 
Summary: Scalable Secure Storage when Half the System is Faulty§
Noga Alon
Haim Kaplan
Michael Krivelevich
Dahlia Malkhi
Julien Stern
February 22, 2002
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 n
n2t+1 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 ReedSolomon 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 d 80 is a fixed constant. Then we attach to
