A Randomnesss-Rounds Tradeoff in Private Computation

We study the role of randomness in multi-party private computations. In particular, we give several results that prove the existence of a randomness-rounds tradeoff in multi-party private computation of xor. We show that with a single random bit, �(n) rounds are necessary and sufficient to privately compute xor of n input bits. With d � 2 random bits, �(log n/d) rounds are necessary, and O(log n/ log d) are sufficient.More generally, we show that the private computation of a boolean function. f, using d � 2 random bits, requires �(log S(f)/d) rounds, where S(f) is the sensitivity of f. Using a single random bit, �(S(f)) rounds are necessary.

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