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1. Batched Differentially Private Information Retrieval

   Albab, Kinan Dak ; Issa, Rawane ; Varia, Mayank ; Graffi, Kalman ( August 2022 , 31st USENIX Security Symposium)

   Private Information Retrieval (PIR) allows several clients to query a database held by one or more servers, such that the contents of their queries remain private. Prior PIR schemes have achieved sublinear communication and computation by leveraging computational assumptions, federating trust among many servers, relaxing security to permit differentially private leakage, refactoring effort into an offline stage to reduce online costs, or amortizing costs over a large batch of queries. In this work, we present an efficient PIR protocol that combines all of the above techniques to achieve constant amortized communication and computation complexity in the size of the database and constant client work. We leverage differentially private leakage in order to provide better trade-offs between privacy and efficiency. Our protocol achieves speedups up to and exceeding 10x in practical settings compared to state of the art PIR protocols, and can scale to batches with hundreds of millions of queries on cheap commodity AWS machines. Our protocol builds upon a new secret sharing scheme that is both incremental and non-malleable, which may be of interest to a wider audience. Our protocol provides security up to abort against malicious adversaries that can corrupt all but one party. 

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2. Heterogeneous Private Information Retrieval

   https://doi.org/10.14722/ndss.2020.24363  

   Mozaffari, Hamid ; Houmansadr, Amir ( January 2020 , Network and Distributed Systems Security (NDSS) Symposium 2020)

   Private information retrieval (PIR) enables clients to query and retrieve data from untrusted servers without the untrusted servers learning which data was retrieved. In this paper, we present a new class of multi-server PIR protocols, which we call heterogeneous PIR (HPIR). In such multi-server PIR protocols, the computation and communication overheads imposed on the PIR servers are non-uniform, i.e., some servers handle higher computation/communication burdens than the others. This enables heterogeneous PIR protocols to be suitable for a range of new PIR applications. What enables us to enforce such heterogeneity is a unique PIR-tailored secret sharing algorithm that we leverage in building our PIR protocol. We have implemented our HPIR protocol and evaluated its performance in comparison with regular (i.e., homogenous) PIR protocols. Our evaluations demonstrate that a querying client can trade off the computation and communication loads of the (heterogeneous) PIR servers by adjusting some parameters. For example in a two-server scenario with a heterogeneity degree of 4/1, to retrieve a 456KB file from a 0.2GB database, the rich (i.e., resourceful) PIR server will do 1.1 seconds worth of computation compared to 0.3 seconds by the poor (resource-constrained) PIR server; this is while each of the servers would do the same 1 seconds of computation in a homogeneous setting. Also, for this given example, our HPIR protocol will impose a 912KB communication bandwidth on the rich server compared to 228KB on the poor server (by contrast to 456KB overheads on each of the servers for a traditional homogeneous design). 

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3. On Single Server Private Information Retrieval With Private Coded Side Information

   https://doi.org/10.1109/TIT.2023.3253078  

   Lu, Yuxiang ; Jafar, Syed A. ( May 2023 , IEEE Transactions on Information Theory)

   Matthieu Bloch (Ed.)

   Motivated by an open problem and a conjecture, this work studies the problem of single server private information retrieval with private coded side information (PIR-PCSI) that was recently introduced by Heidarzadeh et al. The goal of PIR-PCSI is to allow a user to efficiently retrieve a desired message Wθ, which is one of K independent messages that are stored at a server, while utilizing private side information of a linear combination of a uniformly chosen size-M subset (S ⊂ [K]) of messages. The settings PIR-PCSI-I and PIR-PCSI-II correspond to the constraints that θ is generated uniformly from [K]\S, and S, respectively. In each case, (θ, S) must be kept private from the server. The capacity is defined as the supremum over message and field sizes, of achievable rates (number of bits of desired message retrieved per bit of download) and is characterized by Heidarzadeh et al. for PIR-PCSI-I in general, and for PIR- PCSI-II for M > (K + 1)/2 as (K − M + 1)−1. For 2 ≤ M ≤ (K + 1)/2 the capacity of PIR-PCSI-II remains open, and it is conjectured that even in this case the capacity is (K − M + 1)−1. We show the capacity of PIR-PCSI-II is equal to 2/K for 2 ≤ M ≤ K+1, which is strictly larger 2 than the conjectured value, and does not depend on M within this parameter regime. Remarkably, half the side-information is found to be redundant. We also characterize the infimum capacity (infimum over fields instead of supremum), and the capacity with private coefficients. The results are generalized to PIR-PCSI-I (θ ∈ [K] \ S) and PIR-PCSI (θ ∈ [K]) settings. 

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4. The Capacity of 4-Star-Graph PIR

   https://doi.org/10.1109/ISIT54713.2023.10206729  

   Yao, Yuhang ; Jafar, Syed A. ( June 2023 , IEEE)

   Introduced by Sadeh et al., the K-star-graph private information retrieval (PIR) problem, so-labeled because the storage graph is a star-graph with K leaf nodes, is comprised of K messages that are stored separately (one-each) at K dedicated servers, and a universal server that stores all K messages, for a total of K + 1 servers. While it is one of the simplest PIR settings to describe, the capacity CK of K-star-graph PIR is open for K ≥ 4. We study the critical K = 4 setting, for which prior work establishes the bounds 2/5 ≤ C4 ≤ 3/7. As our main contribution, we characterize the exact capacity of 4-star-graph PIR as C4 = 5/12, thus improving upon both the prior lower- bound as well as the prior upper-bound. The main technical challenge resides in the new converse bound, whose non-trivial structure is deduced indirectly from the achievable schemes that emerge from the study of a finer tradeoff between the download costs from the dedicated servers versus the universal server. A sharp characterization of this tradeoff is also obtained for K = 4. 

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5. The Capacity of Uncoded Storage Constrained PIR

   https://doi.org/10.1109/ISIT.2018.8437729  

   Attia, Mohamed Adel ; Kumar, Deepak ; Tandon, Ravi ( June 2018 , 2018 IEEE International Symposium on Information Theory (ISIT))

   Private information retrieval (PIR) allows a user to retrieve a desired message out of K possible messages from N databases (DBs) without revealing the identity of the desired message. In this work, we consider the problem of PIR from uncoded storage constrained DBs. Each DB has a storage capacity of μKL bits, where L is the size of each message in bits, and μ ∈ [1/N, 1] is the normalized storage. In the storage constrained PIR problem, there are two key challenges: a) construction of communication efficient schemes through storage content design at each DB that allow download efficient PIR; and b characterizing the optimal download cost via information-theoretic lower bounds. The novel aspect of this work is to characterize the optimum download cost of PIR with storage constrained DBs for any value of storage. In particular, for any (N, K), we show that the optimal tradeoff between storage (μ) and the download cost (D(μ)) is given by the lower convex hull of the pairs ([t/N](1+[1/t]+[1/(t 2 )]+...+[1/(t K-1 )])) for t = 1,2, ..., N. The main contribution of this paper is the converse proof, i.e., obtaining lower bounds on the download cost for PIR as a function of the available storage. 

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