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Randomness in interactive proofs

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3 Author(s)
M. Bellare ; Lab. for Comput. Sci., MIT, Cambridge, MA, USA ; O. Goldreich ; S. Goldwasser

The quantitative aspects of randomness in interactive proof systems are studied. The result is a randomness-efficient error-reduction technique: given an Arthur-Merlin proof system (error probability ⩽1/3) in which Arthur sends l=l(n ) random bits per rounds, a proof system that achieves error probability 2-k at the cost of Arthur sending only 2l+O(k) random bits per round is constructed. The method maintains the number of rounds in the game. Underlying the transformation is a novel sampling method for approximating the average value of an arbitrary function f: {0,1}l→[0,1]. The method evaluates the function on O-2 log δ-1) sample points generated using only 2l+O(log δ-1) coin tosses to get an estimate which with probability ⩾1-δ is within ε of the average value of the function

Published in:

Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on

Date of Conference:

22-24 Oct 1990