Completeness theorems for non-cryptographic fault-tolerant distributed computation

Every function of <italic>n</italic> inputs can be efficiently computed by a complete network of <italic>n</italic> processors in such a way that:<list><item>If no faults occur, no set of size <italic>t</italic> < <italic>n</italic>/2 of players gets any additional information (other than the function value), </item><item>Even if Byzantine faults are allowed, no set of size <italic>t</italic> < <italic>n</italic>/3 can either disrupt the computation or get additional information. </item></list> Furthermore, the above bounds on <italic>t</italic> are tight!

[1]  W. W. Peterson,et al.  Error-Correcting Codes , 1962 .

[2]  James L. Massey,et al.  Review of 'Error-Correcting Codes, 2nd edn.' (Peterson, W. W., and Weldon, E. J., Jr.; 1972) , 1973, IEEE Trans. Inf. Theory.

[3]  Whitfield Diffie,et al.  New directions in cryptography , 1976, IEEE Trans. Inf. Theory.

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

[5]  Leslie Lamport,et al.  Reaching Agreement in the Presence of Faults , 1980, JACM.

[6]  Danny Dolev,et al.  Polynomial algorithms for multiple processor agreement , 1982, STOC '82.

[7]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[8]  Andrew Chi-Chih Yao,et al.  How to Generate and Exchange Secrets (Extended Abstract) , 1986, FOCS.

[9]  A. Yao How to generate and exchange secrets , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[10]  Silvio Micali,et al.  Proofs that yield nothing but their validity and a methodology of cryptographic protocol design , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[11]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[12]  David Chaum,et al.  Multiparty unconditionally secure protocols , 1988, STOC '88.

[13]  Nathan Linial,et al.  Collective Coin Flipping , 1989, Advances in Computational Research.