## Cryptology ePrint Archive: Report 2021/1174

On Communication-Efficient Asynchronous MPC with Adaptive Security

Annick Chopard and Martin Hirt and Chen-Da Liu-Zhang

Abstract: Secure multi-party computation (MPC) allows a set of $n$ parties to jointly compute an arbitrary computation over their private inputs. Two main variants have been considered in the literature according to the underlying communication model. Synchronous MPC protocols proceed in rounds, and rely on the fact that the communication network provides strong delivery guarantees within each round. Asynchronous MPC protocols achieve security guarantees even when the network delay is arbitrary.

While the problem of MPC has largely been studied in both variants with respect to both feasibility and efficiency results, there is still a substantial gap when it comes to communication complexity of adaptively secure protocols. Concretely, while adaptively secure synchronous MPC protocols with linear communication are known for a long time, the best asynchronous protocol communicates $\mathcal{O}(n^4 \kappa)$ bits per multiplication.

In this paper, we make progress towards closing this gap by providing two protocols. First, we present an adaptively secure asynchronous protocol with optimal resilience $t<n/3$ and $\mathcal{O}(n^2 \kappa)$ bits of communication per multiplication, improving over the state of the art protocols in this setting by a quadratic factor in the number of parties. The protocol has cryptographic security and follows the CDN approach [Eurocrypt'01], based on additive threshold homomorphic encryption.

Second, we show an optimization of the above protocol that tolerates up to $t<(1-\epsilon)n/3$ corruptions and communicates $\mathcal{O}(n\cdot \poly(\kappa))$ bits per multiplication under stronger assumptions.

Category / Keywords: cryptographic protocols / Multi-party computation, asynchronous, adaptive security

Original Publication (with major differences): IACR-TCC-2021

Date: received 13 Sep 2021, last revised 8 Nov 2021

Contact author: achopard at ethz ch, hirt at ethz ch, cliuzhan at andrew cmu edu

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2021/1174

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