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On the Computational Overhead of MPC with Dishonest Majority

  • Jesper Buus Nielsen
  • Samuel Ranellucci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10175)

Abstract

We consider the situation where a large number n of players want to securely compute a large function f with security against an adaptive, malicious adversary which might corrupt \(t < c n\) of the parties for some given \(c \in [0,1)\). In other words, only some arbitrarily small constant fraction of the parties are assumed to be honest. For any fixed c, we consider the asymptotic complexity as n and the size of f grows. We are in particular interested in the computational overhead, defined as the total computational complexity of all parties divided by the size of f. We show that it is possible to achieve poly-logarithmic computational overhead for all \(c < 1\). Prior to our result it was only known how to get poly-logarithmic overhead for \(c < \frac{1}{2}\). We therefore significantly extend the area where we can do secure multiparty computation with poly-logarithmic overhead. Since we allow that more than half the parties are corrupted, we can only get security with abort, i.e., the adversary might make the protocol abort before all parties learn their outputs. We can, however, for all c make a protocol for which there exists \(d > 0\) such that if at most dn parties are actually corrupted in a given execution, then the protocol will not abort. Our result is solely of theoretical interest. In its current form, it has not practical implications whatsoever.

Keywords

Secret Share Secret Share Scheme Ideal Functionality Expander Graph Virtual Server 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work is supported by European Research Council Starting Grant 279447. Samuel Ranellucci is supported by NSF grants #1564088 and #1563722. This work is partially supported by the H2020-LEIT-ICT project SODA, project number 731583. The authors would also like to thank the anonymous reviewers for their valuable comments and suggestions. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceAarhus UniversityAarhusDenmark
  2. 2.Department of Computer ScienceGeorge Mason UniversityVirginiaUSA
  3. 3.Department of Computer ScienceUniversity of MarylandMarylandUSA

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