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Physical Review A

Quantum oblivious set-member decision protocol

Runhua Shi, Yi Mu, Hong Zhong, Shun Zhang

Published Aug 5, 2015• 38 citations
Publisher

Abstract

We present and define a privacy-preserving problem called the oblivious set-member decision problem, which allows a server to decide whether a private secret of a user is a member of his private set in an oblivious manner. Namely, if the secret belongs to his private set, he does not know which member it is. We propose a quantum solution to the oblivious set-member decision problem. Compared to classical solutions, the proposed quantum protocol achieves an exponential reduction in communication complexity, since it only needs $O(1)$ communication cost.

DOI
10.1103/physreva.92.022309

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We present and define a privacy-preserving problem called the oblivious set-member decision problem, which allows a server to decide whether a private secret of a user is a member of his private set in an oblivious manner. Namely, if the secret belongs to his private set, he does not know which member it is. We propose a quantum solution to the oblivious set-member decision problem. Compared to classical solutions, the proposed quantum protocol achieves an exponential reduction in communication complexity, since it only needs O(1)O(1)O(1) communication cost.
In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology.
In a recent paper [Phys. Rev. A 92, 022309 (2015)], the authors proposed a quantum oblivious set-member decision protocol, which is designed to allow a server to check whether a private secret of a user is a member of his private set in an oblivious manner. Such protocols should protect the privacies of both the server and the user. However, we find that the user in their protocol can steal $l\ensuremath{-}1$ bits of information about the server's private set by sending the false decoy states.
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.
Symmetrically private information retrieval, a fundamental problem in the field of secure multiparty computation, is defined as follows: A database DDD of NNN bits held by Bob is queried by a user Alice who is interested in the bit Db{D}_{b}Db​ in such a way that (1) Alice learns Db{D}_{b}Db​ and only Db{D}_{b}Db​ and (2) Bob does not learn anything about Alice's choice bbb. While solutions to this problem in the classical domain rely largely on unproven computational complexity theoretic assumptions, it is also known that perfect solutions that guarantee both database and user privacy are impossible in the quantum domain. Jakobi et al. [Phys. Rev. A 83, 022301 (2011)] proposed a protocol for oblivious transfer using well-known quantum key device (QKD) techniques to establish an oblivious key to solve this problem. Their solution provided a good degree of database and user privacy (using physical principles like the impossibility of perfectly distinguishing nonorthogonal quantum states and the impossibility of superluminal communication) while being loss-resistant and implementable with commercial QKD devices (due to the use of the Scarani-Acin-Ribordy-Gisin 2004 protocol). However, their quantum oblivious key distribution (QOKD) protocol requires a communication complexity of O(NlogN)O(N\mathrm{log}N)O(NlogN). Since modern databases can be extremely large, it is important to reduce this communication as much as possible. In this paper, we first suggest a modification of their protocol wherein the number of qubits that need to be exchanged is reduced to O(N)O(N)O(N). A subsequent generalization reduces the quantum communication complexity even further in such a way that only a few hundred qubits are needed to be transferred even for very large databases.
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.
We propose a cheat sensitive quantum protocol to perform a private search on a classical database which is efficient in terms of communication complexity. It allows a user to retrieve an item from the database provider without revealing which item he or she retrieved: if the provider tries to obtain information on the query, the person querying the database can find it out. The protocol ensures also perfect data privacy of the database: the information that the user can retrieve in a single query is bounded and does not depend on the size of the database. With respect to the known (quantum and classical) strategies for private information retrieval, our protocol displays an exponential reduction in communication complexity and in running-time computational complexity.