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2017 | OriginalPaper | Buchkapitel

Four Round Secure Computation Without Setup

verfasst von : Zvika Brakerski, Shai Halevi, Antigoni Polychroniadou

Erschienen in: Theory of Cryptography

Verlag: Springer International Publishing

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Abstract

We construct a 4-round multi-party computation protocol in the plain model for any functionality, secure against a malicious adversary. Our protocol relies on the sub-exponential hardness of the Learning with Errors (LWE) problem with slightly super-polynomial noise ratio, and on the existence of adaptively secure commitments based on standard assumptions. Our round complexity matches a lower bound of Garg et al. (EUROCRYPT ’16), and outperforms the state of the art of 6 rounds based on similar assumptions to ours, and 5 rounds relying on indistinguishability obfuscation and other strong assumptions.

To do this, we construct an LWE based multi-key FHE scheme with a very simple one-round distributed setup procedure (vs. the trusted setup required in previous LWE based constructions). This lets us construct the first 3-round semi-malicious MPC protocol without setup from standard LWE using the approach of Mukherjee and Wichs (EUROCRYPT ’16). Finally, subexponential hardness and adaptive commitments are used to “compile” the protocol into the fully malicious setting.

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Vorheriges Kapitel On Secure Two-Party Computation in Three Rounds

Nächstes Kapitel Round-Optimal Secure Two-Party Computation from Trapdoor Permutations

Nur mit Berechtigung zugänglich

Such commitments can be instantiated from one-way permutations secure w.r.t. sub-exponential time adversaries [COSV16].

Essentially its public matrix for a dual-Regev encryption scheme [Reg09, GPV08].

Technically we “only” need to assume standard security in a world with such a breaking oracle, which is a weaker assumption than full sub-exponential security.

We often consider a slightly weaker notion of homomorphism, where the Setup algorithm gets also a depth-bound d and correctness is then defined only relative to circuits of depth upto d.

Parmeters q, n, w are global and fixed once at the onset of the protocol.

Known transformations yield also protocols for randomized functionalities without increasing the rounds, see [Gol04, Sect. 7.3].

For simplicity of exposition, we omit the rest of the witness values.

To use \(\mathcal{S}^T\) from [MW16, Sect. 6.2] we need to evaluate the protocol on a different function \(\mathcal {F}'\) rather than \(\mathcal {F}\), we ignore this detail in the rest of the presentation here.

The commitment \(\mathsf {bCom}\) starts in the second round, but this is a two-round commitment so the committed value only affects the second message in the commitment, which happens in the third round of the larger protocol.

The concurrent work of [ACJ17] achieves a “compilation” of their robust semi-honest protocol to the malicious setting based on non-malleable commitments but still requires complexity leveraging.

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Titel: Four Round Secure Computation Without Setup
verfasst von: Zvika Brakerski
Shai Halevi
Antigoni Polychroniadou
Verlag: Springer International Publishing
Buch: Theory of Cryptography
Print ISBN: 978-3-319-70499-9

Electronic ISBN: 978-3-319-70500-2

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-70500-2_22

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