesdropping.This paper designs two new protocols for quantum secure multi-party computation,in order to provides more thoughts and methods for QSMC.This paper first proposes a novel secure multi-party quantum summation protocol based on quantum Fourier transform,where the travelling particles are transmitted in a tree-type mode.The party who prepares the initial quantum states is assumed to be semi-honest,which means that he may misbehave on his own but will not conspire with anyone.The proposed secure multi-party quantum summation protocol can resist both the outside attacks and the participant attacks.Especially,one party cannot obtain other parties;private integer strings;and it is secure for the colluding attack performed by at most n-2 parties,where n is the number of parties.Next,by incorporating quantum summation into quantum key agreement(QKA),this paper puts forward a new concept named quantum summation agreement(QSA),and construct a novel secure multi-party QSA protocol based on quantum Fourier transform,where the travelling particles are transmitted in a complete-graph-type mode.The proposed secure multi-party QSA protocol can resist both the outside attacks and the participant attacks.In this protocol,nontrivial subset of parties cannot succeed in determining the shared computation result of summation alone.In addition,both of the two proposed protocols calculate the addition of modulo d,and implement the calculation of addition in a secret-by-secret way rather than a bit-by-bit way.