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

Authors:
Ronald Cramer
Ivan Damgård
Daniel Escudero
Peter Scholl
Chaoping Xing
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DOI: 10.1007/978-3-319-96881-0_26
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Conference: CRYPTO 2018
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.
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BibTeX
@inproceedings{crypto-2018-28832,
  title={SPD$$\mathbb {Z}_{2^k}$$: Efficient MPC mod $$2^k$$ for Dishonest Majority},
  booktitle={Advances in Cryptology – CRYPTO 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={10992},
  pages={769-798},
  doi={10.1007/978-3-319-96881-0_26},
  author={Ronald Cramer and Ivan Damgård and Daniel Escudero and Peter Scholl and Chaoping Xing},
  year=2018
}