Randomness in Interactive Proofs

Mihir Bellare, Oded Goldreich, Shafi Goldwasser

Abstract: 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 <or=1/3) in which Arthur sends l=l(n) random bits per rounds, a proof system that achieves error probability 2/sup -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: