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Brief Announcement
DOI: 10.4230/LIPIcs.ICALP.2018.103
Brief Announcement: On Secure m-Party Computation, Commuting Permutation Systems and Unassisted Non-Interactive MPC

Authors: Navneet Agarwal, Sanat Anand, and Manoj Prabhakaran

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
A fundamental problem in the theory of secure multi-party computation (MPC) is to characterize functions with more than 2 parties which admit MPC protocols with information-theoretic security against passive corruption. This question has seen little progress since the work of Chor and Ishai (2001), which demonstrated difficulties in resolving it. In this work, we make significant progress towards resolving this question in the important case of aggregating functionalities, in which m parties P1,...,Pm hold inputs x1,...,xm and an aggregating party P0 must learn f(x1,...,xm). We give a necessary condition and a slightly stronger sufficient condition for f to admit a secure protocol. Both the conditions are stated in terms of an algebraic structure we introduce called Commuting Permutations Systems (CPS), which may be of independent combinatorial interest. When our sufficiency condition is met, we obtain a perfectly secure protocol with minimal interaction, that fits the model of Non-Interactive MPC or NIMPC (Beimel et al., 2014), but without the need for a trusted party to generate correlated randomness. We define Unassisted Non-Interactive MPC (UNIMPC) to capture this variant. We also present an NIMPC protocol for all functionalities, which is simpler and more efficient than the one given in the prior work.
Cite as

Navneet Agarwal, Sanat Anand, and Manoj Prabhakaran. Brief Announcement: On Secure m-Party Computation, Commuting Permutation Systems and Unassisted Non-Interactive MPC. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 103:1-103:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{agarwal_et_al:LIPIcs.ICALP.2018.103,
  author =	{Agarwal, Navneet and Anand, Sanat and Prabhakaran, Manoj},
  title =	{{Brief Announcement: On Secure m-Party Computation, Commuting Permutation Systems and Unassisted Non-Interactive MPC}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{103:1--103:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.103},
  URN =		{urn:nbn:de:0030-drops-91079},
  doi =		{10.4230/LIPIcs.ICALP.2018.103},
  annote =	{Keywords: Secure Multi-Party Computation, Combinatorial Characterization, Latin Hypercube, Permutation Hypercube Complex}
}
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