Bounds on the Capacity of PIR over Graphs

Sadeh, Bar; Gu, Yujie; Tamo, Itzhak

doi:10.48550/arxiv.2105.07704

Cited by 1 publication

(2 citation statements)

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“…The problem of MDS-PIR with colluding databases turns out to be more challenging and the capacity remains unknown for general parameters; see [39], [40]. Several other variants have been studied including PIR from databases storing data using an arbitrary linear code [41], [42], impact on capacity versus storage when using arbitrary (possibly, non-linear codes) [43]- [47], when databases only store fraction of uncoded messages [48]- [50], and when data is not perfectly replicated across the databases, but rather partially replicated according to graph based structures [51]- [54].…”

Section: ) Pir From Databases With Limited Storagementioning

confidence: 99%

“…In reality, the databases will have some overlap in content and will also have distinct items. When the databases have arbitrary contents, the PIR capacity problem is open, with a few notable exceptions [51]- [54]. The challenge here is to be able exploit the replication to reduce the download cost, while at the same time deal with non-replication as efficiently as possible.…”

Section: Secure Model Aggregation In Federated Learningmentioning

confidence: 99%

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Private Retrieval, Computing and Learning: Recent Progress and Future Challenges

Ulukuş¹,

Avestimehr²,

Gastpar³

et al. 2021

Preprint

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Most of our lives are conducted in the cyberspace. The human notion of privacy translates into a cyber notion of privacy on many functions that take place in the cyberspace. This article focuses on three such functions: how to privately retrieve information from cyberspace (privacy in information retrieval), how to privately leverage large-scale distributed/parallel processing (privacy in distributed computing), and how to learn/train machine learning models from private data spread across multiple users (privacy in distributed (federated) learning). The article motivates each privacy setting, describes the problem formulation, summarizes breakthrough results in the history of each problem, and gives recent results and discusses some of the major ideas that emerged in each field. In addition, the crosscutting techniques and interconnections between the three topics are discussed along with a set of open problems and challenges. I. INTRODUCTIONPrivacy is an important part of human life. This article considers privacy in the context of three distinct but related engineering applications, namely, privacy in retrieving information, privacy in computing functions, and privacy in learning. In the first sub-topic of private information retrieval, a user wishes to download a content from publicly accessible databases in such a way that the databases do not learn which particular content the user has downloaded. Towards that goal, the user creates ambiguity by its actions during the download. This strategy prevents databases from guessing which content the user has downloaded. This in turn preserves the user's privacy because what is downloaded leaks information about interest and intent on the part of the user. In the second sub-topic of private computing, a user wishes to compute a function but

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