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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum private data sampling

David A. Fattal, Marco Fiorentino B, Raymond G. Beausoleil

Published Aug 11, 2009• 0 citations
Publisher

Abstract

We present a novel quantum communication protocol for "Private Data Sampling", where a player (Bob) obtains a random sample of limited size of a classical database, while the database owner (Alice) remains oblivious as to which bits were accessed. The protocol is efficient in the sense that the communication complexity per query scales at most linearly with the size of the database. It does not violate Lo's "no-go" theorem for one-sided twoparty secure computation, since a given joint input by Alice and Bob can result in randomly different protocol outcomes. After outlining the main security features of the protocol, we present our first experimental results.

DOI
10.1117/12.826727

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We present a novel quantum communication protocol for "Private Data Sampling", where a player (Bob) obtains a random sample of limited size of a classical database, while the database owner (Alice) remains oblivious as to which bits were accessed. The protocol is efficient in the sense that the communication complexity per query scales at most linearly with the size of the database. It does not violate Lo's "no-go" theorem for one-sided twoparty secure computation, since a given joint input by Alice and Bob can result in randomly different protocol outcomes. After outlining the main security features of the protocol, we present our first experimental results.
We present an unconditionally secure Oblivious Transfer protocol relying on two rounds of entanglement-free quantum communication. When played honestly, the protocol only requires the ability to measure a single qubit in a fixed basis, and to perform a coherent bit-flip (Pauli X) operation. We present a generalization to a "Private Data Sampling" protocol, where a player (Bob) can obtain a random sample of fixed size from a classical database of size N, while the database owner (Alice) remains oblivious as to which bits were accessed. The protocol is efficient in the sense that the communication complexity per query scales at most linearly with the size of the database. It does not violate Lo's "no-go" theorem for one-sided two-party secure computation, since a given joint input by Alice and Bob can result in randomly different protocol outcomes. Finally it could be used to implement a practical bit string commitment protocol, among other applications.
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.
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.
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.
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 104{10}^{4}104-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.
We propose a quantum solution to the classical private information retrieval (PIR) problem, which allows one to query a database in a private manner. The protocol offers privacy thresholds and allows the user to obtain information from a database in a way that offers the potential adversary, in this model the database owner, no possibility of deterministically establishing the query contents. This protocol may also be viewed as a solution to the symmetrically private information retrieval problem in that it can offer database security (inability for a querying user to steal its contents). Compared to classical solutions, the protocol offers substantial improvement in terms of communication complexity. In comparison with the recent quantum private queries [Phys. Rev. Lett. 100, 230502 (2008)] protocol, it is more efficient in terms of communication complexity and the number of rounds, while offering a clear privacy parameter. We discuss the security of the protocol and analyze its strengths and conclude that using this technique makes it challenging to obtain the unconditional (in the information-theoretic sense) privacy degree; nevertheless, in addition to being simple, the protocol still offers a privacy level. The oracle used in the protocol is inspired both by the classical computational PIR solutions as well as the Deutsch-Jozsa oracle.