Research On Quantum Private Size Comparison Protocols Based On Quantum Entangled States

Theoretically,quantum communication can guarantee the unconditional security of communication based on the basic principles or characteristics of quantum mechanics.Quantum Private Comparison(QPC)is one of the hot research projects in quantum communication.It refers to the fact that a private comparison protocol is proposed based on the quantum technology conditions such as the preparation,regulation and measurement of quantum states.Namely,two or more participants holding privacies,using the quantum state as the information carriers,can obtain the equal and size relationship of their privacies without revealing them by implementing a quantum communication protocol(the manipulation processes of quantum states).The manipulation technique of quantum state cannot be separated from the progress of material science.For example,the barium metaborate is the key device for the preparation of entangled states by parametric down conversion.The QPC with high commercial value can be applied in secret ballot elections,private bidding and auctions,confidential transactions and so on.Compared with other mature quantum communication technologies,the research about the QPC is still in the theoretical and experimental stage.The core equipment of QPC and the progress of material preparation are first described in the paper,and then four different types of QPC protocols are proposed using several kinds of entangled states as signal source as follows:1.A feasible comparison protocol of multi-party quantum privacy based on the ddimensional Bell states is proposed.In the protocol,all participants can independently encrypt their privacies and send them to a semi-honest quantum third party through authenticated channels.Then,the third party can determine the size relationship among all participants’ privacies without gaining access to the private information.We verify correctness and effectiveness of the proposed protocol with some examples.In addition,compared with other similar protocols,it is not necessary to perform unitary operation on particles and only single-particle measurement is required.Furthermore,the relatively high qubit efficiency is promised.The security analysis verifies that the proposed protocol can counteract external and internal attacks.However,the QPC protocol requires each participant to be able to perform quantum operations and carry quantum devices.2.A novel efficient comparison protocol of semi-quantum privacy based on the ddimensional GHZ states is proposed.With the assistance of semi-honest third party,two classical participants can compare the size relation of their privacies without any information leakage.To reduce the consumption of quantum devices,the semi-quantum conception is introduced in this research.Compared with other SQPC protocol,the qubit efficiency is improved.Furthermore,it is unnecessary to prepare the secure classical authentication channel among participants in advance.It is shown that our protocol is not only correct and efficient,but also free from external and internal attacks.However,the protocol can only accommodate two classical participants at a time for a private comparison.3.Based on the d-dimensional multiparticle maximal entangled states,a novel multiparty private comparison protocol under semi-quantum condition is proposed.With the help of a semi-honest quantum third party,N classical participants can determine the size relationship of their privacies while keeping them private in devised protocol.Compared with some similar protocols,the presented protocol performs better in terms of security and qubit efficiency.In addition,the effectiveness and the correctness of our protocol are verified with some examples and proofs.By the decoy particles and the pre-shared keys,the presented protocol can defend against the internal and the external attacks.4.Taking the high-dimensional quantum state as the signal source is the mainstream choice in most QPC protocols,such as the three protocols proposed above in this paper.However,under the existing conditions of quantum information processing technology,it is difficult to manipulate the high-dimensional quantum states.Therefore,the practicability and engineering feasibility of this kind of QPC protocol are low.Considering this situation,an innovative protocol is proposed in this paper.The presented protocol utilizes only 2-dimensional Bell states to significantly enhance its feasibility under the current conditions of quantum technology.Furthermore,the protocol enables multiple participants to compare their privacies based on the semi-quantum model.The communication processes of the protocol are also simulated on the IBM Quantum Experience platform to validate its effectiveness.Security analysis shows that the proposed protocol can withstand common attacks while preserving all participants’ privacies.