Private Information Retrieval Research Articles

A Shannon-Theoretic Approach to the Storage–Retrieval Trade-Off in PIR Systems

We consider the storage–retrieval rate trade-off in private information retrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostly on the canonical two-message two-database case, for which a coding scheme based on random codebook generation and the binning technique is proposed. This coding scheme reveals a hidden connection between PIR and the classic multiple description source coding problem. We first show that when the retrieval rate is kept optimal, the proposed non-linear scheme can achieve better performance over any linear scheme. Moreover, a non-trivial storage-retrieval rate trade-off can be achieved beyond space-sharing between this extreme point and the other optimal extreme point, achieved by the retrieve-everything strategy. We further show that with a method akin to the expurgation technique, one can extract a zero-error PIR code from the random code. Outer bounds are also studied and compared to establish the superiority of the non-linear codes over linear codes.

Quantum private information retrieval over a collective noisy channel

Quantum Private Information Retrieval (QPIR) allows a user (Alice) to retrieve a database item from the database owned by the database holder (Bob) in such a way that Alice can query only the database item she wants, but cannot get other items, and Bob does not know which item Alice queries. However, the real quantum channel between Alice and Bob is noisy, and the noise may result in not only the chance that Alice obtains a false item, but also that both parties may cheat by camouflaging themselves with noise. In this paper, we use the decoherence-free subspace (DFS) for QPIR, which we call DFS-QPIR. The DFS-QPIR protocol removes the effect of the channel noise on the errors in the retrieved item so that two parties cannot cheat by replacing the noisy channel with a noiseless one. It can work over a collective noisy channel while retaining high reliability, database security and user privacy simultaneously. While only the collective unitary noise is taken into account, the proposed DFS-QPIR protocol can be straightforwardly extended to more general collective noise channel.

Bounds on the Capacity of Private Information Retrieval Over Graphs

In the private information retrieval (PIR) problem, a user wants to retrieve a file from a database without revealing any information about the desired file’s identity to the servers that store the database. In this paper, we study the PIR capacity of a graph-based replication system, in which each file is stored on two distinct servers according to an underlying graph. This paper aims to provide upper and lower bounds to the PIR capacity of graphs via various graph properties. In particular, we provide several upper bounds on the PIR capacity that apply to all graphs. We further improve the bounds for specific graph families (which turn out to be tight in certain cases) by utilizing the underlying graph structure. For the lower bounds, we establish optimal rate PIR schemes for star graphs via edge-coloring techniques. Lastly, we provide an improved PIR scheme for complete graphs, implying an improved general lower bound on all graphs’ PIR capacity.

VeriDedup: A Verifiable Cloud Data Deduplication Scheme With Integrity and Duplication Proof

Data deduplication is a technique to eliminate duplicate data in order to save storage space and enlarge upload bandwidth, which has been applied by cloud storage systems. However, a cloud storage provider (CSP) may tamper user data or cheat users to pay unused storage for duplicate data that are only stored once. Although previous solutions adopt message-locked encryption along with Proof of Retrievability (PoR) to check the integrity of deduplicated encrypted data, they ignore proving the correctness of duplication check during data upload and require the same file to be derived into same verification tags, which suffers from brute-force attacks and restricts users from flexibly creating their own individual verification tags. In this paper, we propose a verifiable deduplication scheme called VeriDedup to address the above problems. It can guarantee the correctness of duplication check and support flexible tag generation for integrity check over encrypted data deduplication in an integrative way. Concretely, we propose a novel Tag-flexible Deduplication-supported Integrity Check Protocol (TDICP) based on Private Information Retrieval (PIR) by introducing a novel verification tag called <inline-formula><tex-math notation="LaTeX">${note\ set}$</tex-math></inline-formula> , which allows multiple users holding the same file to generate their individual verification tags and still supports tag deduplication at the CSP. Furthermore, we make the first attempt to guarantee the correctness of data duplication check by introducing a novel User Determined Duplication Check Protocol (UDDCP) based on Private Set Intersection (PSI), which can resist a CSP from providing a fake duplication check result to users. Security analysis shows the correctness and soundness of our scheme. Simulation studies based on real data show the efficacy and efficiency of our proposed scheme and its significant advantages over prior arts.

