Round-Optimal Secure Two-Party Computation from Trapdoor Permutations
Michele Ciampi, Rafail Ostrovsky, Luisa Siniscalchi, Ivan ViscontiAbstract:
In this work we continue the study on the round complexity if 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 recive the output. They also provide that their result is round optimal. This lower bound has been recently revised by garf 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. aWe 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 in non-malleability: a delayed input 4- round non-malleable aero knowledge argument.
comment: TCC (1) 2017: 678-710
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