Private Information Retrieval Protocols Research Articles

Parallel private information retrieval protocol with index anonymity for untrusted databases

Private information retrieval (PIR) enables a client to search data from a single (or multiple) untrusted server, without revealing which entry was queried. PIR can be divided into two categories: information-theoretic PIR (IT-PIR) and computational PIR (CPIR). However, there is a deployment challenge with IT-PIR because the non-collusion assumption is difficult to implement in practice. Meanwhile, due to the fact that CPIR involves performing cryptographic operations on each element, its performance significantly decreases as the size and number of database entries increase. To overcome these problems, based on homomorphic encryption, this paper presents a parallel PIR (ParPIR) with index anonymity for untrusted databases, which uses the batch encoding to compress request size. Furthermore, our ParPIR eliminates computationally expensive ciphertext multiplication operations, which improves the response time. Moreover, our ParPIR packs multiple responses through rotation column operations on ciphertext, thereby reducing the response size. Compared to previous PIR protocols, the offline time in our ParPIR has almost 1∼63× improvement; the online time in our ParPIR decreases by at least 49.9∼98.9%. Meanwhile, although the request size of our ParPIR has a 0∼31× increase, the response size of our ParPIR has a 0∼4095× improvement.

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.

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.

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.

Binary Locally Repairable Codes With Large Availability and its Application to Private Information Retrieval

Locally Repairable codes (LRCs) have gained significant interest due to applications in distributed storage systems since they enable systems to recover a failed node by accessing few other active nodes. In particular, LRCs with large availability are highly desirable for parallel reading of hot data. In addition to the above applications in distributed storage systems, it was shown by Fazeli et al. that an LRC with large availability can produce a good private information retrieval (PIR) code which allows to reduce the storage overhead of a PIR protocol. Roughly speaking, one can obtain a good PIR code as long as there exists an LRC with large availability. One of the main tasks in studying PIR codes is to design a <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> -server PIR code with small length for the given dimension. In particular, the construction of binary PIR codes is of great interest. In this paper, we consider a construction of binary LRCs from polynomial evaluations. As a result, a new class of binary LRCs with large availability are obtained. Applying such LRCs to PIR codes, we obtain a new class of binary PIR codes. On one hand, the binary LRCs constructed are new in the sense that the parameter regime is not covered by the known LRCs. On the other hand, the parameters of PIR codes derived from our LRCs outperform the known results in certain parameter regimes and achieve the lower bound given by Fazeli et al. up to an absolute constant.

Optimal Rate-Distortion-Leakage Tradeoff for Single-Server Information Retrieval

Private information retrieval protocols guarantee that a user can <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">privately</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">losslessly</i> retrieve a single file from a database stored across multiple servers. In this work, we propose to simultaneously relax the conditions of perfect retrievability and privacy in order to obtain improved download rates when all files are stored uncoded on a single server. Information leakage is measured in terms of the average success probability for the server of correctly guessing the identity of the desired file. The main findings are: i) The derivation of the optimal tradeoff between download rate, distortion, and information leakage when the file size is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infinite</i> . Closed-form expressions of the optimal tradeoff for the special cases of “no-leakage” and “no-privacy” are also given. ii) A novel approach based on linear programming (LP) to construct schemes for a finite file size and an arbitrary number of files. The proposed LP approach can be leveraged to find provably optimal schemes with corresponding closed-form expressions for the rate-distortion-leakage tradeoff when the database contains at most four bits. Finally, for a database that contains 320 bits, we compare two construction methods based on the LP approach with a nonconstructive scheme downloading subsets of files using a finite-length lossy compressor based on random coding.

Multi-Server Weakly-Private Information Retrieval

Private information retrieval (PIR) protocols ensure that a user can download a file from a database without revealing any information on the identity of the requested file to the servers storing the database. While existing protocols strictly impose that no information is leaked on the file&#x2019;s identity, this work initiates the study of the tradeoffs that can be achieved by relaxing the perfect privacy requirement. We refer to such protocols as weakly-private information retrieval (WPIR) protocols. In particular, for the case of multiple noncolluding replicated servers, we study how the download rate, the upload cost, and the access complexity can be improved when relaxing the perfect privacy constraint. To quantify the information leakage on the requested file&#x2019;s identity we consider mutual information (MI), worst-case information leakage, and maximal leakage (MaxL). We present two WPIR schemes, denoted by Scheme A and Scheme B, based on two recent PIR protocols and show that the download rate of the former can be optimized by solving a convex optimization problem. We also show that Scheme A achieves an improved download rate compared to the recently proposed scheme by Samy <i>et al.</i> under the so-called <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-privacy metric. Additionally, a family of schemes based on partitioning is presented. Moreover, we provide an information-theoretic converse bound for the maximum possible download rate for the MI and MaxL privacy metrics under a practical restriction on the alphabet size of queries and answers. For two servers and two files, the bound is tight under the MaxL metric, which settles the WPIR capacity in this particular case. Finally, we compare the performance of the proposed schemes and their gap to the converse bound.

