Private Information Retrieval Research Articles

PIR Codes with Short Block Length

In this work private information retrieval (PIR) codes are studied. In a $k$-PIR code, $s$ information bits are encoded in such a way that every information bit has $k$ mutually disjoint recovery sets. The main problem under this paradigm is to minimize the number of encoded bits given the values of $s$ and $k$, where this value is denoted by $P(s,k)$. The main focus of this work is to analyze $P(s,k)$ for a large range of parameters of $s$ and $k$. In particular, we improve upon several of the existing results on this value.

Double Blind T-Private Information Retrieval

Double blind $T$-private information retrieval (DB-TPIR) enables two users, each of whom specifies an index ($\theta_1, \theta_2$, resp.), to efficiently retrieve a message $W(\theta_1,\theta_2)$ labeled by the two indices, from a set of $N$ servers that store all messages $W(k_1,k_2), k_1\in\{1,2,\cdots,K_1\}, k_2\in\{1,2,\cdots,K_2\}$, such that the two users' indices are kept private from any set of up to $T_1,T_2$ colluding servers, respectively, as well as from each other. A DB-TPIR scheme based on cross-subspace alignment is proposed in this paper, and shown to be capacity-achieving in the asymptotic setting of large number of messages and bounded latency. The scheme is then extended to $M$-way blind $X$-secure $T$-private information retrieval (MB-XS-TPIR) with multiple ($M$) indices, each belonging to a different user, arbitrary privacy levels for each index ($T_1, T_2,\cdots, T_M$), and arbitrary level of security ($X$) of data storage, so that the message $W(\theta_1,\theta_2,\cdots, \theta_M)$ can be efficiently retrieved while the stored data is held secure against collusion among up to $X$ colluding servers, the $m^{th}$ user's index is private against collusion among up to $T_m$ servers, and each user's index $\theta_m$ is private from all other users. The general scheme relies on a tensor-product based extension of cross-subspace alignment and retrieves $1-(X+T_1+\cdots+T_M)/N$ bits of desired message per bit of download.

New Results on the Storage-Retrieval Tradeoff in Private Information Retrieval Systems

In a private information retrieval (PIR) system, the user needs to retrieve one of the possible messages from a set of storage servers, but wishes to keep the identity of the requested message private from any given server. Existing efforts in this area have made it clear that the efficiency of the retrieval will be impacted significantly by the amount of the storage space allowed at the servers. In this work, we consider the tradeoff between the storage cost and the retrieval cost. We first present three fundamental results: 1) a regime-wise approximate characterization of the optimal tradeoff with a factor of two, 2) a cyclic permutation lemma that can produce more sophisticated codes from simpler base codes, and 3) a relaxed entropic linear program (LP) lower bound that has a polynomial complexity. Equipped with the cyclic permutation lemma, we then propose two novel code constructions, and by applying the lemma, obtain new storage-retrieval points. Furthermore, we derive more explicit lower bounds by utilizing only a subset of the constraints in the relaxed entropic LP in a systematic manner. Though the new upper bound and lower bound do not lead to a better approximation factor uniformly, they are significantly tighter than the existing art in some regimes.

A novel index retrieval and query optimisation method for private information retrieval in location-based service application

Location-based service is a popular information and communications technology. Security, trust and privacy are the major concerns preventing the wide deployment of LBS. In this paper, we address privacy issues by employing computational private information retrieval schemes and highlight a few optimisation methods. We propose a novel index retrieval technique which helps the user to identify his grid ID and know the index value for the point-of-interest (POI) type of his interest, and an adaptive computation method (flip-optimisation) to reduce multiplication cost for PIR query used to retrieve the POI item at the specified index. The adaptive computation method proposed in this paper is generic and can be applied to any application which uses PIR protocol to access data privately. Our work empirically evaluated the proposed method by implementing the PIR prototype and found it suitable for a practical purpose.

A novel index retrieval and query optimisation method for private information retrieval in location-based service application

A novel index retrieval and query optimisation method for private information retrieval in location-based service application

Provably Secure Symmetric Private Information Retrieval with Quantum Cryptography.

