In Appendix G of the Hawk paper, where it talks about financially fair SFE, it mentions that it's possible to run a SMPC protocol where, at the end, each party has a share of their own output y, and a share of a nonce ρ, where ρ must be reconstructed in a fair exchange, and the party obtains their output by computing xor(y, ρ). In Theorem 3, the paper implies that the underlying secret-sharing protocol is information-theoretically secret against n-1 corruptions (i.e. t=n) and that this SMPC protocol is UC-secure against an arbitrary number of corruptions, while still being able to evaluate arbitrary functions.

This is a much better security property than any SMPC protocol I'm aware of, and certainly better than what I've come to expect of SMPC. I've tried looking up this protocol, but with no name or citation I can't find anything. What SMPC/secret-sharing protocols satisfy all these requirements? I want to learn more about them.

  • $\begingroup$ SPDZ uses additive secret sharing, is UC-secure against an arbitrary number of corruptions, can evaluate arbitrary functions. The online phase is information theoretically secure. $\endgroup$
    – mikeazo
    Mar 30 '18 at 17:32

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