Abstract
We study the communication complexity of unconditionally secure MPC with guaranteed output delivery over point-to-point channels for corruption threshold \(t < n/3\). We ask the question: “is it possible to construct MPC in this setting s.t. the communication complexity per multiplication gate is linear in the number of parties?” While a number of works have focused on reducing the communication complexity in this setting, the answer to the above question has remained elusive for over a decade.
We resolve the above question in the affirmative by providing an MPC with communication complexity \(O(Cn\kappa + n^3\kappa )\) where \(\kappa \) is the size of an element in the field, C is the size of the (arithmetic) circuit, and, n is the number of parties. This represents a strict improvement over the previously best known communication complexity of \(O(Cn\kappa +D_Mn^2\kappa +n^3\kappa )\) where \(D_M\) is the multiplicative depth of the circuit. To obtain this result, we introduce a novel technique called 4-consistent tuples of sharings which we believe to be of independent interest.
V. Goyal and Y. Song—Research supported in part by a JP Morgan Faculty Fellowship, a gift from Ripple, a gift from DoS Networks, a grant from Northrop Grumman, and, a Cylab seed funding award.
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Goyal, V., Liu, Y., Song, Y. (2019). Communication-Efficient Unconditional MPC with Guaranteed Output Delivery. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11693. Springer, Cham. https://doi.org/10.1007/978-3-030-26951-7_4
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