A performance tunable CPIR-based privacy protection method for location based service

Location-based service has become one of the essential parts of our daily lives, which raises a problem: how to preserve location privacy. Computational Private Information Retrieval (CPIR) protocol, which does not need a trusted third party, allows users to retrieve data from a service provider without revealing users’ query information. However, the CPIR protocol scans the entire data space, which causes high costs and limits the scale of CPIR-based applications. To address this problem, we propose a performance tunable Computational Private Information Retrieval (PTCPIR) model. We divide data space into subspaces and scan a subset of subspaces to achieve better performance while sacrificing some privacy. By tuning the percentage of scanned subspaces, we can achieve a tradeoff between performance and privacy. We design a hierarchical encrypted secure index to support data users to retrieve subspace information safely and efficiently, which facilitates privacy-preserving subspace information retrieval. Furthermore, we propose a novel subspace information retrieval method where the confused query keyword sequence makes servers unable to count query probability. Hence access pattern privacy is protected. Experiments on Sequoia and synthetic datasets demonstrate that our PTCPIR model provides a tunable tradeoff between performance and privacy with high efficiency and good scalability.

The Generalized Covering Radii of Linear Codes

Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of linear codes– the generalized covering radius. The generalized covering-radius hierarchy of a linear code characterizes the trade-off between storage amount, latency, and access complexity, in such database systems. Several equivalent definitions are provided, showing this as a combinatorial, geometric, and algebraic notion. We derive bounds on the code parameters in relation with the generalized covering radii, study the effect of simple code operations, and describe a connection with generalized Hamming weights.

You May Also Like... Privacy: Recommendation Systems Meet PIR

AbstractWe describe the design, analysis, implementation, and evaluation of Pirsona, a digital content delivery system that realizes collaborative-filtering recommendations atop private information retrieval (PIR). This combination of seemingly antithetical primitives makes possible—for the first time—the construction of practically efficient e-commerce and digital media delivery systems that can provide personalized content recommendations based on their users’ historical consumption patterns while simultaneously keeping said consumption patterns private. In designing Pirsona, we have opted for the most performant primitives available (at the expense of rather strong non-collusion assumptions); namely, we use the recent computationally 1-private PIR protocol of Hafiz and Henry (PETS 2019.4) together with a carefully optimized 4PC Boolean matrix factorization.

Efficient Private Information Retrieval Protocol with Homomorphically Computing Univariate Polynomials

Private information retrieval (PIR) protocol is a powerful cryptographic tool and has received considerable attention in recent years as it can not only help users to retrieve the needed data from database servers but also protect them from being known by the servers. Although many PIR protocols have been proposed, it remains an open problem to design an efficient PIR protocol whose communication overhead is irrelevant to the database sizeN. In this paper, to answer this open problem, we present a new communication-efficient PIR protocol based on our proposed single-ciphertext fully homomorphic encryption (FHE) scheme, which supports unlimited computations with single variable over a single ciphertext even without access to the secret key. Specifically, our proposed PIR protocol is characterized by combining our single-ciphertext FHE with Lagrange interpolating polynomial technique to achieve better communication efficiency. Security analyses show that the proposed PIR protocol can efficiently protect the privacy of the user and the data in the database. In addition, both theoretical analyses and experimental evaluations are conducted, and the results indicate that our proposed PIR protocol is also more efficient and practical than previously reported ones. To the best of our knowledge, our proposed protocol is the first PIR protocol achievingO1communication efficiency on the user side, irrelevant to the database sizeN.

The Capacity of Single-Server Weakly-Private Information Retrieval

A private information retrieval (PIR) protocol guarantees that a user can privately retrieve files stored in a database without revealing any information about the identity of the requested file. Existing information-theoretic PIR protocols ensure perfect privacy, i.e., zero information leakage to the servers storing the database, but at the cost of high download. In this work, we present weakly-private information retrieval (WPIR) schemes that trade off perfect privacy to improve the download cost when the database is stored on a single server. We study the tradeoff between the download cost and information leakage in terms of mutual information (MI) and maximal leakage (MaxL) privacy metrics. By relating the WPIR problem to rate-distortion theory, the download-leakage function, which is defined as the minimum required download cost of all single-server WPIR schemes for a given level of information leakage and a fixed file size, is introduced. By characterizing the download-leakage function for the MI and MaxL metrics, the capacity of single-server WPIR is fully described.

