1. SPDZ2k: Efficient MPC mod 2^k for Dishonest Majority 2018 Crypto MPC
    Ronald Cramer and Ivan Damgård and Daniel Escudero and Peter Scholl and Chaoping Xing
    [View PDF on eprint.iacr.org]
    [Show BibTex Citation]

    @misc{cryptoeprint:2018:482,
    author = {Ronald Cramer and Ivan Damgård and Daniel Escudero and Peter Scholl and Chaoping Xing},
    title = {SPDZ2k: Efficient MPC mod 2^k for Dishonest Majority},
    howpublished = {Cryptology ePrint Archive, Report 2018/482},
    year = {2018},
    note = {\url{https://eprint.iacr.org/2018/482}},
    }

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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