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arXiv:2308.10883 · IEEE Globecom Workshops (GC Wkshps)

Quantum Symmetric Private Information Retrieval with Secure Storage and Eavesdroppers

Alptug Aytekin, Mohamed W. Nomeir, Sajani Vithana, Şennur Ulukuş

Published Dec 4, 2023• 13 citations
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Abstract

We consider both the classical and quantum variations of X-secure, E-eavesdropped and$T$-colluding symmetric private information retrieval (SPIR). This is the first work to study SPIR with X-security in classical or quantum variations. We first develop a scheme for classical X-secure, E-eavesdropped and$T$-colluding SPIR (XSETSPIR) based on a modified version of cross subspace alignment (CSA), which achieves a rate of$R=1-\displaystyle \frac{X+\overline{\max}(T,E)}{N}$. The modified scheme achieves the same rate as the scheme used for X-secure PIR with the extra benefit of symmetric privacy. Next, we extend this scheme to its quantum counterpart based on the$N$-sum box abstraction. This is the first work to consider the presence of eavesdroppers in quantum private information retrieval (QPIR). In the quantum variation, the eavesdroppers have better access to information over the quantum channel compared to the classical channel due to the over-the-air decodability. To that end, we develop another scheme specialized to combat eavesdroppers over quantum channels. The scheme proposed for X-secure, E-eavesdropped and T-colluding quantum SPIR (XSETQSPIR) in this work maintains the super-dense coding gain from the shared entanglement between the databases, i.e., achieves a rate of$R_{Q}=\displaystyle \min\{1,2(1-\frac{X+\max(T,E)}{N})\}$.

DOI
10.1109/gcwkshps58843.2023.10464963

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We consider the quantumsymmetricprivate information retrieval (QSPIR) problem in a system withNdatabases andKmessages, withUunresponsive servers,T-colluding servers, andX-security parameter, under several fundamental threat models. In the first model, there areE1eavesdropped links in the uplink direction (the direction from the user to theNservers),E2eavesdropped links in the downlink direction (the direction from the servers to the user), where |E1|, |E2| ≤E; we coin this eavesdropper setting asdynamiceavesdroppers. We show that super-dense coding gain can be achieved for some regimes. In the second model, we consider the case with Byzantine servers, i.e., servers that can coordinate to devise a plan to harm the privacy and security of the system together with static eavesdroppers, by listening to the same links in both uplink and downlink directions. It is important to note the considerable difference between the two threat models, since the eavesdroppers can take huge advantage of the presence of the Byzantine servers. Unlike the previous works in SPIR with Byzantine servers, that assume that the Byzantine servers can send only random symbols independent of the stored messages, we follow the definition of Byzantine servers in [1], where the Byzantine servers can send symbols that can be functions of the storage, queries, as well as the random symbols in a way that can produce worse harm to the system. In the third and the most novel threat model, we consider the presence of Byzantine servers and dynamic eavesdroppers together. We show that having dynamic eavesdroppers along with Byzantine servers in the same system model creates more threats to the system than having static eavesdroppers with Byzantine servers. This is the first work that considers the quantum version of unresponsive and eavesdropped threat model. In addition, this is the first work, classical or quantum, that considers the presence of Byzantine servers together with eavesdroppers in the same system model (static or dynamic eavesdroppers). Another layer of difficulty that we handle in this work stems from the symmetric privacy requirement in the presence of Byzantine servers, which by itself has never been studied before in classical or quantum variations; here the Byzantine servers may attempt to leak information about undesired messages to the user, which is not allowed in SPIR.

