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The Capacity of Private Information Retrieval With Eavesdroppers
KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Teknisk informationsvetenskap.ORCID-id: 0000-0001-9471-1409
Univ North Texas, Dept Elect Engn, Denton, TX 76203 USA..
KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Teknisk informationsvetenskap.ORCID-id: 0000-0002-7926-5081
2019 (engelsk)Inngår i: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 65, nr 5, s. 3198-3214Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We consider the problem of private information retrieval (PIR) with colluding servers and eavesdroppers (abbreviated as ETPIR). The ETPIR problem is comprised of K messages and N servers where each server stores all K messages, a user who wants to retrieve one of the K messages without revealing the desired message index to any set of T colluding servers, and an eavesdropper who can listen to the queries and answers of any E servers but is prevented from learning any information about the messages. The information theoretic capacity of ETPIR is defined to be the maximum number of desired message symbols retrieved privately per information symbol downloaded. We show that the capacity of ETPIR is C = (1 - (E/N))(1 + (T - E/N - E) + . . . +((T - E/N - E))(K-1))(-1) when E < T, and C = (1 - (E/N)) when E >= T. To achieve the capacity, the servers need to share a common random variable (independent of the messages), and its size must be at least (E/N) . (1/C) symbols per message symbol. Otherwise, with less amount of shared common randomness, ETPIR is not feasible and the capacity reduces to zero. An interesting observation is that the ETPIR capacity expression takes different forms in two regimes. When E < T, the capacity equals the inverse of a sum of a geometric series with K terms and decreases with K; this form is typical for capacity expressions of PIR. When E >= T, the capacity does not depend on K, a typical form for capacity expressions of SPIR (symmetric PIR, which further requires data-privacy, i.e., the user learns no information about other undesired messages); the capacity does not depend on T either. In addition, the ETPIR capacity result includes multiple previous PIR and SPIR capacity results as special cases.

sted, utgiver, år, opplag, sider
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2019. Vol. 65, nr 5, s. 3198-3214
Emneord [en]
Private information retrieval, capacity, colluding servers, eavesdroppers
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-270654DOI: 10.1109/TIT.2018.2884891ISI: 000466029900034Scopus ID: 2-s2.0-85058119637OAI: oai:DiVA.org:kth-270654DiVA, id: diva2:1417791
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QC 20200330

Tilgjengelig fra: 2020-03-30 Laget: 2020-03-30 Sist oppdatert: 2022-06-26bibliografisk kontrollert

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