Организация конфиденциальных запросов к облаку

The article examines the well-known cryptographic problem of obtaining data from a database by a client so that no one with access to the server except the client himself could obtain information about this request. This problem known as PIR (Private Information Retrieval) was formulated in 1995 by Chor, Goldreich, Kushilevitz and Sudan in the information-theoretic setting. A model of cloud computing is proposed. It includes a cloud, an authentication center, a user, clients, trusted dealer, an active adversary executing the protocol in the cloud. The attacking side has the ability to create fake clients to generate an unlimited number of requests. An algorithm for the organization and database distribution on the cloud and an algorithm for obtaining the required bit were proposed. An injective transformation of bit numbers represented in the l-ary number system by words of length d into words without repeating digits of the same length with an alphabet of 𝒍̂ digits is used, i.e. a transformation {𝟎, ..., 𝒍 − 𝟏}^𝒅 → {𝟎, ..., 𝒍̂ − 𝟏}^𝒅 was constructed. This transformation reduces the probability of disclosure of the requested bit number. The communication complexity and probability of revealing required bit were estimated, taking into account the performed transformation.

Information-Theoretically Private Matrix Multiplication From MDS-Coded Storage

We study two problems of private matrix multiplication, over a distributed computing system consisting of a master node, and multiple servers that collectively store a family of public matrices using Maximum-Distance-Separable (MDS) codes. In the first problem of Private and Secure Matrix Multiplication (PSMM) from colluding servers, the master intends to compute the product of its confidential matrix A with a target matrix stored on the servers, without revealing any information about A and the index of target matrix to some colluding servers. In the second problem of Fully Private Matrix Multiplication (FPMM) from colluding servers, the matrix A is also selected from another family of public matrices stored at the servers in MDS form. In this case, the indices of the two target matrices should both be kept private from colluding servers. We develop novel strategies for the two PSMM and FPMM problems, which simultaneously guarantee information-theoretic data/index privacy and computation correctness. We compare the proposed PSMM strategy with a previous PSMM strategy with a weaker privacy guarantee (non-colluding servers), and demonstrate substantial improvements over the previous strategy in terms of communication and computation overheads. Moreover, compared with a baseline FPMM strategy that uses the idea of Private Information Retrieval (PIR) to directly retrieve the desired matrix multiplication, the proposed FPMM strategy significantly reduces storage overhead, but slightly incurs large communication and computation overheads.

FrodoPIR: Simple, Scalable, Single-Server Private Information Retrieval

We design FrodoPIR — a highly configurable, stateful, single-server Private Information Retrieval (PIR) scheme that involves an offline phase that is completely client-independent. Coupled with small online overheads, it leads to much smaller amortized financial costs on the server-side than previous approaches. In terms of performance for a database of 1 million 1KB elements, FrodoPIR requires &lt; 1 second for responding to a client query, has a server response size blow-up factor of &lt; 3.6x, and financial costs are ~$1 for answering 100,000 client queries. Our experimental analysis is built upon a simple, non-optimized Rust implementation, illustrating that FrodoPIR is particularly suitable for deployments that involve large numbers of clients.

