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2020 | OriginalPaper | Buchkapitel

Guaranteed Output Delivery Comes Free in Honest Majority MPC

verfasst von : Vipul Goyal, Yifan Song, Chenzhi Zhu

Erschienen in: Advances in Cryptology – CRYPTO 2020

Verlag: Springer International Publishing

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Abstract

We study the communication complexity of unconditionally secure MPC with guaranteed output delivery over point-to-point channels for corruption threshold \(t < n/2\), assuming the existence of a public broadcast channel. 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 until now. We also focus on the concrete communication complexity of evaluating each multiplication gate.

We resolve the above question in the affirmative by providing an MPC with communication complexity \(O(Cn\phi )\) bits (ignoring fixed terms which are independent of the circuit) where \(\phi \) is the length of an element in the field, C is the size of the (arithmetic) circuit, n is the number of parties. This is the first construction where the asymptotic communication complexity matches the best-known semi-honest protocol. This represents a strict improvement over the previously best-known communication complexity of \(O(C(n\phi \,+\,\kappa )\,+\,D_Mn^2\kappa )\) bits, where \(\kappa \) is the security parameter and \(D_M\) is the multiplicative depth of the circuit. Furthermore, the concrete communication complexity per multiplication gate is 5.5 field elements per party in the best case and 7.5 field elements in the worst case when one or more corrupted parties have been identified. This also roughly matches the best-known semi-honest protocol, which requires 5.5 field elements per gate.

The above also yields the first secure-with-abort MPC protocol with the same cost per multiplication gate as the best-known semi-honest protocol. Our main result is obtained by compiling the secure-with-abort MPC protocol into a fully secure one.

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Titel: Guaranteed Output Delivery Comes Free in Honest Majority MPC
verfasst von: Vipul Goyal
Yifan Song
Chenzhi Zhu
Verlag: Springer International Publishing
Buch: Advances in Cryptology – CRYPTO 2020
Print ISBN: 978-3-030-56879-5

Electronic ISBN: 978-3-030-56880-1

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-56880-1_22

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