Parallel private information retrieval protocol with index anonymity for untrusted databases

Private information retrieval (PIR) protocols allow a user to retrieve a data item from a database without revealing any information about the identity of the item being retrieved. Specifically, in information-theoretic k-server PIR, the database is replicated among k non-communicating servers, and each server learns nothing about the item retrieved by the user. The cost of PIR protocols is usually measured in terms of their communication complexity, which is the total number of bits exchanged between the user and the servers. However, another important cost parameter is the storage overhead, which is the ratio between the total number of bits stored on all the servers and the number of bits in the database. Since single-server information-theoretic PIR is impossible, the storage overhead of all existing PIR protocols is at least 2 (or k, in the case of k-server PIR). In this work, we show that information-theoretic PIR can be achieved with storage overhead arbitrarily close to the optimal value of 1, without sacrificing the communication complexity. Specifically, we prove that all known k-server PIR protocols can be efficiently emulated, while preserving both privacy and communication complexity but significantly reducing the storage overhead. To this end, we distribute the n bits of the database among s + r servers, each storing n/s coded bits (rather than replicas). Notably, our coding scheme remains the same, regardless of the specific k-server PIR protocol being emulated. For every fixed k, the resulting storage overhead (s +r)/s approaches 1 as s grows; explicitly we have equation. Moreover, in the special case k = 2, the storage overhead is only 1 + 1/s. In order to achieve these results, we introduce and study a new kind of binary linear codes, called here k-server PIR codes. Finally, we show how such codes can be constructed from multidimensional cubic, from Steiner systems, and from one-step majority-logic decodable codes.

Outsourcing database as service instead of using in-house database management is a new trend emerging in a computing industry; there has been growing interest in outsourcing database services in both the commercial world and the research community. In this paper, we present analysis of non-concurrent model of fast single-database Private Information Retrieval (PIR) scheme for maintaining data privacy with data confidentiality using encryption algorithm like AES for Outsourced Database Service (ODBS) Model. In this model encryption method maintains data confidentiality and a utility that help to create PIR reply which maintains data privacy. In PIR Scheme data privacy is achieved by adding noise data into the result of a typical query which is called as PIR reply. Single-database PIR schemes are generally not practical because of its expensiveness from computational point of view. Here we propose a model that suggests the use of General-Purpose computation using Graphic Processing Units (GPGPU) commodity to process such type of computationally intensive operations. This model will help to achieve practical implementation of single-database PIR scheme which uses encryption algorithm to maintain data confidentiality as secondary goal and it serves to create database reply to maintain data privacy as primary goal. This paper shows some real time results that proves need of concurrency in PIR algorithms. It also describes the use of lattice based single-database PIR protocol with GPGPU as a processing unit to achieve high speed-up and hence, the performance of the system.

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.

We present SlicedPIR, a distributed Private Information Retrieval (PIR) protocol. SlicedPIR efficiently alleviates the server's compute bottleneck by offloading its load across multiple untrusted client machines. In contrast to prior work, SlicedPIR induces only a modest network overhead when the server offloads its work. It achieves those communication savings by exploiting the polynomial encoding of homomorphic encryption schemes typically used in PIR protocols. This encoding lets the server make novel use of the Number Theoretic Transform (NTT) to distribute points on the polynomials as ''slices'' of its data rather than the polynomials themselves. Using NTT allows the clients to process recursive PIR queries on their slices and return a succinct result to the server. The server efficiently verifies the clients' results by leveraging the Schwartz-Zippel lemma, which we adapt to the PIR use case. We show how to integrate SlicedPIR into a private messaging system, where clients write messages to the server's database and then use PIR to secretly query for messages from their friends. We implement a prototype of SlicedPIR and run experiments to show that it scales well with the number of clients and database size. Concretely, SlicedPIR achieves better performance and cuts network usage by over 95% compared to the state-of-the-art.

A $(t,r)$ -function secret sharing ( $(t,r)$ -FSS) scheme allows a dealer to secret-share a function $f$ among $r$ parties as $r$ secret keys $k_{1},\ldots,k_{r}$ such that for any input $x$ the parties can compute $r$ output shares that allow the reconstruction of $f(x)$ but any $\leq t$ of the parties cannot learn any information about $f$ . FSS schemes for point functions have been constructed under the name of distributed point functions (DPFs). The existing DPFs are computationally secure and based on the existence of PRGs or OWFs. As a result, the protocols where DPFs work as building blocks are computationally secure as well. In this paper, we study information-theoretically secure $(t,r)$ -FSS (called $(t,r)$ -itFSS) and propose a generic transformation from information-theoretic private information retrieval (PIR) schemes to itFSS schemes for point functions. We measure the efficiency of itFSS with its communication complexity, which can be defined as the total length of the secret keys and the output shares, maximized over the choices of $f$ and $x$ . By instantiating the generic transformation, we obtain $(t,r)$ -itFSS schemes for a variety of choices of $(t,r)$ , which have sublinear (in the functions’ domain size) communication complexity. How to make sure that the parties’ shares of $f(x)$ do not reveal more information than what needed to compute $f(x)$ is an interesting problem. An itFSS with this property is called function-private. In this paper, we also define a parameter called the mutual rate of itFSS in order to measure the amount of information that will be leaked by the parties’ output shares. We calculate the mutual rates for several specific itFSS schemes. We also define computational function privacy and propose a 2-party itFSS scheme with computational function privacy.

