Efficient Information-Theoretic Secure Multiparty Computation over Z/p^k Z via Galois Rings

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At CRYPTO 2018, Cramer et al. introduced a secret-sharing based protocol called SPDZ2k that allows for secure multiparty computation (MPC) in the dishonest majority setting over the ring of integers modulo 2^k, thus solving a long-standing open question in MPC about secure computation over rings in this setting.
In this paper we study this problem in the information-theoretic scenario.
More specifically, we ask the following question: Can we obtain information-theoretic MPC protocols that work over rings with comparable efficiency to corresponding protocols over fields?
We answer this question in the affirmative by presenting an efficient protocol for robust Secure Multiparty Computation over Z/p^k Z (for any prime p and positive integer k) that is perfectly secure against active adversaries corrupting a fraction of at most 1/3 players, and a robust protocol that is statistically secure against an active adversary corrupting a fraction of at most 1/2 players.
Original languageEnglish
Title of host publicationTheory of Cryptography : Proceedings
EditorsDennis Hofheinz, Alon Rosen
Number of pages11
VolumePart 1
Place of publicationCham
PublisherSpringer
Publication year2019
Pages471-501
ISBN (print)978-3-030-36029-0
ISBN (Electronic)978-3-030-36030-6
DOIs
Publication statusPublished - 2019
EventTheory of Cryptography Conference, 17th International Conference: TCC 2019 - Nurnberg, Germany
Duration: 1 Dec 20195 Dec 2019
Conference number: 17

Conference

ConferenceTheory of Cryptography Conference, 17th International Conference
Nummer17
LandGermany
ByNurnberg
Periode01/12/201905/12/2019
SeriesLecture Notes in Computer Science
Volume11891
ISSN0302-9743

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