We revisit the exact round complexity of secure two-party computation. While four rounds are known to be sufficient for securely computing general functions that provide output to one party [Katz-Ostrovsky, CRYPTO’04], Goldreich-Krawczyk [SIAM J. Computing’96] proved that three rounds are insufficient for this task w.r.t. black-box simulation. In this work, we study the feasibility of secure computation in three rounds using non-black-box simulation. Our main result is a three-round two-party computation protocol for general functions against adversaries with auxiliary inputs of a priori bounded size. This result relies on a new two round input-extraction protocol based on succinct randomized encodings. We also provide a partial answer to the question of achieving security against non-uniform adversaries. Assuming sub-exponentially secure iO and one-way functions, we rule out three-round protocols that achieve polynomial simulation-based security against the output party and exponential indistinguishability-based security against the other party.
CITATION STYLE
Ananth, P., & Jain, A. (2017). On Secure Two-Party Computation in Three Rounds. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10677 LNCS, pp. 612–644). Springer Verlag. https://doi.org/10.1007/978-3-319-70500-2_21
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