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-FIR property enables a k-server PIR protocol (with k ≤ 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 <; s ≤ 2. 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.

We have entered an era when most data has been outsourced to a potentially untrusted server. In this setting, even with encryption, the physical location accessed, or access patterns, during a query can reveal significant information about the query or database. This motivates the development of techniques to conceal access patterns, such as Private Information Retrieval (PIR) and Oblivious RAM (ORAM). Both allow retrieval of database item without revealing which item is retrieved at a sub-linear (often polylog) communication/computation cost to the client. ORAM requires the client to have a secret key and the server to keep state, but gets sub-linear (even log) server computation and allows both reads and writes. PIR does not require any client secret and the server is stateless, but requires linear server computation. This motivated the development of Doubly Efficient Private Information Retrieval (DEPIR) by Canetti et al. [CHR'17] and Boyle et al. [BIPW'17]. DEPIR allows a client to interact with a single stateless server and achieve overhead (both bandwidth and server computation) that is sub-linear in the database size. In this thesis, we explore three applications of DEPIR in the outsourced data setting, and tradeoffs that lie between ORAM and PIR. We leverage DEPIR's inherent statelessness and sub-linearity to achieve applications that neither PIR nor ORAM could accomplish. First we will explore a variant of ORAM, Rewindable ORAM (RORAM) that leverages DEPIR's statelessness to maintain security even when an adversary resets client and server state. RORAM is required to create the first heuristic construction of Fully Homomorphic Encryption in the RAM model. Our second application considers secure computation in the RAM model, using DEPIR's sub-linear server work to construct a distributed ORAM with constant rounds and sub-linear server work. Finally, we use techniques from DEPIR to achieve a multi-client private and anonymous data access scheme called PANDA.--Author's abstract

Private information retrieval (PIR) is an essential cryptographic protocol for privacy-preserving applications, enabling a client to retrieve a record from a server's database without revealing which record was requested. Single-server PIR based on homomorphic encryption has particularly gained immense attention for its ease of deployment and reduced trust assumptions. However, single-server PIR remains impractical due to its high computational and memory bandwidth demands. Specifically, reading the entirety of large databases from storage, such as SSDs, severely limits its performance. To address this, we propose IVE, an accelerator for single-server PIR with a systematic extension that enables practical retrieval from large databases using DRAM. Recent advances in DRAM capacity allow PIR for large databases to be served entirely from DRAM, removing its dependence on storage bandwidth. Although the memory bandwidth bottleneck still remains, multi-client batching effectively amortizes database access costs across concurrent requests to improve throughput. However, client-specific data remains a bottleneck, whose bandwidth requirements ultimately limits performance. IVE overcomes this by employing a large on-chip scratchpad with an operation scheduling algorithm that maximizes data reuse, further boosting throughput. Additionally, we introduce sysNTTU, a versatile functional unit that enhances area efficiency without sacrificing performance. We also propose a heterogeneous memory system architecture, which enables a linear scaling of database sizes without a throughput degradation. Consequently, IVE achieves up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1,275 \times$</tex> higher throughput compared to prior PIR hardware solutions.

In cryptography, there has been tremendous success in building various two-party protocols with small communication complexity out of homomorphic semantically-secure encryption schemes, using their homomorphic properties in a black-box way. A few notable examples of such primitives include items like single database Private Information Retrieval (PIR) schemes (introduced in [15]) and private database update with small communication (introduced in [5]). In this paper, we illustrate a general methodology for determining what types of protocols can and cannot be implemented with small communication by using homomorphic encryption in a black-box way. We hope that this work will provide a simple litmus test of feasibility for black-box use of known homomorphic encryption schemes by other cryptographic researchers attempting to develop new protocols with low communication. Additionally, a precise mathematical language for reasoning about such problems is developed in this work, which may be of independent interest. We stress that the class of algebraic structures for which we prove communication complexity lower bounds is large, and covers practically all known semantically-secure homomorphic cryptosystems (including those based upon bilinear maps). Finally, we show the following equivalence which relates group homomorphic encryption and a major open question of designing a so-called fully-homomorphic cryptosystem: a fully homomorphic encryption scheme (over a non-zero ring) exists if and only if there exists homomorphic encryption over any finite non-abelian simple group. This result somewhat generalizes results of Barrington [1] (to any group containing a finite non-abelian simple subgroup) and of Maurer and Rhodes [18], and in fact gives a constructiveproof of the 1974 result Werner [28]. (This also answers an open question posed by Rappe in [23], who in 2004 proved a special case of this result.)