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.

Automated Approach for the Importing the New Photo Set to Private Photo Album to Make it More Searchable

This paper focuses on describing several Informational Retrieval (IR) Multimedia Systems that work primarily with private photo albums and it provides comparison of IR Multimedia Systems in terms of functionality. The Informational Retrieval Multimedia systems, used for comparison are selected as the most known and widely used as well. The Informational Retrieval Multimedia systems compared are Mylio, Google Photo, Apple Photo, Synology Moments and digiKam. Moreover, based on these systems comparison, this paper provides the definition of the end-point user needs. Then it provides the identification and the prioritization (based on the author’s experience and opinion) the issues in private information Retrieval multimedia systems to be addressed by any technical solution. The following issues have been addressed as the most important from the end-point user’s perspective: First of all, it is “Not existing EXIF file metadata”.(It is divided into two sub issues: not existing taken date and GEO data for place it was taken at); as second, the linking a photo to an author person entity (Based on camera brand and model given as metadata); And as the last one, linking the set of photos to the predefined type of event, like birthdays, anniversaries, holidays, trips etc.(Based on tagging the photos in semi-automated way).For each issue, this document has provided the technical approaches and program algorithms (in a pseudo code) as well. Also, the using of relevant tools is provided if applicable. Each tool mentioned is described in a few words and given with a reference to read about. This document has also described the human involvement into the process, if a totally automated process is not possible.As a conclusion this paper describes the key points that were identified during the identification and addressing the issues. The conclusion also gives a proposal for a technical solution (that is required to be used during importing the new photo set into existing IR Multimedia systems) with context diagram that represents the user, its devices with multimedia data, the system to import the data from user multimedia devices and Informational Retrieval multimedia system to keep the whole private multimedia and to search the target photo set. Finally, it gives the definition of workflow steps to describe the main activity flow (with human involvement and software as well) to be implemented in a technical solution in future.Manuscript received 13.05.2020

Efficient and Secure Location-Based Services Scheme in VANET

In VANET, the privacy of the query becomes a serious concern for location-based services (LBS). An LBS scheme must, also, not breach the location privacy of the user vehicle. In order to protect query privacy of the vehicle user, the existing state-of-the-art schemes either reduce the accuracy of LBS or insert a trusted third party (TTP) between the vehicle user and the location server hosting the LBS scheme. Cryptographic constructs such as public-key encryption, Oblivious Transfer (OT), Private Information Retrieval (PIR), and homomorphic encryption are used to remove the TTP or increase the accuracy of the previous schemes. The problem with these existing schemes is that some of them are either inefficient or insecure. In order to address the security and privacy issues, we propose an efficient privacy-preserving mechanism for protecting the query privacy of the user, information content of the location server, and location privacy-preserving of the vehicle in the LBS scheme for VANET. In this scheme, the vehicle requests for services from the location server without revealing the query content to the location server. The location server sends all Point of Interests (POIs) to the vehicle, but the vehicle can only obtain the requested query content. The query privacy of the user and content privacy of the location server is preserved in the exchange. The proposed variant of the OT extension protocol is computationally and communicationally efficient and uses a lattice-based ring-Learning With Errors (ring-LWE) scheme as a Base-OT.

The Role of Coded Side Information in Single-Server Private Information Retrieval

We study the role of coded side information in single-server Private Information Retrieval (PIR). An instance of the single-server PIR problem includes a server that stores a database of K independently and uniformly distributed messages, and a user who wants to retrieve one of these messages from the server. We consider settings in which the user initially has access to a coded side information which includes a linear combination of a subset of M messages in the database. We assume that the identities of the M messages that form the support set of the coded side information as well as the coding coefficients are initially unknown to the server. We consider two different models, depending on whether the support set of the coded side information includes the requested message or not. We also consider the following two privacy requirements: (i) the identities of both the demand and the support set of the coded side information need to be protected, or (ii) only the identity of the demand needs to be protected. For each model and for each of the privacy requirements, we consider the problem of designing a protocol for generating the user's query and the server's answer that enables the user to decode the message they need while satisfying the privacy requirement. We characterize the (scalar-linear) capacity of each setting, defined as the ratio of the number of information bits in a message to the minimum number of information bits downloaded from the server over all (scalar-linear) protocols that satisfy the privacy condition. Our converse proofs rely on new information-theoretic arguments-tailored to the setting of single-server PIR and different from the commonly-used techniques in multi-server PIR settings. We also present novel capacity-achieving scalar-linear protocols for each of the settings being considered.