Information Iterative Retrieval of Internet of Things Communication Terminal Based on Symmetric Algorithm

Through improved similarity analysis algorithm and hybrid local sensitivity hashing method, information is summarized and retrieved by information retrieval method based on EPC network architecture. This method does not consider the symmetry of information, and its retrieval effect is poor, security is low, and resource occupancy rate is high. Therefore, the information iterative retrieval of IoT communication terminal based on symmetric algorithm is proposed to solve these problems. The symmetric private information retrieval protocol based on secret sharing is used to obtain the information set with retrieval, and the Paillier homomorphic information retrieval method is used to obtain the original document of the information communication terminal information. Then, the information detection model based on the iterative algorithm is used to obtain information of the IoT communication terminal. The experimental results show that the retrieval accuracy of the proposed method is higher than 96% when the document set is less than 1000 KB, and the retrieval accuracy is 94.47% when the document set is 10 TB. The CPU usage and memory usage of this method are 8.65 and 3.24%, respectively. Experiments show that the proposed method has extremely high retrieval accuracy and low energy consumption.

NN-QuPiD Attack: Neural Network-Based Privacy Quantification Model for Private Information Retrieval Protocols

Web search engines usually keep users’ profiles for multiple purposes, such as result ranking and relevancy, market research, and targeted advertisements. However, user web search history may contain sensitive and private information about the user, such as health condition, personal interests, and affiliations that may infringe users’ privacy since a user’s identity may be exposed and misused by third parties. Numerous techniques are available to address privacy infringement, including Private Information Retrieval (PIR) protocols that use peer nodes to preserve privacy. Previously, we have proved that PIR protocols are vulnerable to the QuPiD Attack. In this research, we proposed NN-QuPiD Attack, an improved version of QuPiD Attack that uses an Artificial Neural Network (RNN) based model to associate queries with their original users. The results show that the NN-QuPiD Attack gave 0.512 Recall with the Precision of 0.923, whereas simple QuPiD Attack gave 0.49 Recall with the Precision of 0.934 with the same data.

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.

QuPiD Attack: Machine Learning-Based Privacy Quantification Mechanism for PIR Protocols in Health-Related Web Search

With the advancement in ICT, web search engines have become a preferred source to find health-related information published over the Internet. Google alone receives more than one billion health-related queries on a daily basis. However, in order to provide the results most relevant to the user, WSEs maintain the users’ profiles. These profiles may contain private and sensitive information such as the user’s health condition, disease status, and others. Health-related queries contain privacy-sensitive information that may infringe user’s privacy, as the identity of a user is exposed and may be misused by the WSE and third parties. This raises serious concerns since the identity of a user is exposed and may be misused by third parties. One well-known solution to preserve privacy involves issuing the queries via peer-to-peer private information retrieval protocol, such as useless user profile (UUP), thereby hiding the user’s identity from the WSE. This paper investigates the level of protection offered by UUP. For this purpose, we present QuPiD (query profile distance) attack: a machine learning-based attack that evaluates the effectiveness of UUP in privacy protection. QuPiD attack determines the distance between the user’s profile (web search history) and upcoming query using our proposed novel feature vector. The experiments were conducted using ten classification algorithms belonging to the tree-based, rule-based, lazy learner, metaheuristic, and Bayesian families for the sake of comparison. Furthermore, two subsets of an America Online dataset (noisy and clean datasets) were used for experimentation. The results show that the proposed QuPiD attack associates more than 70% queries to the correct user with a precision of over 72% for the clean dataset, while for the noisy dataset, the proposed QuPiD attack associates more than 40% queries to the correct user with 70% precision.

