Research On Quantum Secret Sharing Protocol Based On Bell States

Quantum secret sharing is the expansion of the classical secret sharing in the quantumcryptography field; it is an important branch of quantum cryptography. In this thesis, detailedresearches of quantum secret sharing based on Bell states are done about the selection of unitaryoperations, dynamic parameters update, multiparty-to-multiparty and verifiability. The mainworks and creations are as follows:1. Quantum secret sharing protocol based on the one-particle transform of Bell states. Byanalyzing the security of a kind of quantum secret sharing protocols based on the one-particletransform of Bell states, we firstly propose a novel collective attack strategy based on both theentanglement swapping and intercept-and-resend. In our strategy, the group of in-attackers canobtain the entire secret information without introducing any error, by attacking different particlefrom different in-attacker separately. Secondly, we present the selection conditions of unitaryoperations that meet security requirements of the quantum secret sharing protocols, propose then-element phase shift operations set{U (i q)|q=2p/n, i=0,1, L, n-1}, characterize the relationbetween the set and the security of quantum secret sharing protocol, and prove that the3-elementphase shift operations set{U (0), U (2p/3), U(4p/3)}is the least one which satisfies the securityof quantum secret sharing protocol. At last, a new quantum secret sharing scheme is proposedbased on the3-element phase shift operations set. The scheme can resist not only the compoundentanglement swapping attack, but also the cheating attack from the dishonest agent. Comparedwith the Gao’s scheme, the scheme decrease the numbers of message transmissions and quantumstates preparations by reducing the number of the eavesdropping detections; based on theexchangeability of3-element phase shift operations set, the computation complexity of secretreconstruction is reduced from O (9(n-2))to O (n-2)by replacing the matrix multiplication withthe module addition.2. Research on dynamic quantum secret sharing protocol. To solve the problems of updatingsub-secrets or secret as well as adding or deleting agent in the quantum secret sharing, wepropose the two-particle transform of Bell states, which is the method of performing the differentlocal unitary operations chosen by the dealer and agent separately from the Pauli operations andthe3-element phase shift operations on two particles of Bell states. Based on this two-particletransform of Bell states, we present a novel dynamic quantum secret sharing protocol. The newquantum secret sharing protocol can resist the attack strategies such as the substitute-Bell-stateattack, the compound entanglement swapping attack and cheating attack from the dishonestagent. Based on the high coding-efficiency of two-particle transform of Bell states and the exchangeability of3-element phase shift operations set, the number of coding operations is thehalf of the secret bits, and the computation complexity of secret reconstruction is O (n-1).Furthermore, we take advantage of the new protocol to establish two kinds of quantum statesharing protocols for single quantum state and two-particle entangled states.3. Research on multiparty-to-multiparty quantum secret sharing protocol. A newmultiparty-to-multiparty quantum secret sharing protocol is proposed, which performs differentlocal operations on different particles of the Bell state, choosing separately from the3-elementphase shift operations and the combinations of Pauli operations and either Hadamard operationor I operation. This protocol can resist the attack strategies such as the dense-coding attack, thecollective intercept-and-resend attack, the entanglement swapping attack and the cheating attackfrom the dishonest agent. Compared with the existing protocols, the new protocol ishigh-efficient whose number of coding operations is reduced to half of them, and all the quantumstates can be used to transmit the secret. Based on the independence of operations of two-particletransform of Bell states, this protocol can update the sub-secrets and the group of agentsdynamically.4. Reseach on verifiable quantum secret sharing protocol. Firstly we analyze the security ofa kind of verifiable quantum (k, n) secret sharing protocol proposed by Yu-guang Yang et al, andprove that the protocol cannot resist the cheating attack from the dishonest agent. Furthermore,utilizing the method of message authentication, we present two kinds of verifiable quantumsecret sharing protocol based on quantum one-way function and the two-particle transform ofBell states respectively. Both of two protocols can resist the inner-cheating attack which thedishonest agent cannot obtain any secret message and escape from the eavesdropping detections.When the secret message is l bit, the numbers of quantum states prepared in the secretverification phase of two new protocols is reduced to2log2l and H k(l)respectively, whichhas the lower wastage of quantum states compared with Yang’ s protocol (its numbers ofquantum states is n (n-1)l).