Uncoded Placement With Linear Sub-Messages for Private Information Retrieval From Storage Constrained Databases

We propose capacity-achieving schemes for private information retrieval (PIR) from uncoded databases (DBs) with both homogeneous and heterogeneous storage constraints. In the PIR setting, a user queries a set of DBs to privately download a message, where privacy implies that no one DB can infer which message the user desires. In general, a PIR scheme is comprised of storage placement and delivery designs. Previous works have derived the capacity, or infimum download cost, of PIR with uncoded storage placement and sufficient conditions of storage placement to meet capacity. However, the currently proposed storage placement designs require splitting each message into an exponential number of sub-messages with respect to the number of DBs. In this work, when DBs have the same storage constraint, we propose two simple storage placement designs that satisfy the capacity conditions. Then, for more general heterogeneous storage constraints, we translate the storage placement design process into a “filling problem”. We design an iterative algorithm to solve the filling problem where, in each iteration, messages are partitioned into sub-messages and stored at subsets of DBs. All of our proposed storage placement designs require a number of sub-messages per message at most equal to the number of DBs.

On the Asymptotic Capacity of X-Secure T-Private Information Retrieval With Graph-Based Replicated Storage

The problem of private information retrieval with graph-based replicated storage was recently introduced by Raviv, Tamo and Yaakobi. Its capacity remains open in almost all cases. In this work the asymptotic (large number of messages) capacity of this problem is studied along with its generalizations to include arbitrary T -privacy and X-security constraints, where the privacy of the user must be protected against any set of up to T colluding servers and the security of the stored data must be protected against any set of up to X colluding servers. A general achievable scheme for arbitrary storage patterns is presented that achieves the rate (ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> -X -T )/N, where N is the total number of servers, and each message is replicated at least ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> times. Notably, the scheme makes use of a special structure inspired by dual Generalized Reed Solomon (GRS) codes. A general converse is also presented. The two bounds are shown to match for many settings, including symmetric storage patterns. Finally, the asymptotic capacity is fully characterized for the case without security constraints (X = 0) for arbitrary storage patterns provided that each message is replicated no more than T + 2 times. As an example of this result, consider PIR with arbitrary graph based storage (T = 1, X = 0) where every message is replicated at exactly 3 servers. For this 3-replicated storage setting, the asymptotic capacity is equal to 2/ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (G) where ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (G) is the maximum size of a 2-matching in a storage graph G[V, E]. In this undirected graph, the vertices V correspond to the set of servers, and there is an edge uv ∈ E between vertices u, v only if a subset of messages is replicated at both servers u and v.

Private Information Retrieval Schemes With Product-Matrix MBR Codes

A private information retrieval (PIR) scheme allows a user to retrieve a file from a database without revealing any information on the file being requested. As of now, PIR schemes have been proposed for several kinds of storage systems, including replicated and MDS-coded systems. However, the problem of constructing PIR schemes on regenerating codes has been sparsely considered. A regenerating code is a storage code whose codewords are distributed among nodes, enabling efficient storage of files, as well as low-bandwidth retrieval of files and repair of nodes. Minimum-bandwidth regenerating (MBR) codes define a family of regenerating codes allowing a node repair with optimal bandwidth. Rashmi, Shah, and Kumar obtained a large family of MBR codes using the product-matrix (PM) construction. In this work, a new PIR scheme over PM-MBR codes is designed. The inherent redundancy of the PM structure is used to reduce the download communication complexity of the scheme. A lower bound on the PIR capacity of MBR-coded PIR schemes is derived, showing an interesting storage space vs. PIR rate trade-off compared to existing PIR schemes with the same reconstruction capability. The present scheme also outperforms a recent PM-MBR PIR construction of Dorkson and Ng.

