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SPD\(\mathbb {Z}_{2^k}\): Efficient MPC mod \(2^k\) for Dishonest Majority

  • Ronald Cramer
  • Ivan Damgård
  • Daniel Escudero
  • Peter Scholl
  • Chaoping Xing
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10992)

Abstract

Most multi-party computation protocols allow secure computation of arithmetic circuits over a finite field, such as the integers modulo a prime. In the more natural setting of integer computations modulo \(2^{k}\), which are useful for simplifying implementations and applications, no solutions with active security are known unless the majority of the participants are honest.

We present a new scheme for information-theoretic MACs that are homomorphic modulo \(2^k\), and are as efficient as the well-known standard solutions that are homomorphic over fields. We apply this to construct an MPC protocol for dishonest majority in the preprocessing model that has efficiency comparable to the well-known SPDZ protocol (Damgård et al., CRYPTO 2012), with operations modulo \(2^k\) instead of over a field. We also construct a matching preprocessing protocol based on oblivious transfer, which is in the style of the MASCOT protocol (Keller et al., CCS 2016) and almost as efficient.

Notes

Acknowledgements

This work has been supported by the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No 669255 (MPCPRO); the European Union’s Horizon 2020 research and innovation programme under grant agreement No 731583 (SODA); the European Union’s Horizon 2020 research and innovation programme under grant agreement No 74079 (ALGSTRONGCRYPTO); and the Danish Independent Research Council under Grant-ID DFF-6108-00169 (FoCC).

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Ronald Cramer
    • 1
    • 2
  • Ivan Damgård
    • 3
  • Daniel Escudero
    • 3
  • Peter Scholl
    • 3
  • Chaoping Xing
    • 4
  1. 1.CWIAmsterdamThe Netherlands
  2. 2.Leiden UniversityLeidenThe Netherlands
  3. 3.Aarhus UniversityAarhusDenmark
  4. 4.Nanyang Technological UniversitySingaporeSingapore

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