### Round-Optimal Secure Two-Party Computation from Trapdoor Permutations

Michele Ciampi, Rafail Ostrovsky, Luisa Siniscalchi, and Ivan Visconti

##### Abstract

In this work we continue the study on the round complexity of secure two-party computation with black-box simulation. Katz and Ostrovsky in CRYPTO 2004 showed a 5 (optimal) round construction assuming trapdoor permutations for the general case where both players receive the output. They also proved that their result is round optimal. This lower bound has been recently revisited by Garg et al. in Eurocrypt 2016 where a 4 (optimal) round protocol is showed assuming a simultaneous message exchange channel. Unfortunately there is no instantiation of the protocol of Garg et al. under standard polynomial-time hardness assumptions. In this work we close the above gap by showing a 4 (optimal) round construction for secure two-party computation in the simultaneous message channel model with black-box simulation, assuming trapdoor permutations against polynomial-time adversaries. Our construction for secure two-party computation relies on a special 4-round protocol for oblivious transfer that nicely composes with other protocols in parallel. We define and construct such special oblivious transfer protocol from trapdoor permutations. This building block is clearly interesting on its own. Our construction also makes use of a recent advance on non-malleability: a delayed-input 4-round non-malleable zero knowledge argument.

Available format(s)
Category
Cryptographic protocols
Publication info
A minor revision of an IACR publication in TCC 2017
Keywords
Two-Party ComputationOblivious TransferSimultaneous Model Exchange Channel
Contact author(s)
micheleciampi1990 @ gmail com
History
2018-04-19: revised
See all versions
Short URL
https://ia.cr/2017/920

CC BY

BibTeX

@misc{cryptoeprint:2017/920,
author = {Michele Ciampi and Rafail Ostrovsky and Luisa Siniscalchi and Ivan Visconti},
title = {Round-Optimal Secure Two-Party Computation from Trapdoor Permutations},
howpublished = {Cryptology ePrint Archive, Paper 2017/920},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/920}},
url = {https://eprint.iacr.org/2017/920}
}

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