Information-theoretically secure Symmetric Private Information Retrieval (SPIR) from a single server is known to be infeasible over noiseless channels. Known solutions to overcome this infeasibility involve additional resources such as database replication, shared randomness, or noisy channels. In this paper, we propose an alternative approach for achieving SPIR with information-theoretic security guarantees, without relying on shared randomness, noisy channels, or data replication. Specifically, we demonstrate that it is sufficient to use a noiseless binary adder multiple-access channel, where inputs are controlled by two non-colluding servers and the output is observed by the client, alongside a public noiseless communication channel between the client and the servers. Furthermore, in this setting, we characterize the optimal file rates, i.e., the file lengths normalized by the number of channel uses, that can be transferred.
Information-theoretically secure Symmetric Private Information Retrieval (SPIR) from a single server is known to be infeasible over noiseless channels. Known solutions to overcome this infeasibility involve additional resources such as database replication, shared randomness, or noisy channels. In this paper, we propose an alternative approach for achieving SPIR with information-theoretic security guarantees, without relying on shared randomness, noisy channels, or data replication. Specifically, we demonstrate that it is sufficient to use a noiseless binary adder multiple-access channel, where inputs are controlled by two non-colluding servers and the output is observed by the client, alongside a public noiseless communication channel between the client and the servers. Furthermore, in this setting, we characterize the optimal file rates, i.e., the file lengths normalized by the number of channel uses, that can be transferred.
Information-theoretically secure Symmetric Private Information Retrieval (SPIR) is known to be infeasible over noiseless channels with a single server. Previous solutions in-volved additional resources such as database replication, shared randomness, or noisy channels. This paper demonstrates that, using a noiseless multiple access channel, SPIR with information-theoretic security guarantees is feasible without shared random-ness, a noisy channel, or data replication. Specifically, we leverage a noiseless binary adder channel and employ two non-colluding servers with independent content. Furthermore, we characterize the optimal file rates, i.e., the file lengths normalized by the number of channel uses, that can be transferred.
This paper revisits the problems of Private Information Retrieval (PIR) and Symmetric PIR (SPIR). In PIR, a user retrieves a desired message fromNreplicated, non-communicating databases, each storing the sameMmessages, while preserving the privacy of the requested message index. SPIR extends this notion further by additionally protecting the privacy of the databases, ensuring that the user learns no information beyond the requested message. In this paper, we assume a block-fading Additive White Gaussian Noise Multiple Access Channel (AWGN MAC) linking the user and the databases. Previous work presented a joint channel-PIR scheme utilizing the Compute and Forward (C&F) protocol, demonstrating the potential of a joint PIR-channel coding scheme over a separated one, yet still lagging behind the channel capacity and requiring significant computational complexity. We propose an improved scheme that offers reduced computational complexity while improving the achievable rate for finite parameters, as well as its scaling laws. Specifically, the achievable rate outperforms the C&F-based approach and scales with the number of databasesNand the powerPsimilarly to the channel capacitywithout the privacy constraint. Furthermore, the analysis demonstrates that the improved rate exhibits only a finite gap from this unconstrained channel capacity –1bit/sec/HzasNincreases. Finally, we provide two SPIR schemes. The first is a modification for our PIR scheme to attain SPIR with no rate loss, which is accomplished by introducing shared common randomness among databases. The second is a novel joint channel-SPIR scheme that utilizes the channel and lattice codes characteristics to nontrivially achieve SPIR without requiring common randomness, at the price of a loss in the achievable rate.
We introduce the problem of symmetric private information retrieval (SPIR) on replicated databases modeled by a simple graph. In this model, each vertex corresponds to a server, and a message is replicated on two servers if and only if there is an edge between them. We consider the setting where the server-side common randomness necessary to accomplish SPIR is also replicated at the servers according to the graph, and we call this as message-specific common randomness. In this setting, we establish a lower bound on the SPIR capacity, i.e., the maximum download rate, for general graphs, by proposing an achievable SPIR scheme. Next, we prove that, for any SPIR scheme to be feasible, the minimum size of message-specific randomness should be equal to the size of a message. Finally, by providing matching upper bounds, we derive the exact SPIR capacity for the class of path and regular graphs.
Both the oblivious transfer (OT) problem and the symmetric private information retrieval (SPIR) problem studies the scenario where a client retrieves information privately and securely from databases, i.e., the privacy of the client is protected from the databases, and the undesired information is protected from the client. The OT problem studies the case of one database plus additional noisy resources between the database and the client. The SPIR problem studies the case of multiple replicated and non-colluding databases. In this paper, we combine the two models and propose a new problem of oblivious transfer (OT) with two replicated databases and a binary erasure multiple access channel connecting the databases and the client. We first provide an upper bound on the OT capacity. We then propose a protocol which achieves the upper bound. Therefore, we obtain the capacity of OT for this model. In our achievability and converse proofs, we utilized the techniques from both traditional OT and PIR. Compared to schemes that utilizes only techniques from OT, we see a 100% increase in the achieved OT rate.
In symmetric private information retrieval (SPIR), a user communicates with multiple servers to retrieve from them a message in a database, while not revealing the message index to any individual server (user privacy), and learning no additional information about the database (database privacy). We study the problem of SPIR on graph-replicated database systems, where each node of the graph represents a server and each link represents a message. Each message is replicated at exactly two servers; those at which the link representing the message is incident. To ensure database privacy, the servers share a set of common randomness, independent of the database and the user's desired message index. We study two cases of common randomness distribution to the servers: i) graph-replicated common randomness, and ii) fully-replicated common randomness. Given a graph-replicated database system, in i), we assign one randomness variable independently to every pair of servers sharing a message, while in ii), we assign an identical set of randomness variable to all servers, irrespective of the underlying graph. In both settings, our goal is to characterize the SPIR capacity, i.e., the maximum number of desired message symbols retrieved per downloaded symbol, and quantify the minimum amount of common randomness required to achieve the capacity. To this goal, in setting i), we derive a general lower bound on the SPIR capacity, and show it to be tight for path and regular graphs through a matching converse. Moreover, we establish that the minimum size of common randomness required for SPIR is equal to the message size. In setting ii), the SPIR capacity improves over the first, more restrictive setting. We show this through capacity lower bounds for a class of graphs, by constructing SPIR schemes from PIR schemes.
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.