Capacity of Quantum Private Information Retrieval With Multiple Servers

We study the capacity of quantum private information retrieval (QPIR) with multiple servers. In the QPIR problem with multiple servers, a user retrieves a classical file by downloading quantum systems from multiple servers each of which contains the copy of a classical file set while the identity of the downloaded file is not leaked to each server. The QPIR capacity is defined as the maximum rate of the file size over the whole dimension of the downloaded quantum systems. When the servers are assumed to share prior entanglement, we prove that the QPIR capacity with multiple servers is 1 regardless of the number of servers and files. We construct a rate-one protocol only with two servers. This capacity-achieving protocol outperforms its classical counterpart in the sense of capacity, server secrecy, and upload cost. The strong converse bound is derived concisely without using any secrecy condition. We also prove that the capacity of multi-round QPIR is 1.

The Capacity of Private Information Retrieval From Uncoded Storage Constrained Databases

Private information retrieval (PIR) allows a user to retrieve a desired message from a set of databases without revealing the identity of the desired message. The replicated database scenario, where $N$ databases store each of the $K$ messages was considered by Sun and Jafar, and the optimal download cost was characterized as $\left ({1+ \frac {1}{N}+ \frac {1}{N^{2}}+ \cdots + \frac {1}{N^{K-1}}}\right)$ . In this work, we consider the problem of PIR from uncoded storage constrained databases. Each database has a storage capacity of $\mu KL$ bits, where $L$ is the size of each message in bits, and $\mu \in [{1/N, 1}]$ is the normalized storage. The novel aspect of this work is to characterize the optimum download cost of PIR from uncoded storage constrained databases for any “normalized storage” value in the range $\mu \in [{1/N, 1}]$ . In particular, for any $(N,K)$ , we show that the optimal trade-off between normalized storage, $\mu $ , and the download cost, $D(\mu)$ , is a piece-wise linear function given by the lower convex hull of the $N$ pairs $\left ({\frac {t}{N}, \left ({1+ \frac {1}{t}+ \frac {1}{t^{2}}+ \cdots + \frac {1}{t^{K-1}}}\right)}\right)$ for $t=1,2,\ldots, N$ . To prove this result, we first present a storage constrained PIR scheme for any $(N,K)$ . Next, we obtain a general lower bound on the download cost for PIR, which is valid for any arbitrary storage architecture. The uncoded storage assumption is then applied which allows us to express the lower bound as a linear program (LP). Finally, we solve the LP to obtain tight lower bounds on the download cost for different regimes of storage, which match the proposed storage constrained PIR scheme.

Verifiable single-server private information retrieval from LWE with binary errors

Private Information Retrieval (PIR) allows a client to privately retrieve some data from a public database. There exist two types of PIR: (computational) Single-server PIR (SPIR) and (information-theoretic) multi-server PIR. In this paper, we focus on exploring SPIR. We first propose a simple and efficient additively-homomorphic encryption scheme of which privacy is based on the learning with binary errors assumption that is known as an interesting candidate for practical lattice-based cryptography. Then, according to our proposed homomorphic encryption scheme, we give a Verifiable (single/multi-bit) SPIR (VSPIR) scheme for the single-query case under the malicious server model. To the best of our knowledge, our proposal is the first practical non-interactive VSPIR scheme employing an efficient probabilistic proof that can discover the forged result with overwhelming probability. The corresponding communication complexity and computational complexity are comparable with those of some typical SPIR schemes. Moreover, we extend our single-query VSPIR scheme to construct a non-interactive multi-query solution. In particular, the corresponding communication complexity and computational complexity are the same as those of the single-query scheme. Finally, we provide detailed implementation results to confirm efficiency of our proposals.

