Non-cryptographic fault-tolerant computing in a constant number of rounds of interaction

Judit Bar-Ilan, Donald Beaver

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

200 Scopus citations

Abstract

Let f(x1, ..., xn) be computed by a circuit C with bounded fanin. There are non-cryptographic protocols by which a network of n processors can evaluate C at secret inputs x1, ..., xn, revealing the final value f(x1, ..., xn) without revealing any information about the inputs except what the final result provides. Current methods require O(depth(C)) rounds of communication and messages of size polynomial in size(C) and n. In practical terms, such a degree of interaction is unacceptable. We show how to secretly evaluate any finite function in a constant expected number of rounds, regardless of the minimal depth of a circuit for that function. We provide a means to simulate unbounded fanin multiplicative (or AND) gates using constant rounds. Using our new methods, any function can be evaluated in a constant number of rounds, using messages of size proportional to the size of a constant-depth, unbounded-fanin circuit describing the function. We also show how to secretly evaluate any function described by an algebraic formula of polynomial size (or an NC1 circuit), using a constant number of rounds yet requiring messages of only polynomial size. This provides a speedup over original methods by a factor of log n, while incurring only a polynomial number of bits.

Original languageEnglish
Title of host publicationProc Eighth ACM Symp Princ Distrib Comput
PublisherPubl by ACM
Pages201-209
Number of pages9
ISBN (Print)0897913264
StatePublished - 1989
Externally publishedYes
EventProceedings of the Eighth Annual ACM Symposium on Principles of Distributed Computing - Edmonton, Alberta, Can
Duration: 14 Aug 198916 Aug 1989

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

ConferenceProceedings of the Eighth Annual ACM Symposium on Principles of Distributed Computing
CityEdmonton, Alberta, Can
Period14/08/8916/08/89

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