Asymmetric Consortium Blockchain and Homomorphically Polynomial-Based PIR for Secured Smart Parking Systems

In crowded cities, searching for the availability of parking lots is a herculean task as it results in the wastage of drivers’ time, increases air pollution, and traffic congestion. Smart parking systems facilitate the drivers to determine the information about the parking lot in real time and book them depending on the requirement. But the existing smart parking systems necessitate the drivers to reveal their sensitive information that includes their mobile number, personal identity, and desired destination. This disclosure of sensitive information makes the existing centralized smart parking systems more vulnerable to service providers’ security breaches, single points of failure, and bottlenecks. In this paper, an Improved Asymmetric Consortium Blockchain and Homomorphically Computing Univariate Polynomial-based private information retrieval (IACB-HCUPPIR) scheme is proposed to ensure parking lots’ availability with transparency security in a privacy-preserving smart parking system. In specific, an improved Asymmetric Consortium Blockchain is used for achieving secure transactions between different parties interacting in the smart parking environment. It further adopted the method of Homomorphically Computing Univariate Polynomial-based private information retrieval (HCUPPIR) scheme for preserving the location privacy of drivers. The results of IACB-HCUPPIR confirmed better results in terms of minimized computation and communication overload with throughput, latency, and response time with maximized drivers’ privacy preservation. Moreover, the proposed fully homomorphic algorithm (FHE) was compared against partial-homomorphic encryption (PHE) and technique without encryption and found that the proposed model has quick communication in allocating the parking slots starting with 24.3 s, whereas PHE starts allocating from 24.7 s and the technique without encryption starts at 27.4 s. Thus, we ensure the proposed model performs well in allocating parking slots with less time and high security with privacy preservation.

Pika: Secure Computation using Function Secret Sharing over Rings

Machine learning algorithms crucially depend on non-linear mathematical functions such as division (for normalization), exponentiation (for softmax and sigmoid), tanh (as an activation function), logarithm (for crossentropy loss), and square root (for back-propagation of normalization layers). However, when machine learning is performed over secure computation, these protocols incur a large communication overhead and high round complexity. In this work, we propose new multi-party computation (MPC) protocols for such functions. Our protocols achieve constant round complexity (3 for semi-honest, 4 for malicious), an order of magnitude lower communication (54 − 121× lower than prior art), and high concrete efficiency (2−1163× faster runtime). We rely on recent advances in function secret sharing (FSS) to construct these protocols. Our contributions can be summarized as follows: (1) A constant round protocol to securely evaluate nonlinear functions such as division, exponentiation, logarithm, and tanh (in comparison to prior art which uses round complexity proportional to the rounds of iterative methods/required precision) with high accuracy. This construction largely follows prior work in look-up style secure computation. (2) Our main contribution is the extension of the above protocol to be secure in the presence of malicious adversaries in the honest majority setting. We provide a malicious sketching protocol for FSS schemes that works over rings and in order to prove its security, we extend (and prove) a corresponding form of SchwartzZippel lemma over rings. This is the first such extension of the lemma and it can be of independent interest in other domains of secure computation. (3) We implement our protocol and showcase order of magnitude improvements in runtime and communication. Given the low round complexity and substantially lower communication, our protocols achieve even better performance over network constrained environments such as WAN. Finally, we showcase how such functions can lead to scalability in machine learning. Note that techniques presented are applicable beyond the application of machine learning as the protocols effectively present an efficient 1-out-of-N oblivious transfer or an efficient private information retrieval protocol.

User-Defined Privacy-Preserving Traffic Monitoring Against n-by-1 Jamming Attack

Traffic monitoring services collect traffic reports and respond to users’ traffic queries. However, the reports and queries may reveal the user’s identity and location. Although different anonymization techniques have been applied to protect user privacy, a new security threat arises, namely, n-by-1 jamming attack, in which an anonymous contributing driver impersonates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> drivers and uploads <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> normal reports by using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> reporting devices. Such an attack will mislead the traffic monitoring service provider and further degrade the service quality. Existing traffic monitoring services do not support customized queries, and private information retrieval techniques cannot be applied directly in traffic monitoring. We formally define the new attack and propose a traffic monitoring scheme TraJ to defend the attack and achieve user-defined location privacy. Specifically, we bridge anonymous contributing drivers without disclosing their speed set by using private set intersection. Each RSU collects time traffic reports and structures a weighted proximity graph to filter out malicious colluding drivers. We design a user-defined privacy-preserving query method by encoding complex road network. We leverage the uploading phase from private aggregation to collect traffic conditions and allow requesting drivers to dynamically and privately query traffic conditions. We provide a formal analysis of TraJ to prove its privacy and security properties. We also construct a prototype based on a real-world dataset and Android smartphones to demonstrate its feasibility and efficiency. A formal analysis demonstrates the privacy and security properties. Extensive experiments illustrate the performance and defense efficacy.

