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Secure Multi-party Quantum Computation with a Dishonest Majority

  • Yfke DulekEmail author
  • Alex B. GriloEmail author
  • Stacey JefferyEmail author
  • Christian MajenzEmail author
  • Christian SchaffnerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12107)

Abstract

The cryptographic task of secure multi-party (classical) computation has received a lot of attention in the last decades. Even in the extreme case where a computation is performed between k mutually distrustful players, and security is required even for the single honest player if all other players are colluding adversaries, secure protocols are known. For quantum computation, on the other hand, protocols allowing arbitrary dishonest majority have only been proven for \(k=2\). In this work, we generalize the approach taken by Dupuis, Nielsen and Salvail (CRYPTO 2012) in the two-party setting to devise a secure, efficient protocol for multi-party quantum computation for any number of players k, and prove security against up to \(k-1\) colluding adversaries. The quantum round complexity of the protocol for computing a quantum circuit of \(\{\mathsf {CNOT}, \mathsf {T} \}\) depth d is \(O(k \cdot (d + \log n))\), where n is the security parameter. To achieve efficiency, we develop a novel public verification protocol for the Clifford authentication code, and a testing protocol for magic-state inputs, both using classical multi-party computation.

Notes

Acknowledgments

We thank Frédéric Dupuis, Florian Speelman, and Serge Fehr for useful discussions, and the anonymous EUROCRYPT referees for helpful comments and suggestions. CM is supported by an NWO Veni Innovational Research Grant under project number VI.Veni.192.159. SJ is supported by an NWO WISE Fellowship, an NWO Veni Innovational Research Grant under project number 639.021.752, and QuantERA project QuantAlgo 680-91-03. SJ is a CIFAR Fellow in the Quantum Information Science Program. CS and CM were supported by a NWO VIDI grant (Project No. 639.022.519). Part of this work was done while YD, AG and CS were visiting the Simons Institute for the Theory of Computing.

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Copyright information

© International Association for Cryptologic Research 2020

Authors and Affiliations

  1. 1.QuSoftAmsterdamThe Netherlands
  2. 2.University of AmsterdamAmsterdamThe Netherlands
  3. 3.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands

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