Single-server Multi-message Private Information Retrieval with Side Information

Su, Li; Gastpar, Michael

doi:10.1109/allerton.2018.8635980

Cited by 51 publications

(26 citation statements)

References 22 publications

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“…In particular, capacity is known for disjoint colluding sets [4]. The rapidly growing body of literature in this area has produced capacity results for PIR under a rich variety of constraints [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. However, the capacity for the natural setting of secure storage remains unknown, and relatively unexplored.…”

Section: Introductionmentioning

confidence: 99%

Cross Subspace Alignment and the Asymptotic Capacity of $X$ -Secure $T$ -Private Information Retrieval

Jia

Sun

Jafar

2019

IEEE Trans. Inform. Theory

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X-secure and T -private information retrieval (XSTPIR) is a form of private information retrieval where data security is guaranteed against collusion among up to X servers and the user's privacy is guaranteed against collusion among up to T servers. The capacity of XSTPIR is characterized for arbitrary number of servers N , and arbitrary security and privacy thresholds X and T , in the limit as the number of messages K → ∞. Capacity is also characterized for any number of messages if either N = 3, X = T = 1 or if N ≤ X + T . Insights are drawn from these results, about aligning versus decoding noise, dependence of PIR rate on field size, and robustness to symmetric security constraints. In particular, the idea of cross subspace alignment, i.e., introducing a subspace dependence between Reed-Solomon code parameters, emerges as the optimal way to align undesired terms while keeping desired terms resolvable.

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Section: Introductionmentioning

confidence: 99%

Cross Subspace Alignment and the Asymptotic Capacity of $X$ -Secure $T$ -Private Information Retrieval

Jia

Sun

Jafar

2019

IEEE Trans. Inform. Theory

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“…If all databases collude or belong to the same entity, the system essentially becomes a single-database system [13]. The single-database PIR problem has been studied under extended conditions, e.g., side-information [14]- [17]. Here, we investigate singledatabase SPIR under extended conditions, with the goal of making it feasible.…”

Section: Introductionmentioning

confidence: 99%

Symmetric Private Information Retrieval with Mismatched Coded Messages and Randomness

Wang

Sun

Skoglund

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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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). SPIR has a capacity smaller than the PIR capacity which requires only user privacy, is infeasible in the case of a single database, and requires 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 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.

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“…It is straightforward to show that the W -privacy condition (19) implies the following necessary condition on a PIR code.…”

Section: Equivalence Results For Non-linear Schemesmentioning

confidence: 99%

“…It was shown that the side information enables the user to substantially reduce the download cost and still achieve information-theoretic privacy for the requested message. The multi-message extension of PIR-SI, which enables a user to privately download multiple messages from the server, is considered by Heidarzadeh et al [10] as well as Li and Gastpar [11].…”

Section: Introductionmentioning

confidence: 99%

On an Equivalence Between Single-Server PIR with Side Information and Locally Recoverable Codes

Kadhe

Heidarzadeh

Sprintson

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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Private Information Retrieval (PIR) problem has recently attracted a significant interest in the information-theory community. In this problem, a user wants to privately download one or more messages belonging to a database with copies stored on a single or multiple remote servers. In the single server scenario, the user must have prior side information, i.e., a subset of messages unknown to the server, to be able to privately retrieve the required messages in an efficient way.In the last decade, there has also been a significant interest in Locally Recoverable Codes (LRC), a class of storage codes in which each symbol can be recovered from a limited number of other symbols. More recently, there is an interest in cooperative locally recoverable codes, i.e., codes in which multiple symbols can be recovered from a small set of other code symbols.In this paper, we establish a relationship between coding schemes for the single-server PIR problem and LRCs. In particular, we show the following results: (i) PIR schemes designed for retrieving a single message are equivalent to classical LRCs; and (ii) PIR schemes for retrieving multiple messages are equivalent to cooperative LRCs. These equivalence results allow us to recover upper bounds on the download rate for PIR-SI schemes, and to obtain a novel rate upper bound on cooperative LRCs. We show results for both linear and non-linear codes.

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Single-server Multi-message Private Information Retrieval with Side Information

Cited by 51 publications

References 22 publications

Cross Subspace Alignment and the Asymptotic Capacity of $X$ -Secure $T$ -Private Information Retrieval

Cross Subspace Alignment and the Asymptotic Capacity of $X$ -Secure $T$ -Private Information Retrieval

Symmetric Private Information Retrieval with Mismatched Coded Messages and Randomness

On an Equivalence Between Single-Server PIR with Side Information and Locally Recoverable Codes

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