Quantum Private Set Relational Computation Under Privacy Protectio

Quantum private set cardinalities,including quantum private intersection cardinality and quantum private concatenation cardinality,are one of the most important research directions in quantum cryptography,and its functions are to calculate the number of common customers and the total number of users without disclosing elements.Since quantum private set cardinality does not output specific elements,it can be used in scenarios with high privacy requirements,such as business alliances,distributed social networks,etc.Since quantum private set cardinality does not output specific elements,it has higher confidentiality of information.However,in the current context,quantum private set cardinality protocols require that all parties involved in the communication process are able to perform complex quantum operations or prepare more complex quantum states.Obviously,this is di cult to achieve because existing quantum devices are expensive.Therefore,this paper needs to consider a private set cardinalities protocol that is secure,e cient and reduces the quantum burden on participants.Further,as the number of participants increases,it is di cult to satisfy the requirements of some scenarios by calculating the collective cardinality with only two-party quantum private collective cardinality protocols,so multi-party quantum private collective cardinality protocols are more suitable for the future.The main findings and contributions of this paper are as follows.1.A two party semi-quantum private set cardinality protocol based on Greenberger-Home-Zeilinger(GHZ)states.This paper utilizes the entanglement of GHZ states to propose a semi-quantum private set cardinality protocol,which can help two semi-quantum participants to compute the private intersection cardinality and the private union cardinality,and realize the combination of semi-quantum concept and private set cardinalities to reduce the quantum power required by the participants.In this protocol,the information about the elements of the set is encoded into a private vector,and the participants perform the corresponding operations on the received particle sequence based on the private vector.With the help of a semi-honest third party,the participants can obtain the intersection cardinality and concatenation cardinality of their sets.By comparing this protocol with existing private set cardinalities protocols,this protocol ensures functionality and cost savings.To illustrate the security of the protocol,intercept-resend attacks,entanglementattachment attacks,man-in-the-middle attacks,and collusion between participants and external attackers are discussed.2.Multi-party quantum private set cardinalities protocol based on d-level single-particle states.This paper proposes a multi-party quantum private set cardinalities protocol based on d-level single particles,using a shift operation to encrypt the information of the participants.The intersection cardinality and union cardinality of multiple participants are computed with the help of a semi-honest third party.Compared with existing multi-party quantum private set cardinalities protocols,this protocol does not require much complex quantum operations and prepare complex quantum states.Security analysis shows that the protocol is resistant to intercept-resend attacks,TP attacks,collusion attacks,entanglement-attachment attacks,etc.