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 -