Security in Distributed Storage Systems by Communicating a Logarithmic Number of Bits

Abstract

We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that are built into the existing redundancy of the system, we propose a simple linear hashing scheme to detect errors in the storage nodes. Our main result is that for storing a data object of total size M using an (n,k) MDS code over a finite field F_q, up to t_1 = ⌊(n - k)/2⌋ errors can be detected, with probability of failure smaller than 1/M, by communicating only O(n(n-k) log M) bits to a trusted verifier. Our result constructs small projections of the data that preserve the errors with high probability and builds on a pseudorandom generator that fools linear functions. The transmission rate achieved by our scheme is asymptotically equal to the min-cut capacity between the source and any receiver.

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