Private information retrieval (PIR) protocols allow a user to retrieve a data item from a database while hiding the identity of the item being retrieved. Specifically, in information-theoretic, k-server PIR protocols the database is replicated among k servers, and each server learns nothing about the item the user retrieves. The cost of such protocols is measured by the communication complexity of retrieving one out of n bits of data. For any fixed k, the complexity of the best protocols prior to our work was O(n/sup 1/2k-1/). Since then several methods were developed in an attempt to beat this bound, but all these methods yielded the same asymptotic bound. In this paper, this barrier is finally broken and the complexity of information-theoretic k-server PIR is improved to n/sup O(log log k/k log k)/. The new PIR protocols can also be used to construct k-query binary locally decodable codes of length exp(n/sup O(log log k/k log k)/), compared to exp(n/sup 1/k-1/) in previous constructions. The improvements presented in this paper apply even for small values of k: the PIR protocols are more efficient than previous ones for every k/spl ges/3, and the locally decodable codes are shorter for every k/spl ges/4.

This paper presents an overview of the current single-database private information retrieval (PIR) schemes and proposes to explore the usage of these protocols with statistical databases. The vicinity of this research field with the one of Oblivious Transfer, and the different performance measures used for the last few years have resulted in re-discoveries and contradictory comparisons of performance in different publications. The contribution of this paper is twofold. First, we present the different schemes through the innovations they have brought to this field of research, which gives a global view of the evolution since the first of these schemes was presented by Kushilevitz and Ostrovsky in 1997. We know of no other survey of the current PIR protocols. We also compare the most representative of these schemes with a single set of communication performance measures. When compared to the usage of global communication cost as a single measure, we assert that this set simplifies the evaluation of the cost of using PIR and reveals the best adapted scheme to each situation. We conclude this overview and performance study by introducing some important issues resulting from PIR usage with statistical databases and highlighting some directions for further research.

Motivated by cryptographic applications such as predicate encryption, we consider the problem of representing an arbitrary predicate as the inner product predicate on two vectors. Concretely, fix a Boolean function P and some modulus q. We are interested in encoding x to x_vector and y to y_vector so that P(x,y) = 1 = 0 mod q, where the vectors should be as short as possible. This problem can also be viewed as a generalization of matching vector families, which corresponds to the equality predicate. Matching vector families have been used in the constructions of Ramsey graphs, private information retrieval (PIR) protocols, and more recently, secret sharing. Our main result is a simple lower bound that allows us to show that known encodings for many predicates considered in the cryptographic literature such as greater than and threshold are essentially optimal for prime modulus q. Using this approach, we also prove lower bounds on encodings for composite q, and then show tight upper bounds for such predicates as greater than, index and disjointness.

We propose a private information retrieval (PIR) protocol for distributed storage systems (DSSs) with noncolluding nodes where data is stored using an arbitrary linear code. An expression for the PIR rate, i.e., the ratio of the amount of retrieved stored data per unit of downloaded data, is derived, and a necessary and a sufficient condition for codes to achieve the PIR capacity are given. The necessary condition is based on the generalized Hamming weights of the storage code, while the sufficient condition is based on code automorphisms. We show that cyclic codes and Reed-Muller codes satisfy the sufficient condition and are thus PIR capacity-achieving.

Private Information Retrieval (PIR) allows to privately request a block of data from a database such that no information about the queried block is revealed to the database owner. With the rapid rise of cloud computing, data is often shared across multiple servers, making multi-server PIR a promising privacy-enhancing technology.In this paper, we introduce RAID-PIR, an efficient and simple multi-server PIR scheme, which has similar approach to RAID (Redundant Arrays of Inexpensive Disks) systems. Each server stores only a part of the database, its computational complexity depends only on this part, and multiple blocks can be queried efficiently in parallel. RAID-PIR improves efficiency over known PIR protocols, using only very efficient cryptographic primitives (pseudo-random generator). We demonstrate that RAID-PIR is practical and well-suited for cloud deployment as it reduces the communication as well as the computational workload per server.

With advances in the field of cloud computing many computing rsources and/or services are being provided to the end user on a pay -as-you-use basis. Data outsourcing is a new paradigm in which a third party provides storage services. This is more cost e ffective for the user as there is no need of purchasing expensive hardware and software for data storage. The user is also relieved from administrative activities of software upgrades and maintenance.Before data out sourcing can become viable, the data pr ovider needs to guarantee that the datais secure, be able to execute queries on the data, and the results of the queries must also be secure and not visible to the data provider. Data encryption, Homomorphic Encryption, Secret Sharing algorithms and Private Information R etrieval (PIR) are the techniques widely used for secure data outsourcing. CIA (Confidentiality, Integrity and Availability) are the challenging issues associated with data storage management with/without data outsourcing. In this paper the performance of two secret sharing algo rithms are compared. The Shamir’s secret sharing algorithm and Rabin’s Information Dispersal Algorithm (IDA) are implemented in a private cloud setup using the OpenStack Cloud framework.