Towards Practical Private Information Retrieval From MDS Array Codes

Private information retrieval (PIR) is the problem of privately retrieving one out of $M$ original files from $N$ severs, i.e., each individual server learns nothing about the file that the user is requesting. Usually, the $M$ files are replicated or encoded by a maximum distance separable (MDS) code and then stored across the $N$ servers. Compared to mere replication, MDS coded servers can significantly reduce the storage overhead. Particularly, PIR from minimum storage regenerating (MSR) coded servers can simultaneously reduce the repair bandwidth when repairing failed servers. Existing PIR schemes from MSR coded servers either require large sub-packetization levels or are not capacity-achieving. In this paper, a PIR protocol from MDS array codes is proposed, subsuming PIR from MSR coded servers as a special case. Particularly, the case of non-colluding, honest-but-curious servers is considered. The retrieval rate of the new PIR protocol achieves the capacity of PIR from MDS/MSR coded servers. By choosing different MDS array codes, the new PIR protocol can have some advantages when compared with existing protocols, e.g., 1) small sub-packetization, 2) (near-) optimal repair bandwidth, 3) implementable over the binary field $\mathbf{F}_2$.

Private Information Retrieval in Graph-Based Replication Systems

In a Private Information Retrieval (PIR) protocol, a user can download a file from a database without revealing the identity of the file to each individual server. A PIR protocol is called $t$ -private if the identity of the file remains concealed even if $t$ of the servers collude. Graph based replication is a simple technique, which is prevalent in both theory and practice, for achieving robustness in storage systems. In this technique each file is replicated on two or more storage servers, giving rise to a (hyper-)graph structure. In this paper we study private information retrieval protocols in graph based replication systems. The main interest of this work is understanding the collusion structures which emerge in the underlying graph. Our main contribution is a 2-replication scheme which guarantees perfect privacy from acyclic sets in the graph, and guarantees partial-privacy in the presence of cycles. Furthermore, by providing an upper bound, it is shown that the PIR rate of this scheme is at most a factor of two from its optimal value for regular graphs. Lastly, we extend our results to larger replication factors and to graph-based coding, a generalization of graph based replication that induces smaller storage overhead and larger PIR rate in many cases.

Location Privacy in Cognitive Radios With Multi-Server Private Information Retrieval

Spectrum database-based cognitive radio networks (CRNs) have become the de facto approach for enabling unlicensed secondary users (SUs) to identify spectrum vacancies in channels owned by licensed primary users (PUs). Despite its merits, the use of spectrum databases incurs privacy concerns for both SUs and PUs. Single-server private information retrieval (PIR) has been used as the main tool to address this problem. However, such techniques incur extremely large communication and computation overheads while offering only computational privacy. Besides, some of these PIR protocols have been broken. In this paper, we show that it is possible to achieve high efficiency and (information-theoretic) privacy for both PUs and SUs in database-driven CRN with multi-server PIR. Our key observation is that, by design, database-driven CRNs comprise multiple databases that are required, by the Federal Communications Commission, to synchronize their records. To the best of our knowledge, we are the first to exploit this observation to harness multi-server PIR technology to guarantee an optimal privacy for both SUs and PUs, thanks to the unique properties of database-driven CRN . We showed, analytically and empirically with deployments on actual cloud systems, that multi-server PIR is an ideal tool to provide efficient location privacy in database-driven CRN.

PIR Array Codes With Optimal Virtual Server Rate

There has been much recent interest in private information retrieval (PIR) in models where a database is stored across several servers using coding techniques from distributed storage, rather than being a simply replicated. In particular, a recent breakthrough result of Fazelli, Vardy, and Yaakobi introduces the notion of a PIR code and a PIR array code, and uses this notion to produce efficient PIR protocols. In this paper, we are interested in designing PIR array codes. We consider the case when we have $m$ servers, with each server storing a fraction $(1/s)$ of the bits of the database; here $s$ is a fixed rational number with $s > 1$ . A PIR array code with the $k$ -PIR property enables a $k$ -server PIR protocol (with $k\leq m$ ) to be emulated on $m$ servers, with the overall storage requirements of the protocol being reduced. The communication complexity of a PIR protocol reduces as $k$ grows, so the virtual server rate , defined to be $k/m$ , is an important parameter. We study the maximum virtual server rate of a PIR array code with the $k$ -PIR property. We present upper bounds on the achievable virtual server rate, some constructions, and ideas how to obtain the PIR array codes with the highest possible virtual server rate. In particular, we present constructions that asymptotically meet our upper bounds and the exact largest virtual server rate is obtained when $1 . A $k$ -PIR code (and similarly a $k$ -PIR array code) is also a locally repairable code with symbol availability $k-1$ . Such a code ensures $k$ parallel reads for each information symbol. So the virtual server rate is very closely related to the symbol availability of the code when used as a locally repairable code. The results of this paper are discussed also in this context where subspace codes also have an important role.