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We consider both the classical and quantum variations of X-secure, E-eavesdropped andTTT-colluding symmetric private information retrieval (SPIR). This is the first work to study SPIR with X-security in classical or quantum variations. We first develop a scheme for classical X-secure, E-eavesdropped andTTT-colluding SPIR (XSETSPIR) based on a modified version of cross subspace alignment (CSA), which achieves a rate ofR=1−X+max⁡‾(T,E)NR=1-\displaystyle \frac{X+\overline{\max}(T,E)}{N}R=1−NX+max(T,E)​. The modified scheme achieves the same rate as the scheme used for X-secure PIR with the extra benefit of symmetric privacy. Next, we extend this scheme to its quantum counterpart based on theNNN-sum box abstraction. This is the first work to consider the presence of eavesdroppers in quantum private information retrieval (QPIR). In the quantum variation, the eavesdroppers have better access to information over the quantum channel compared to the classical channel due to the over-the-air decodability. To that end, we develop another scheme specialized to combat eavesdroppers over quantum channels. The scheme proposed for X-secure, E-eavesdropped and T-colluding quantum SPIR (XSETQSPIR) in this work maintains the super-dense coding gain from the shared entanglement between the databases, i.e., achieves a rate ofRQ=min⁡{1,2(1−X+max⁡(T,E)N)}R_{Q}=\displaystyle \min\{1,2(1-\frac{X+\max(T,E)}{N})\}RQ​=min{1,2(1−NX+max(T,E)​)}.
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Private information retrieval (PIR) is a database query protocol that provides user privacy in that the user can learn a particular entry of the database of his interest but his query would be hidden from the data centre. Symmetric private information retrieval (SPIR) takes PIR further by additionally offering database privacy, where the user cannot learn any additional entries of the database. Unconditionally secure SPIR solutions with multiple databases are known classically, but are unrealistic because they require long shared secret keys between the parties for secure communication and shared randomness in the protocol. Here, we propose using quantum key distribution (QKD) instead for a practical implementation, which can realise both the secure communication and shared randomness requirements. We prove that QKD maintains the security of the SPIR protocol and that it is also secure against any external eavesdropper. We also show how such a classical-quantum system could be implemented practically, using the example of a two-database SPIR protocol with keys generated by measurement device-independent QKD. Through key rate calculations, we show that such an implementation is feasible at the metropolitan level with current QKD technology.
Byzantine-Eavesdropper Alliance: How to Achieve Symmetric Privacy in Quantum XXX-Secure BBB-Byzantine EEE-Eavesdropped UUU-Unresponsive TTT-Colluding PIR?
We consider the quantum \emph{symmetric} private information retrieval (QSPIR) problem in a system with NNN databases and KKK messages, with UUU unresponsive servers, TTT-colluding servers, and XXX-security parameter, under several fundamental threat models. In the first model, there are E1\mathcal{E}_1E1​ eavesdropped links in the uplink direction (the direction from the user to the NNN servers), E2\mathcal{E}_2E2​ eavesdropped links in the downlink direction (the direction from the servers to the user), where ∣E1∣,∣E2∣≤E|\mathcal{E}_1|, |\mathcal{E}_2| \leq E∣E1​∣,∣E2​∣≤E; we coin this eavesdropper setting as \emph{dynamic} eavesdroppers. We show that super-dense coding gain can be achieved for some regimes. In the second model, we consider the case with Byzantine servers, i.e., servers that can coordinate to devise a plan to harm the privacy and security of the system together with static eavesdroppers, by listening to the same links in both uplink and downlink directions. It is important to note the considerable difference between the two threat models, since the eavesdroppers can take huge advantage of the presence of the Byzantine servers. Unlike the previous works in SPIR with Byzantine servers, that assume that the Byzantine servers can send only random symbols independent of the stored messages, we follow the definition of Byzantine servers in \cite{byzantine_tpir}, where the Byzantine servers can send symbols that can be functions of the storage, queries, as well as the random symbols in a way that can produce worse harm to the system. In the third and the most novel threat model, we consider the presence of Byzantine servers and dynamic eavesdroppers together. We show that having dynamic eavesdroppers along with Byzantine servers in the same system model creates more threats to the system than having static eavesdroppers with Byzantine servers.
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.
Quantum XXX-Secure BBB-Byzantine TTT-Colluding Private Information Retrieval
We consider the problems arising from the presence of Byzantine servers in a quantum private information retrieval (QPIR) setting. This is the first work to precisely define what the capabilities of Byzantine servers could be in a QPIR context. We show that quantum Byzantine servers have more capabilities than their classical counterparts due to the possibilities created by quantum encoding procedures. We focus on quantum Byzantine servers that can apply any reversible operation on their individual qudits. In this case, Byzantine servers can generate any error, i.e., this covers all possible single qudit operations that can be applied by Byzantine servers on their qudits. We design a scheme based on cross-subspace alignment (CSA) and we show that this scheme achieves superdense coding gain in some cases.
We consider the quantumsymmetricprivate information retrieval (QSPIR) problem in a system withNdatabases andKmessages, withUunresponsive servers,T-colluding servers, andX-security parameter, under several fundamental threat models. In the first model, there areE1eavesdropped links in the uplink direction (the direction from the user to theNservers),E2eavesdropped links in the downlink direction (the direction from the servers to the user), where |E1|, |E2| ≤E; we coin this eavesdropper setting asdynamiceavesdroppers. We show that super-dense coding gain can be achieved for some regimes. In the second model, we consider the case with Byzantine servers, i.e., servers that can coordinate to devise a plan to harm the privacy and security of the system together with static eavesdroppers, by listening to the same links in both uplink and downlink directions. It is important to note the considerable difference between the two threat models, since the eavesdroppers can take huge advantage of the presence of the Byzantine servers. Unlike the previous works in SPIR with Byzantine servers, that assume that the Byzantine servers can send only random symbols independent of the stored messages, we follow the definition of Byzantine servers in [1], where the Byzantine servers can send symbols that can be functions of the storage, queries, as well as the random symbols in a way that can produce worse harm to the system. In the third and the most novel threat model, we consider the presence of Byzantine servers and dynamic eavesdroppers together. We show that having dynamic eavesdroppers along with Byzantine servers in the same system model creates more threats to the system than having static eavesdroppers with Byzantine servers. This is the first work that considers the quantum version of unresponsive and eavesdropped threat model. In addition, this is the first work, classical or quantum, that considers the presence of Byzantine servers together with eavesdroppers in the same system model (static or dynamic eavesdroppers). Another layer of difficulty that we handle in this work stems from the symmetric privacy requirement in the presence of Byzantine servers, which by itself has never been studied before in classical or quantum variations; here the Byzantine servers may attempt to leak information about undesired messages to the user, which is not allowed in SPIR.