Explicit expanders and the Ramanujan conjectures
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Efficient dispersal of information for security, load balancing, and fault tolerance
Journal of the ACM (JACM)
Integrating security with fault-tolerant distributed databases
The Computer Journal - Special issue on databases
Highly resilient correctors for polynomials
Information Processing Letters
Distributed fingerprints and secure information dispersal
PODC '93 Proceedings of the twelfth annual ACM symposium on Principles of distributed computing
Tolerating a linear number of faults in networks of bounded degree
Information and Computation
Computational Complexity
Practical loss-resilient codes
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Practical Byzantine fault tolerance
OSDI '99 Proceedings of the third symposium on Operating systems design and implementation
Escaping the evils of centralized control with self-certifying pathnames
Proceedings of the 8th ACM SIGOPS European workshop on Support for composing distributed applications
An Architecture for Survivable Coordination in Large Distributed Systems
IEEE Transactions on Knowledge and Data Engineering
Secure Distributed Storage and Retrieval
WDAG '97 Proceedings of the 11th International Workshop on Distributed Algorithms
How to Make Replicated Data Secure
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Learning polynomials with queries: The highly noisy case
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A linear time erasure-resilient code with nearly optimal recovery
IEEE Transactions on Information Theory - Part 1
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Efficient decoding of Reed-Solomon codes beyond half the minimum distance
IEEE Transactions on Information Theory
Towards tamper-evident storage on patterned media
FAST'08 Proceedings of the 6th USENIX Conference on File and Storage Technologies
Vertex percolation on expander graphs
European Journal of Combinatorics
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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 Reed-Solomon code, one can take n pieces of a document, replace each piece with another piece of size larger by a factor of 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 blowup factor of this scheme is close to n, and the overhead of an ECC such as the Reed-Solomon code degenerates to that of 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 d80 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 d-regular expander graph to compute the bits required for the identification of n/2-O (n/d) good pieces.