Weighted Lifted Codes: Local Correctabilities and Application to Robust Private Information Retrieval

Low degree Reed-Muller codes are known to satisfy local decoding properties which find applications in private information retrieval (PIR) protocols, for instance. However, their practical instantiation encounters a first barrier due to their poor information rate in the low degree regime. This lead the community to design codes with similar local properties but larger dimension, namely the lifted Reed-Solomon codes. However, a second practical barrier appears when one requires that the PIR protocol resists collusion of servers. In this paper, we propose a solution to this problem by considering weighted Reed-Muller codes. We prove that such codes allow us to build PIR protocols with optimal computation complexity and resisting to a small number of colluding servers. In order to improve the dimension of the codes, we then introduce an analogue of the lifting process for weighted degrees. With a careful analysis of their degree sets, we notably show that the weighted lifting of Reed-Solomon codes produces families of codes with remarkable asymptotic parameters.

On the Storage Cost of Private Information Retrieval

We consider the fundamental tradeoff between the storage cost and the download cost in private information retrieval systems, without any explicit structural restrictions on the storage codes, such as maximum distance separable codes or uncoded storage. Two novel outer bounds are provided, which have the following implications. When the messages are stored without any redundancy across the databases, the optimal PIR strategy is to download all the messages; on the other hand, for PIR capacity-achieving codes, each database can reduce the storage cost, from storing all the messages, by no more than one message on average. We then focus on the two-message two-database case, and show that a stronger outer bound can be derived through a novel pseudo-message technique. This stronger outer bound suggests that a precise characterization of the storage-download tradeoff may require non-Shannon type inequalities, or at least more sophisticated bounding techniques.

The Capacity of T-Private Information Retrieval With Private Side Information

We consider the problem of $T$-Private Information Retrieval with private side information (TPIR-PSI). In this problem, $N$ replicated databases store $K$ independent messages, and a user, equipped with a local cache that holds $M$ messages as side information, wishes to retrieve one of the other $K-M$ messages. The desired message index and the side information must remain jointly private even if any $T$ of the $N$ databases collude. We show that the capacity of TPIR-PSI is $\left(1+\frac{T}{N}+\cdots+\left(\frac{T}{N}\right)^{K-M-1}\right)^{-1}$. As a special case obtained by setting $T=1$, this result settles the capacity of PIR-PSI, an open problem previously noted by Kadhe et al. We also consider the problem of symmetric-TPIR with private side information (STPIR-PSI), where the answers from all $N$ databases reveal no information about any other message besides the desired message. We show that the capacity of STPIR-PSI is $1-\frac{T}{N}$ if the databases have access to common randomness (not available to the user) that is independent of the messages, in an amount that is at least $\frac{T}{N-T}$ bits per desired message bit. Otherwise, the capacity of STPIR-PSI is zero.

Quantum Private Information Retrieval From Coded and Colluding Servers

In the classical private information retrieval (PIR) setup, a user wants to retrieve a file from a database or a distributed storage system (DSS) without revealing the file identity to the servers holding the data. In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by receiving quantum information from the servers. The QPIR problem has been treated by Song et al. in the case of replicated servers, both without collusion and with all but one servers colluding. In this paper, the QPIR setting is extended to account for maximum distance separable (MDS) coded servers. The proposed protocol works for any $[n,k]$ -MDS code and $t$ -collusion with $t=n-k$ . Similarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts. Further, it is demonstrated how the protocol can adapted to achieve significantly higher retrieval rates from DSSs encoded with a locally repairable code (LRC) with disjoint repair groups, each of which is an MDS code.

Capacity-Achieving Private Information Retrieval Codes From MDS-Coded Databases With Minimum Message Size

We consider constructing capacity-achieving linear codes with minimum message size for private information retrieval (PIR) from N non-colluding databases, where each message is coded using maximum distance separable (MDS) codes, such that it can be recovered from accessing the contents of any T databases. It is shown that the minimum message size (sometimes also referred to as the sub-packetization factor) is significantly, in fact exponentially, lower than previously believed. More precisely, when K > T/ gcd(N, T) where K is the total number of messages in the system and gcd(·, ·) means the greatest common divisor, we establish, by providing both novel code constructions and a matching converse, the minimum message size as lcm(N - T, T), where lcm(·, ·) means the least common multiple. On the other hand, when K is small, we show that it is in fact possible to design codes with a message size even smaller than lcm(N - T, T).