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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti


CiteScore 2017: 1.43

SCImago Journal Rank (SJR) 2017: 0.293
Source Normalized Impact per Paper (SNIP) 2017: 1.117

Mathematical Citation Quotient (MCQ) 2017: 0.51

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1862-2984
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Volume 12, Issue 4

Issues

Multi-prover proof of retrievability

Maura B. Paterson
  • Department of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London WC1E 7HX, United Kingdom
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/ Douglas R. Stinson
  • Corresponding author
  • David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
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/ Jalaj Upadhyay
Published Online: 2018-09-20 | DOI: https://doi.org/10.1515/jmc-2018-0012

Abstract

There has been considerable recent interest in “cloud storage” wherein a user asks a server to store a large file. One issue is whether the user can verify that the server is actually storing the file, and typically a challenge-response protocol is employed to convince the user that the file is indeed being stored correctly. The security of these schemes is phrased in terms of an extractor which will recover the file given any “proving algorithm” that has a sufficiently high success probability. This forms the basis of proof-of-retrievability (PoR) systems. In this paper, we study multiple server PoR systems. We formalize security definitions for two possible scenarios: (i) A threshold of servers succeeds with high enough probability (worst case), and (ii) the average of the success probability of all the servers is above a threshold (average case). We also motivate the study of confidentiality of the outsourced message. We give MPoR schemes which are secure under both these security definitions and provide reasonable confidentiality guarantees even when there is no restriction on the computational power of the servers. We also show how classical statistical techniques previously used by us can be extended to evaluate whether the responses of the provers are accurate enough to permit successful extraction. We also look at one specific instantiation of our construction when instantiated with the unconditionally secure version of the Shacham–Waters scheme. This scheme gives reasonable security and privacy guarantee. We show that, in the multi-server setting with computationally unbounded provers, one can overcome the limitation that the verifier needs to store as much secret information as the provers.

Keywords: Proof of retrievability; multiple users; secret sharing

MSC 2010: 94A60

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About the article


Received: 2018-03-17

Revised: 2018-07-03

Accepted: 2018-08-10

Published Online: 2018-09-20

Published in Print: 2018-12-01


Citation Information: Journal of Mathematical Cryptology, Volume 12, Issue 4, Pages 203–220, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2018-0012.

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