A Universal Problem in Secure and Verifiable Distributed Computation

A notion of reduction among multi-party distributed computing problems is introduced and formally defined. Here the reduction from one multi-party distributed computing problem to another means, roughly speaking, a secure and verifiable protocol for the first problem can be constructed solely from a secure and verifiable protocol of the second. A universal or complete multi-party distributed computing problem is defined to be one to which the whole class of multiparty problems is reducible. One is interested in finding a simple and natural multi-party problem which is universal. The distributed sum problem, of summing secret inputs from N parties, is shown to be such a universal problem. The reduction yields an efficient systematic method for the automatic generation of secure and verifiable protocols for all multi-party distributed computing problems. Incorporating the result from [14], it also yields an alternative proof to the completeness theorem of [9] that assiuxung honest majority and the existence of a trap-door function, for all multi-party problems, there is a secure and verifiable protocol.

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

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

[3]  Nancy A. Lynch,et al.  Cryptographic protocols , 1982, STOC '82.

[4]  Shang-Hua Teng,et al.  Secure and verifiable schemes for election and general distributed computing problems , 1988, PODC '88.

[5]  David Chaum,et al.  Untraceable electronic mail, return addresses, and digital pseudonyms , 1981, CACM.

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

[7]  Andrew Chi-Chih Yao,et al.  Protocols for secure computations , 1982, FOCS 1982.

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

[9]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[10]  Andrew Chi-Chih Yao,et al.  Theory and application of trapdoor functions , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[11]  Michael J. Fischer,et al.  A robust and verifiable cryptographically secure election scheme , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[12]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[13]  Josh Benaloh,et al.  Secret Sharing Homomorphisms: Keeping Shares of A Secret Sharing , 1986, CRYPTO.

[14]  Moti Yung,et al.  Cryptographic Computation: Secure Faut-Tolerant Protocols and the Public-Key Model , 1987, CRYPTO.

[15]  Gilles Brassard,et al.  Non-transitive transfer of confidence: A perfect zero-knowledge interactive protocol for SAT and beyond , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

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

[17]  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).