Discrete configurations and combinatorial methods originated from distributed network

In recent years, many new problems of information science originating from distributed networks have brought new challenges to the classical information theory and coding theory. The research of these problems involves many discrete configurations. Combinatorial methods such as combinatorial design theory, graph theory, combinatorial coding theory and extremal combinatorics have been playing an important role in the research of these problems. In this paper, we briefly survey the progress on five hot frontier topics originating from distributed networks, including network coding, index coding, coded caching, distributed computing, and private information retrieval. In particular, we emphasize the discrete configurations and combinatorial methods related to these topics. For some of the topics, we also provide a few new results.

Experimental symmetric private information retrieval with measurement-device-independent quantum network

Secure information retrieval is an essential task in today’s highly digitised society. In some applications, it may be necessary that user query’s privacy and database content’s security are enforced. For these settings, symmetric private information retrieval (SPIR) could be employed, but its implementation is known to be demanding, requiring a private key-exchange network as the base layer. Here, we report for the first time a realisation of provably-secure SPIR supported by a quantum-secure key-exchange network. The SPIR scheme looks at biometric security, offering secure retrieval of 582-byte fingerprint files from a database with 800 entries. Our experimental results clearly demonstrate the feasibility of SPIR with quantum secure communications, thereby opening up new possibilities in secure distributed data storage and cloud computing over the future Quantum Internet.

Anonymous and Linkable Location-Based Services

In the location-based services (LBS) scheme, the vehicle user sends his query to the LBS server and gets the data corresponding to the requested query from it. Therefore, vehicle user’s query privacy and LBS server’s data privacy are serious issues in LBS. Several LBS schemes, like <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -anonymity, private-information retrieval, and homomorphic encryption-based, have been proposed to solve these issues. These schemes either provide vehicle user’s query privacy or LBS server’s data privacy. Some of the oblivious transfer (OT) protocol-based LBS schemes preserve vehicle users’ query privacy and LBS server’s data privacy. However, the OT-based LBS schemes do not preserve vehicle user’s identity privacy. Moreover, the efficiency (communication and computation costs) of the OT protocol-based LBS schemes depends on the LBS server’s database size, which is very high. In this work, we propose an anonymous linkable location-based services (AL2BS) scheme using linkable ring signcryption technique. The scheme provides vehicle user’s query privacy and LBS server’s data privacy without revealing the vehicle user’s identity. The efficiency of the AL2BS scheme is independent of the size of the LBS server’s database. The AL2BS scheme requires only one pairing operation on both ends and a few point multiplications. The theoretical and experimental results show that the performance of the AL2BS scheme in terms of communication and computation costs is better than the existing LBS schemes.

Robust private information retrieval for low encoding/decoding complexity distributed storage

AbstractPrivate information retrieval (PIR) means a user retrieves a file while revealing no information on which file is being retrieved. In classic PIR, the user needs to wait for the responses of all the storage nodes. However, in general, there may be some nodes that are unresponsive, in which case it is formulated as v‐robust PIR in the network coding (NC) structured distributed storage system (DSS), where v denotes the number of unresponsive nodes. We consider PIR with unresponsive nodes under the framework of NC structured DSS. In particular, the storage nodes adopt combination property with zigzag decodable (CP‐ZD) storage code since it has the advantage of extremely low decoding complexity, which is promised by zigzag decoding (ZD) within a binary field. We design a v‐robust PIR scheme with its download communication cost slightly larger than existing studies, but its decoding complexity is significantly reduced when compared with existing studies.

