We investigate the relations between two major properties of multiparty protocols: fault tolerance (or resilience ) and randomness . Fault-tolerance is measured in terms of the maximum number of colluding faulty parties, t , that a protocol can withstand and still maintain the privacy of the inputs and the correctness of the outputs (of the honest parties). Randomness is measured in terms of the total number of random bits needed by the parties in order to execute the protocol.
Previously, the upper bound on the amount of randomness required by general constructions for securely computing any nontrivial function f was polynomial both in n , the total number of parties, and the circuit-size C(f) . This was the state of knowledge even for the special case t=1 (i.e., when there is at most one faulty party). In this paper we show that for any linear-size circuit, and for any number t < n/3 of faulty
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