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Entropy

A New Quantum Private Protocol for Set Intersection Cardinality Based on a Quantum Homomorphic Encryption Scheme for Toffoli Gate

Wen Liu, Yangzhi Li, Zhirao Wang, Yugang Li

Published Mar 16, 2023• 12 citations
Publisher

Abstract

Set Intersection Cardinality (SI-CA) computes the intersection cardinality of two parties' sets, which has many important and practical applications such as data mining and data analysis. However, in the face of big data sets, it is difficult for two parties to execute the SI-CA protocol repeatedly. In order to reduce the execution pressure, a Private Set Intersection Cardinality (PSI-CA) protocol based on a quantum homomorphic encryption scheme for the Toffoli gate is proposed. Two parties encode their private sets into two quantum sequences and encrypt their sequences by way of a quantum homomorphic encryption scheme. After receiving the encrypted results, the semi-honest third party (TP) can determine the equality of two quantum sequences with the Toffoli gate and decrypted keys. The simulation of the quantum homomorphic encryption scheme for the Toffoli gate on two quantum bits is given by the IBM Quantum Experience platform. The simulation results show that the scheme can also realize the corresponding function on two quantum sequences.

DOI
10.3390/e25030516

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Set Intersection Cardinality (SI-CA) computes the intersection cardinality of two parties' sets, which has many important and practical applications such as data mining and data analysis. However, in the face of big data sets, it is difficult for two parties to execute the SI-CA protocol repeatedly. In order to reduce the execution pressure, a Private Set Intersection Cardinality (PSI-CA) protocol based on a quantum homomorphic encryption scheme for the Toffoli gate is proposed. Two parties encode their private sets into two quantum sequences and encrypt their sequences by way of a quantum homomorphic encryption scheme. After receiving the encrypted results, the semi-honest third party (TP) can determine the equality of two quantum sequences with the Toffoli gate and decrypted keys. The simulation of the quantum homomorphic encryption scheme for the Toffoli gate on two quantum bits is given by the IBM Quantum Experience platform. The simulation results show that the scheme can also realize the corresponding function on two quantum sequences.
Private Set Intersection Cardinality (PSI-CA) and Private Set Union Cardinality (PSU-CA) are two cryptographic primitives whereby two or more parties are able to obtain the cardinalities of the intersection and the union of their respective private sets, and the privacy of their sets is preserved. In this paper, we propose a three-party protocol to finish these tasks by using quantum resources, where every two, as well as three, parties can obtain the cardinalities of the intersection and the union of their private sets with the help of a semi-honest third party (TP). In our protocol, GHZ states play a role in encoding private information that will be used by TP to compute the cardinalities. We show that the presented protocol is secure against well-known quantum attacks. In addition, we analyze the influence of six typical kinds of Markovian noise on our protocol.
Private Set Intersection Cardinality (PSI-CA) is one of the most concerned issues with the protection of privacy, in which two parties jointly compute the intersection cardinality without revealing their respective private sets. There are important applications of PSI-CA in real society, e.g., strongly privacy-preserving data statistics in contact tracing for health authorities to fight the outbreaks of highly contagious diseases. In this paper, we present a novel quantum PSI-CA protocol, in which we adopt oblivious quantum key distribution, secure quantum summation and quantum counting algorithm. The proposed PSI-CA protocol not only ensures the approximatively perfect security but also achieves the linear communication complexity, i.e.,O(N){O(N)}O(N). Furthermore, we define a new privacy protection problem, i.e., Privacy-preserving Condition Query (PCQ), and provide an efficient solution to the PCQ problem based on the proposed quantum PSI-CA protocol. Finally, we verify the correctness and the feasibility of the proposed quantum PSI-CA protocol by circuit simulations in IBM Qiskit.
Recently, we proposed a quantum solution to the problem of private set intersection cardinality (PSI-CA) (Information Sciences 370–371 (2016) 147–158). Compared to classical solutions, the proposed quantum PSI-CA protocol achieves an exponential reduction in communication complexity, since it only needsO(1)O(1)O(1)communication cost. However, this protocol requires two additional assumptions about the cardinalities of the sets, which may limit its wider applications. In this paper, we successfully discard these assumptions and present a stronger quantum PSI-CA protocol without any limitation. The new protocol ensures the parties’ private security, i.e., unconditionally secure server privacy and statistically secure client privacy, and it achieves the constant computation and communication complexities, which are independent of the size of the sets. Therefore, it is more suitable for practical applications with big data sets.
Private Set Intersection Cardinality (PSI - CA) is a cryptographic primitive through which two or more participants can obtain the intersection cardinality of their private sets and the privacy of the sets is protected. In this paper, we propose a tripartite protocol that utilizes quantum resources to accomplish these tasks, in which each two or more parties can obtain the intersection cardinality of their private sets with the help of semi-honest third parties (TP). Using this property, a voting protocol is designed. In our protocol, the GHZ state is used to encode private information that TP will use to compute the cardinality. We prove that the proposed protocol is secure against well-known quantum attacks. Furthermore, compared with existing quantum voting schemes, the protocol achieves higher efficiency.
Private Set Intersection Cardinality (PSI-CA) is to compute privately the cardinality of the intersection of two sets, and there are many practical applications of PSI-CA, e.g., data mining and data analysis with the privacy protection. The current classical protocols for PSI-CA could not resist the attacks of quantum computers. In this paper, we present a novel quantum protocol for PSI-CA based on the basic laws of quantum mechanics, which can resist well-known quantum attacks. This protocol utilizes single photons as quantum resources and only needs to apply simple single-photon operators and measurements. Therefore, it is more feasible to implement this protocol, compared with the related quantum protocols, which require entangled states and other complicated operators.
In this paper, we introduce a quantum private set intersection (QPSI) scheme that leverages Bell states as quantum information carriers. Our approach involves encoding private sets into Bell states using unitary operations, enabling the computation of the intersection between two private sets from different users while keeping their individual sets undisclosed to anyone except for the intersection result. In our scheme, a semi-honest third party (TP) distributes the first and second qubits of the Bell states to the two users. Each user encodes their private sets by applying unitary operations on the received qubits according to predefined encoding rules. The modified sequence is encrypted and then sent back to TP, who can compute the set intersection without learning any information about the users’ private inputs. The simulation outcomes on the IBM quantum platform substantiate the viability of our scheme. We analyze the security and privacy aspects of the sets, showing that both external attacks and internal threats do not compromise the security of the private inputs. Furthermore, our scheme exhibits better practicality by utilizing easily implementable Bell states and unitary operations, rather than relying on multiple encoded states for set intersection calculations.