X-Secure T-Private Federated Submodel Learning With Elastic Dropout Resilience

Motivated by recent interest in federated submodel learning, this work explores the fundamental problem of privately reading from and writing to a database comprised of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> files (submodels) that are stored across <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> distributed servers according to an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> -secure threshold secret sharing scheme. One after another, various users wish to retrieve their desired file, locally process the information and then update the file in the distributed database while keeping the identity of their desired file private from any set of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> colluding servers. The availability of servers changes over time, so elastic dropout resilience is required. The main contribution of this work is an adaptive scheme, called ACSA-RW, that takes advantage of all currently available servers to reduce its communication costs, fully updates the database after each write operation even though the database is only partially accessible due to server dropouts, and ensures a memoryless operation of the network in the sense that the storage structure is preserved and future users may remain oblivious of the past history of server dropouts. The ACSA-RW construction builds upon cross-subspace alignment (CSA) codes that were originally introduced for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> -secure <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> -private information retrieval and have been shown to be natural solutions for secure distributed batch matrix multiplication problems. ACSA-RW achieves the desired private read and write functionality with elastic dropout resilience, matches the best results for private-read from PIR literature, improves significantly upon available baselines for private-write, reveals a striking symmetry between upload and download costs, and exploits storage redundancy to accommodate arbitrary read and write dropout servers up to certain threshold values. It also answers in the affirmative an open question by Kairouz et al. for the case of partially colluding servers (i.e., tolerating collusion up to a threshold) by exploiting synergistic gains from the joint design of private read and write operations.

A location-based privacy-preserving oblivious sharing scheme for indoor navigation

In recent years, with the rapid development of wireless communication technology and mobile devices, etc., indoor localization and navigation using WiFi sensing are increasingly being widely employed in life. On this basis, various applications of location-based services have been rapidly developed. However, when users enjoy the location query service of LBS providers, there is a risk of exposing personal information and location privacy simultaneously. In particular, the sensitive information about users based on their location privacy can be inferred by malicious users. Therefore, how to implement location hiding, query privacy protection and query result feedback at the same time is one of the crucial issues of LBS privacy protection. A novel oblivious data sharing scheme employing the designed 1-out-of-n oblivious transfer protocol is proposed to achieve an efficient location-based service for users while effectively hiding location coordinates and protecting the privacy of users and servers. In addition, once a user accesses the same keyword several times, the server is bound to be able to master the accessed frequency of keywords. For this reason, the string length-based transformation algorithm based on private information retrieval is designed and added as a part of OT protocol, which effectively reduces the communication overhead and ensures the privacy of required keywords. The security and performance analysis indicate that the proposed protocol can be instantiated in indoor navigation with high security and efficiency.

Quantum Anonymous Private Information Retrieval for Distributed Networks

Quantum cybersecurity is the study of all facets regarding the security of communication and computation in a distributed network. Significant developments in quantum technologies have outclassed their classical counterparts, thus envisioning the realization of a quantum internet. However, such quantum resources, in the hands of an adversary, can jeopardize network security. In this paper, we study two secure network connectivity concerns, namely, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">privacy</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">anonymity</i> , in quantum information retrieval systems. To this end, we propose a state-of-the-art single-server multi-user quantum anonymous private information retrieval (QAPIR) protocol. To actualize this, we utilize anonymous entanglement as a quantum resource. We show that the QAPIR protocol not only provides privacy but also introduces anonymity as an added layer of security in quantum networks. Furthermore, we also detail a comparative security analysis that establishes the desirable properties of our proposal.

