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Quantum Private Information Retrieval

Ämin Baumeler

Published Jan 1, 2012• 2 citations
Publisher

Abstract

This thesis discusses Quantum Private Information Retrieval in the single-server scenario with information-theoretic privacy.We show that for such a protocol to be secure against the weakest reasonable adversary, the protocol requires a linear amount of communication.Hence, the trivial protocol for Quantum Private Information Retrieval is optimal.Furthermore, we discuss the mentioned weakest reasonable adversaries, called specious.As a motivation to this research, we analyze and break a recent protocol for Quantum Private Information Retrieval.i Note that due to the effect of phase-kickback, the above unitary may leak information about the index i to the register DB.However, this happens only in the case of non-classical inputs on the registers A or IDX.Because we assume that the client is honest, and hence does not perform queries in superpositions, we nevertheless use this unitary as the ideal functionality.

DOI
10.3929/ethz-a-007580626

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This thesis discusses Quantum Private Information Retrieval in the single-server scenario with information-theoretic privacy.We show that for such a protocol to be secure against the weakest reasonable adversary, the protocol requires a linear amount of communication.Hence, the trivial protocol for Quantum Private Information Retrieval is optimal.Furthermore, we discuss the mentioned weakest reasonable adversaries, called specious.As a motivation to this research, we analyze and break a recent protocol for Quantum Private Information Retrieval.i Note that due to the effect of phase-kickback, the above unitary may leak information about the index i to the register DB.However, this happens only in the case of non-classical inputs on the registers A or IDX.Because we assume that the client is honest, and hence does not perform queries in superpositions, we nevertheless use this unitary as the ideal functionality.
In (single-server) Private Information Retrieval (PIR), a server holds a large database DBDBDB of size nnn, and a client holds an index i∈[n]i \in [n]i∈[n] and wishes to retrieve DB[i]DB[i]DB[i] without revealing iii to the server. It is well known that information theoretic privacy even against an `honest but curious' server requires Ω(n)Ω(n)Ω(n) communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (`input purification attack'). Nevertheless, there have been some proposals of protocols that achieve sub-linear communication and appear to provide some notion of privacy. Most notably, a protocol due to Le Gall (ToC 2012) with communication complexity O(n)O(\sqrt{n})O(n​), and a protocol by Kerenidis et al. (QIC 2016) with communication complexity O(log⁡(n))O(\log(n))O(log(n)), and O(n)O(n)O(n) shared entanglement. We show that, in a sense, input purification is the only potent adversarial strategy, and protocols such as the two protocols above are secure in a restricted variant of the quantum honest but curious (a.k.a specious) model. More explicitly, we propose a restricted privacy notion called \emph{anchored privacy}, where the adversary is forced to execute on a classical database (i.e. the execution is anchored to a classical database). We show that for measurement-free protocols, anchored security against honest adversarial servers implies anchored privacy even against specious adversaries. Finally, we prove that even with (unlimited) pre-shared entanglement it is impossible to achieve security in the standard specious model with sub-linear communication, thus further substantiating the necessity of our relaxation. This lower bound may be of independent interest (in particular recalling that PIR is a special case of Fully Homomorphic Encryption).
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.
This note presents a quantum protocol for private information retrieval, in the case of a single (honest) server and with information-theoretical privacy, that has O(n)O(\sqrt{n})O(n​)-qubit communication complexity, where nnn denotes the size of the database. In comparison, it is known that any classical protocol must use Ω(n)\Omega(n)Ω(n) bits of communication in this setting.
In the era of extensive data growth, robust and efficient mechanisms are needed to store and manage vast amounts of digital information, such as Data Storage Systems (DSSs). Concurrently, privacy concerns have arisen, leading to the development of techniques like Private Information Retrieval (PIR) to enable data access while preserving privacy. A PIR protocol allows users to retrieve information from a database without revealing the specifics of their query or the data they are accessing. With the advent of quantum computing, researchers have explored the potential of using quantum systems to enhance privacy in information retrieval. In a Quantum Private Information Retrieval (QPIR) protocol, a user can retrieve information from a database by downloading quantum systems from multiple servers, while ensuring that the servers remain oblivious to the specific information being accessed. This scenario offers a unique advantage by leveraging the inherent properties of quantum systems to provide enhanced privacy guarantees and improved communication rates compared to classical PIR protocols. In this thesis we consider the QPIR setting where the queries and the coded storage systems are classical, while the responses from the servers are quantum. This problem was treated by Song et al. for replicated storage and different collusion patterns. This thesis aims to develop QPIR protocols for coded storage by combining known classical PIR protocols with quantum communication algorithms, achieving enhanced privacy and communication costs. We consider different storage codes and robustness assumptions, and we prove that the achieved communication cost is always lower than the classical counterparts.
When a user retrieves information from databases, it is often required to protect the privacy of the user.Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of 𝑓𝑓 messages from non-communicating 𝑛𝑛 servers by downloading quantum systems without revealing the identity of the retrieved message to any individual server.Symmetric QPIR is a QPIR with server secrecy in which the user obtains no information of non-targeted messages.This thesis investigates the fundamental communication limit of the symmetric and nonsymmetric QPIR and constructs the optimal QPIR protocols achieving the communication limit.The communication cost of a QPIR protocol is evaluated by the QPIR rate defined as
Security and privacy are of paramount importance in the modern information age. Secure multi-party computation and private information retrieval are canonical and representative problems in cryptography that capture the key challenges in understanding the fundamentals of security and privacy. In this dissertation, we use information theoretic tools to tackle these two classical cryptographic primitives. In the first part, we consider the secure multi-party computation problem, where multiple users, each holding an independent message, wish to compute a function on the messages without revealing any additional information. We present an efficient protocol in terms of randomness cost to securely compute a vector linear function. In the second part, we discuss the symmetric private information retrieval problem, where a user wishes to retrieve one message from a number of replicated databases while keeping the desired message index a secret from each individual database. Further, the user learns nothing about the other messages. We present an optimal protocol that achieves the minimum upload cost for symmetric private information retrieval, i.e., the queries sent from the user to the databases have the minimum number of bits.