New Quantum Private Comparison Protocol Without Entanglement

Abstract

After analyzing the main quantum private comparison (QPC) protocols based on the entanglement states, we propose a new QPC protocol using only polarized single photons. It will be shown that entanglement is not necessary for QPC. Most importantly, it will be pointed out that QPC protocols can be constructed by adapting the current quantum three-party secret sharing models properly. protocols are, or can be rephrased to be, special cases of the multiparty computation problems. Design and analysis of the special multiparty computation protocols is meaningful and has attracted much interest in this¯eld.In the traditional secure two-party computation scenario, 2,3 Alice has secret input x, Bob has secret input y, and both of them wish to compute fðx; yÞ which is wellknown to the two parties; the usual example is that of Yao's millionaires' problem to determine who is richer than whom without knowing each others' actual property. 3 Based on Yao's millionaires' problem, Boudot 4 subsequently proposed a protocol to decide whether two millionaires are equally rich. However, Lo 5 pointed out that the equality function cannot be securely evaluated with a two-party scenario. Therefore, a third party is necessary to reach the goal of private comparison. Now, private comparison of equality problem has been discussed and attracted more and more attention in the quantum cryptographic¯eld. Recently, Yang et al. 6 proposed the¯rst e±cient quantum private comparison (QPC) protocol based on the decoy photons and two-photon entangled EinsteinÀPodolskyÀRosen (EPR) pairs. Yang's protocol included a dishonest TP. Then, Chen et al. 7 proposed a new protocol for dealing with the private comparison of equal information based on the triplet GreenbergerÀHorneÀZeilinger (GHZ) entangled states. In Ref. 8, Tseng et al. proposed a new QPC protocol using EPR pairs. And this protocol provided easier implementation as well as better qubit e±ciency than the other QPCs. In Refs. 9 and 10, Liu et al. proposed two new QPC protocols based on the triplet W states and -type genuine four-particle entangled states. These two protocols also included a semihonest TP. Enlightened by the works of Refs. 6À10, Liu et al. proposed a new protocol for dealing with the private comparison of equal information based on -type state. 11 These protocols also included a semi-honest TP. 7À11 The role of the semi-honest TP is to execute the protocol loyally and record all the results of its intermediate computations. However, TP might try to steal the information from the record.After reading Refs. 6À11 we¯nd that the entangled states are used in all these protocols. Although prior research 12À18 has experimentally proven the feasibility of Bell states, entanglement is not necessary for QPC. In this paper, we propose a new QPC protocol using only polarized single photons. Most importantly, we¯nd that QPC protocols can be constructed by adapting the current quantum three-party secret sharing models properly. To show our view of point, we present our new QPC protocol by adapt...

Device-independent quantum private comparison protocol without a third party

“…QPC is also covered. To circumvent the problem, almost all existing QPC protocols ( [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] and the references therein) added a third party to help Alice and Bob accomplish the comparison. The protocol in Ref.…”

Quantum private comparison protocol without a third party

“…Quantum private comparison (QPC) is also covered. To circumvent the problem, almost all existing QPC protocols ( [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and the references therein) added a third party to help Alice and Bob accomplish the comparison. The only exception is Ref.…”

Quantum protocols for the millionaire problem with a third party are trivial

“…Therefore, many quantum protocols were proposed. Jia et al [9] gave a solution to the millionaire problem, while the others [10][11][12][13][14][15][16][17][18][19][20][21][22] studied the socialist millionaire problem under the name "quantum private comparison" (QPC).…”

“…Moreover, our protocols have two security advantages over the others. First, we will show that all previous protocols [9][10][11][12][13][14][15][16][17][18][19][20][21][22] inevitably leak a non-trivial amount of information to Trent or both Alice and Bob, while in our protocols this can be avoided. Secondly, a dishonest Trent can spoil many of the previous protocols [9,[13][14][15][16][17][18][19][20][21][22].…”

“…First, we will show that all previous protocols [9][10][11][12][13][14][15][16][17][18][19][20][21][22] inevitably leak a non-trivial amount of information to Trent or both Alice and Bob, while in our protocols this can be avoided. Secondly, a dishonest Trent can spoil many of the previous protocols [9,[13][14][15][16][17][18][19][20][21][22]. That is, he can mislead Alice and Bob to wrong results even though it brings no advantage to himself.…”