Symmetric Private Information Retrieval at the Private Information Retrieval Rate

We consider the problem of symmetric private information retrieval (SPIR) with user-side common randomness. In SPIR, a user retrieves a message out of K messages from N non-colluding and replicated databases in such a way that no single database knows the retrieved message index (user privacy), and the user gets to know nothing further than the retrieved message (database privacy), i.e., the privacy constraint between the user and the databases is symmetric. SPIR has the following three properties: its capacity is smaller than the capacity of PIR which requires only user privacy; it is infeasible in the case of a single database; and it requires presence of shared common randomness among the databases. We introduce a new variant of SPIR where the user is provided with a random subset of the shared database common randomness, which is unknown to the databases. We determine the exact capacity region of the triple (d,ρS,ρU), where d is the download cost, ρS is the amount of shared database (server) common randomness, and ρU is the amount of available user-side common randomness. We show that with a suitable amount of ρU, this new SPIR achieves the capacity of the conventional PIR. As a corollary, single-database SPIR becomes feasible. Further, the presence of user-side ρU reduces the amount of required server-side ρS.

Towards practical privacy-preserving protocols

Abstract Protecting users’ privacy in digital systems becomes more complex and challenging over time, as the amount of stored and exchanged data grows steadily and systems become increasingly involved and connected. Two techniques that try to approach this issue are the privacy-preserving protocols secure multi-party computation (MPC) and private information retrieval (PIR), which aim to enable practical computation while simultaneously keeping sensitive data private. In the dissertation [Daniel Demmler. “Towards Practical Privacy-Preserving Protocols”. Diss. Darmstadt: Technische Universität, 2018. url: http://tuprints.ulb.tu-darmstadt.de/8605/], summarized in this article, we present results showing how real-world applications can be executed in a privacy-preserving way. This is not only desired by users of such applications, but since 2018 also based on a strong legal foundation with the GDPR in the European Union, that enforces privacy protection of user data by design.

New Bounds and a Generalization for Share Conversion for 3-Server PIR.

Private Information Retrieval (PIR) protocols, which allow the client to obtain data from servers without revealing its request, have many applications such as anonymous communication, media streaming, blockchain security, advertisement, etc. Multi-server PIR protocols, where the database is replicated among the non-colluding servers, provide high efficiency in the information-theoretic setting. Beimel et al. in CCC 12’ (further referred to as BIKO) put forward a paradigm for constructing multi-server PIR, capturing several previous constructions for servers, as well as improving the best-known share complexity for 3-server PIR. A key component there is a share conversion scheme from corresponding linear three-party secret sharing schemes with respect to a certain type of “modified universal” relation. In a useful particular instantiation of the paradigm, they used a share conversion from -CNF over to three-additive sharing over for primes where and , and the relation is modified universal relation . They reduced the question of the existence of the share conversion for a triple to the (in)solvability of a certain linear system over , and provided an efficient (in ) construction of such a sharing scheme. Unfortunately, the size of the system is which entails the infeasibility of a direct solution for big m’s in practice. Paskin-Cherniavsky and Schmerler in 2019 proved the existence of the conversion for the case of odd , when , obtaining in this way infinitely many parameters for which the conversion exists, but also for infinitely many of them it remained open. In this work, using some algebraic techniques from the work of Paskin-Cherniavsky and Schmerler, we prove the existence of the conversion for even m’s in case (we computed in this case) and the absence of the conversion for even m’s in case . This does not improve the concrete efficiency of 3-server PIR; however, our result is promising in a broader context of constructing PIR through composition techniques with servers, using the relation where m has more than two prime divisors. Another our suggestion about 3-server PIR is that it’s possible to achieve a shorter server’s response using the relation for extended . By computer search, in BIKO framework we found several such sets for small m’s which result in share conversion from -CNF over to 3-additive secret sharing over , where is several times less than , which implies several times shorter server’s response. We also suggest that such extended sets can result in better PIR due to the potential existence of matching vector families with the higher Vapnik-Chervonenkis dimension.