Efficient dispersal of information for security, load balancing, and fault tolerance

An Information Dispersal Algorithm (IDA) is developed that breaks a file <italic>F</italic> of length <italic>L</italic> = ↿ <italic>F</italic>↾ into <italic>n</italic> pieces <italic>F<subscrpt>i</subscrpt></italic>, l ≤ <italic>i</italic> ≤ <italic>n</italic>, each of length ↿<italic>F<subscrpt>i</subscrpt></italic>↾ = <italic>L</italic>/<italic>m</italic>, so that every <italic>m</italic> pieces suffice for reconstructing <italic>F</italic>. Dispersal and reconstruction are computationally efficient. The sum of the lengths ↿<italic>F</italic><subscrpt>i</subscrpt>↾ is (<italic>n</italic>/<italic>m</italic>) · <italic>L</italic>. Since <italic>n</italic>/<italic>m</italic> can be chosen to be close to l, the IDA is space efficient. IDA has numerous applications to secure and reliable storage of information in computer networks and even on single disks, to fault-tolerant and efficient transmission of information in networks, and to communications between processors in parallel computers. For the latter problem provably time-efficient and highly fault-tolerant routing on the <italic>n</italic>-cube is achieved, using just constant size buffers.

[1]  L. Mirsky.  An introduction to linear algebra , 1965 .

[2]  Journal of the Association for Computing Machinery , 1961, Nature.

[3]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[4]  Howard Jay Siegel,et al.  A Model of SIMD Machines and a Comparison of Various Interconnection Networks , 1979, IEEE Transactions on Computers.

[5]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[6]  Michael O. Rabin,et al.  Probabilistic Algorithms in Finite Fields , 1980, SIAM J. Comput..

[7]  G. R. Blakley,et al.  Pooling, Splitting, and Restituting Information to Overcome Total Failure of Some Channels of Communication , 1982, 1982 IEEE Symposium on Security and Privacy.

[8]  Leslie G. Valiant,et al.  A Scheme for Fast Parallel Communication , 1982, SIAM J. Comput..

[9]  Nicholas Pippenger,et al.  Parallel Communication with Limited Buffers (Preliminary Version) , 1984, FOCS.

[10]  Charles L. Seitz,et al.  The cosmic cube , 1985, CACM.

[11]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[12]  P. Raghavan.  Probabilistic construction of deterministic algorithms: Approximating packing integer programs , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[13]  Prabhakar Raghavan,et al.  Probabilistic construction of deterministic algorithms: Approximating packing integer programs , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).