TY - GEN

T1 - Non-cryptographic fault-tolerant computing in a constant number of rounds of interaction

AU - Bar-Ilan, Judit

AU - Beaver, Donald

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0024940038&partnerID=8YFLogxK

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AN - SCOPUS:0024940038

SN - 0897913264

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 201

EP - 209

BT - Proc Eighth ACM Symp Princ Distrib Comput

PB - Publ by ACM

T2 - Proceedings of the Eighth Annual ACM Symposium on Principles of Distributed Computing

Y2 - 14 August 1989 through 16 August 1989

ER -