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Modern Physics Letters A

Two quantum private query protocols based on Bell states and single photons

Dong-Mei Liu, Lili Yan, Yan Zuo Chang, Shibin Zhang, Tian Cao

Published Jan 11, 2021• 7 citations

Abstract

This paper proposes two quantum privacy query protocols. In the single vector sub-privacy query of protocol 1, it is proposed for the first time to distinguish different measurement results by publishing 2 bits of classic information. In the protocol, the database Bob selects the Z base and the Bell base to measure the particles sent by Alice according to the key value of the encrypted database and publishes 2 bits of classic information based on the measurement results. The user Alice infers the key value of the encrypted database through these two pieces of classic information. In the two-way quantum privacy query of protocol 2, the database Bob measures the particles sent back by Alice, converts the measurement result into a key value of length 3, and prepares a particle that is the same as the measurement result and sends it back to Alice. Alice returns the measurement of particles can infer a set of data encryption keys, and the length of each key is 3 bits. Users in the two protocols proposed in the article can obtain the query key with a probability of 1/4. As the key length increases, the number of query bits in protocol 2 decreases, but the probability of execution failure increases. But protocol 2 has a higher quantum efficiency. Both protocols can guarantee the privacy of users and databases.

DOI: 10.1142/s021773232150005x

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Abstract In order to protect the privacy of query user and database, some QKD-based quantum private query (QPQ) protocols were proposed. Unfortunately some of them cannot resist internal attack from database perfectly; some others can ensure better user privacy but require a reduction of database privacy. In this paper, a novel two-way QPQ protocol is proposed to ensure the privacy of both sides of communication. In our protocol, user makes initial quantum states and derives the key bit by comparing initial quantum state and outcome state returned from database by ctrl or shift mode instead of announcing two non-orthogonal qubits as others which may leak part secret information. In this way, not only the privacy of database be ensured but also user privacy is strengthened. Furthermore, our protocol can also realize the security of loss-tolerance, cheat-sensitive, and resisting JM attack etc.

As a kind of practical protocol, quantum-key-distribution (QKD)-based quantum private queries (QPQs) have drawn lots of attention. However, joint-measurement (JM) attack poses a noticeable threat to the database security in such protocols. That is, by JM attack a malicious user can illegally elicit many more items from the database than the average amount an honest one can obtain. Taking Jacobi et al.'s protocol as an example, by JM attack a malicious user can obtain as many as 500 bits, instead of the expected 2.44 bits, from a

{10}^{4}

-bit database in one query. It is a noticeable security flaw in theory, and would also arise in application with the development of quantum memories. To solve this problem, we propose a QPQ protocol based on a two-way QKD scheme, which behaves much better in resisting JM attack. Concretely, the user Alice cannot get more database items by conducting JM attack on the qubits because she has to send them back to Bob (the database holder) before knowing which of them should be jointly measured. Furthermore, JM attack by both Alice and Bob would be detected with certain probability, which is quite different from previous protocols. Moreover, our protocol retains the good characters of QKD-based QPQs, e.g., it is loss tolerant and robust against quantum memory attack.

By adding a parameter θ in M. Jakobi et al's protocol [Phys. Rev. A 83, 022301 (2011)], we present a flexible quantum-key-distribution-based protocol for quantum private queries. We show that, by adjusting the value of θ, the average number of the key bits Alice obtains can be located on any fixed value the users wanted for any database size. And the parameter k is generally smaller (even k = 1 can be achieved) when θ < π/4, which implies lower complexity of both quantum and classical communications. Furthermore, the users can choose a smaller θ to get better database security, or a larger θ to obtain a lower probability with which Bob can correctly guess the address of Alice's query.

Abstract In order to protect the privacy of the query user and database, some QKD-based quantum private query (QPQ) protocols were proposed. One example is the protocol proposed by Zhou et al, in which the user makes initial quantum states and derives the key bit by comparing the initial quantum state and the outcome state returned from the database by ctrl or shift mode, instead of announcing two non-orthogonal qubits as others which may leak part secret information. To some extent, the security of the database and the privacy of the user are strengthened. Unfortunately, we find that in this protocol, the dishonest user could be obtained, utilizing unambiguous state discrimination, much more database information than that is analyzed in Zhou et al’s original research. To strengthen the database security, we improved the mentioned protocol by modifying the information returned by the database in various ways. The analysis indicates that the security of the improved protocols is greatly enhanced.

As an important topic in quantum secure multiparty computing, quantum privacy query (QPQ) can solve the problem of information query between users and database owners without compromising privacy. In the existing research, most of them focus on its functions, not its applications. In this paper, a new QPQ protocol based on two-particle states is proposed. In our protocol, we use two-particle states combined with the Ctrl or Shift operations to give the user a partial key sequence and the database cannot recognize the user's key sequence. Meanwhile, we conduct simulation experiments at the IBM quantum experience and show that it is feasible. We discuss its application in the private set intersection (PSI), which is derived from QPQ. According to our analysis, the QPQ protocol and PSI protocol are secure.