Abstract
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, Θ(n) rounds are necessary and sufficient to privately compute xor of n input bits. With d ≥ 2 random bits, Ω(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 Ω(log S(f)/d) rounds, where S(f) is the sensitivity of f. Using a single random bit, Ω(S(f)) rounds are necessary.
Work on this paper by the first author was supported by the E. and J. Bishop Research Fund, and by the Fund for the Promotion of Research at the Technion. Part of his research was performed while he was at Aiken Computation Laboratory, Harvard University, supported by research contracts ONR-N0001491-J-1981 and NSF-CCR-90-07677.
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Kushilevitz, E., Rosén, A. (1994). A Randomness-Rounds Tradeoff in Private Computation. In: Desmedt, Y.G. (eds) Advances in Cryptology — CRYPTO ’94. CRYPTO 1994. Lecture Notes in Computer Science, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48658-5_36
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