**Asynchronous Secure Multiparty Computation in Constant Time**

*Ran Cohen*

**Abstract: **In the setting of secure multiparty computation, a set of mutually distrusting parties wish to securely compute a joint function. It is well known that if the communication model is asynchronous, meaning that messages can be arbitrarily delayed by an unbounded (yet finite) amount of time, secure computation is feasible if and only if at least two-thirds of the parties are honest, as was shown by Ben-Or, Canetti, and Goldreich [STOC'93] and by Ben-Or, Kelmer, and Rabin [PODC'94]. The running-time of all currently known protocols depends on the function to evaluate. In this work we present the first asynchronous MPC protocol that runs in constant time.

Our starting point is the asynchronous MPC protocol of Hirt, Nielsen, and Przydatek [Eurocrypt'05, ICALP'08]. We integrate \emph{threshold fully homomorphic encryption} in order to reduce the interactions between the parties, thus completely removing the need for the expensive \emph{king-slaves} approach taken by Hirt et al.. Initially, assuming an honest majority, we construct a constant-time protocol in the asynchronous Byzantine agreement (ABA) hybrid model. Using a concurrent ABA protocol that runs in constant expected time, we obtain a constant expected time asynchronous MPC protocol, secure facing static malicious adversaries, assuming t<n/3.

**Category / Keywords: **cryptographic protocols / multiparty computation, asynchronous communication, threshold FHE, constant-time protocols, Byzantine agreement.

**Original Publication**** (with minor differences): **IACR-PKC-2016

**Date: **received 29 Dec 2015, last revised 4 Jan 2016

**Contact author: **cohenrb at cs biu ac il

**Available format(s): **PDF | BibTeX Citation

**Version: **20160104:161334 (All versions of this report)

**Short URL: **ia.cr/2015/1238

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