One extra bit of download ensures perfectly private information retrieval

Shah, Nihar B.; Rashmi, K. V.; Ramchandran, Kannan

doi:10.1109/isit.2014.6874954

Cited by 226 publications

(246 citation statements)

References 9 publications

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“…where D is download cost (the total length of the answers) from the N servers averaged over random query realizations. Notice that the R and D are independent of θ by the privacy constraint in (8).…”

Section: I(qmentioning

confidence: 99%

A New Capacity-Achieving Private Information Retrieval Scheme With (Almost) Optimal File Length for Coded Servers

Zhu

Yan

et al. 2020

IEEE Trans.Inform.Forensic Secur.

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In a distributed storage system, private information retrieval (PIR) guarantees that a user retrieves one file from the system without revealing any information about the identity of its interested file to any individual server. In this paper, we investigate (N, K, M ) coded sever model of PIR, where each of M files is distributed to the N servers in the form of (N, K) maximum distance separable (MDS) code for some N > K and M > 1. As a result, we propose a new capacity-achieving (N, K, M ) coded linear PIR scheme such that it can be implemented with file length K(N−K) gcd(N,K) , which is much smaller than the previous best result K N gcd(N,K) M −1 . Notably, among all the capacity-achieving coded linear PIR schemes, we show that the file length is optimal if M > K gcd(N,K) − K N−K + 1, and within a multiplicative gap K gcd(N,K) of a lower bound on the minimum file length otherwise. Index TermsPrivate information retrieval, distributed storage system, file length, coded servers, capacity-achieving. N M −1 −1 for any N and M .

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Section: I(qmentioning

confidence: 99%

A New Capacity-Achieving Private Information Retrieval Scheme With (Almost) Optimal File Length for Coded Servers

Zhu

Yan

et al. 2020

IEEE Trans.Inform.Forensic Secur.

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show abstract

“…The following results are based on the results for binary schemes in [23], where it was proved that if L ≤ n − 1, the optimal download is L + 1 bits. Now consider a scheme over a q-ary alphabet and transmission using a q ′ -ary alphabet.…”

Section: A Replicated No Collusion/adversariesmentioning

confidence: 99%

On the Capacity of Private Information Retrieval from Coded, Colluding, and Adversarial Servers

Holzbaur

Freij-Hollanti

Hollanti

2019

2019 IEEE Information Theory Workshop (ITW)

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In this work, two practical concepts related to private information retrieval (PIR) are introduced and coined symbol-separated PIR and strongly linear PIR. Being symbolseparated is a sufficient condition for being strongly linear, and strong linearity enables implementation over small finite fields with low sub-packetization degree.Then, the capacity of MDS-coded, linear, symbol-separated PIR in the presence of colluding servers is derived, as well as the capacity of symmetric, linear PIR with colluding, adversarial, and nonresponsive servers for the recently introduced concept of matched randomness. This positively settles the capacity conjectures stated by Freij-Hollanti et al. and Tajeddine et al. in the presented cases. It is also shown that, further restricting to strongly-linear PIR schemes with deterministic linear interference cancellation, the so-called star product scheme proposed by Freij-Hollanti et al. is essentially optimal and induces no capacity loss.

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“…C(3,4,3), which is strictly higher than C ⊥ (3, 4, 3) = (1 + 3 4 + ( 3 4 ) 2 ) −1 = 16 37 , the capacity of separate MDS storage code.…”

mentioning

confidence: 83%

Breaking the MDS-PIR Capacity Barrier via Joint Storage Coding

Sun

Tian

2019

Information

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The capacity of private information retrieval (PIR) from databases coded using maximum distance separable (MDS) codes has been previously characterized by Banawan and Ulukus, where it was assumed that the messages are encoded and stored separably into the databases. This assumption was also usually taken in other related works in the literature, and this capacity is usually referred to as the MDS-PIR capacity colloquially. In this work, we considered the question if and when this capacity barrier can be broken through joint encoding and storing of the messages. Our main results are two classes of novel code constructions which allow joint encoding as well as the corresponding PIR protocols, which indeed outperform the separate MDS-coded systems. Moreover, we show that a simple but novel expansion technique allows us to generalize these two classes of codes, resulting in a wider range of the cases where this capacity barrier can be broken.

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One extra bit of download ensures perfectly private information retrieval

Cited by 226 publications

References 9 publications

A New Capacity-Achieving Private Information Retrieval Scheme With (Almost) Optimal File Length for Coded Servers

A New Capacity-Achieving Private Information Retrieval Scheme With (Almost) Optimal File Length for Coded Servers

On the Capacity of Private Information Retrieval from Coded, Colluding, and Adversarial Servers

Breaking the MDS-PIR Capacity Barrier via Joint Storage Coding

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