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Title:
Improved Black-Box Constructions of Composable Secure Computation
Authors: Rohit Chatterjee, Xiao Liang, Omkant Pandey
Abstract:We close the gap between black-box and non-black-box constructions of \mathit{composable} secure multiparty computation in the plain model under the \mathit{minimal} assumption of semi-honest oblivious transfer. The notion of protocol composition we target is \mathit{angel\text{-}based} security, or more precisely, security with super-polynomial helpers. In this notion, both the simulator and the adversary are given access to an oracle called an \mathit{angel} that can perform some predefined super-polynomial time task. Angel-based security maintains the attractive properties of the universal composition framework while providing meaningful security guarantees in complex environments without having to trust anyone. Angel-based security can be achieved using non-black-box constructions in \max(R_{\mathsf{OT}},\widetilde{O}(\log n)) rounds where R_{\mathsf{OT}} is the round-complexity of the semi-honest oblivious transfer. However, currently, the best known \mathit{black\text{-}box} constructions under the same assumption require \max(R_{\mathsf{OT}},\widetilde{O}(\log^2 n)) rounds. If R_{\mathsf{OT}} is a constant, the gap between non-black-box and black-box constructions can be a multiplicative factor \log n. We close this gap by presenting a \max(R_{\mathsf{OT}},\widetilde{O}(\log n))-round black-box construction. We achieve this result by constructing constant-round 1-1 CCA-secure commitments assuming only black-box access to one-way functions.
ePrint: https://eprint.iacr.org/2020/494
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