Automata, Languages and Programming
Volume 1853 of the series Lecture Notes in Computer Science pp 576587
Scalable Secure Storage when Half the System Is Faulty
 Noga AlonAffiliated withSchool of Mathematical Sciences, Tel Aviv University
 , Haim KaplanAffiliated withSchool of Mathematical Sciences, Tel Aviv University
 , Michael KrivelevichAffiliated withSchool of Mathematical Sciences, Tel Aviv University
 , Dahlia MalkhiAffiliated withSchool of Computer Science and Engineering, The Hebrew University of Jerusalem
 , Julien SternAffiliated withLaboratoire de Recherche en Informatique, CNRS  Universite de Paris Sud
Abstract
In this paper, we provide a method to safely store a document in perhaps the most challenging settings, a highly decentralized replicated storage system where up to half of the storage servers may incur arbitrary failures, including alterations to data stored in them.
Using an error correcting code (ECC), e.g., a ReedSolomon code, one can take n pieces of a document, replace each piece with another piece of size larger by a factor of \( \frac{n} {{n  2t}} \) such that it is possible to recover the original set even when up to t of the larger pieces are altered. For t close to n/2 the space overhead of this scheme is close to n, and an ECC such as the ReedSolomon code degenerates to a trivial replication code.
We show a technique to reduce this large space overhead for high values of t. Our scheme blows up each piece by a factor slightly larger than two using an erasure code which makes it possible to recover the original set using n/2  O(n/d) of the pieces, where d ≈ 80 is a fixed constant. Then we attach to each piece O(d log n/ log d) additional bits to make it possible to identify a large enough set of unmodified pieces, with negligible error probability, assuming that at least half the pieces are unmodified, and with low complexity. For values of t close to n/2 we achieve a large asymptotic space reduction over the best possible space blowup of any ECC in deterministic setting. Our approach makes use of a dregular expander graph to compute the bits required for the identification of n/2  O(n/d) good pieces.
 Title
 Scalable Secure Storage when Half the System Is Faulty
 Book Title
 Automata, Languages and Programming
 Book Subtitle
 27th International Colloquium, ICALP 2000 Geneva, Switzerland, July 9–15, 2000 Proceedings
 Pages
 pp 576587
 Copyright
 2000
 DOI
 10.1007/354045022X_49
 Print ISBN
 9783540677154
 Online ISBN
 9783540450221
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1853
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Ugo Montanari ^{(4)}
 José D. P. Rolim ^{(5)}
 Emo Welzl ^{(6)}
 Editor Affiliations

 4. Department of Computer Sciences, University of Pisa
 5. Center for Computer Sciences, University of Geneva
 6. Department of Computer Sciences, ETH Zurich
 Authors

 Noga Alon ^{(7)}
 Haim Kaplan ^{(7)}
 Michael Krivelevich ^{(7)}
 Dahlia Malkhi ^{(8)}
 Julien Stern ^{(9)}
 Author Affiliations

 7. School of Mathematical Sciences, Tel Aviv University, Israel
 8. School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel
 9. Laboratoire de Recherche en Informatique, CNRS  Universite de Paris Sud, France
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