## Cryptology ePrint Archive: Report 2022/257

Guaranteed Output in $O(\sqrt{n})$ Rounds for Round-Robin Sampling Protocols

Ran Cohen and Jack Doerner and Yashvanth Kondi and abhi shelat

Abstract: We introduce a notion of round-robin secure sampling that captures several protocols in the literature, such as the "powers-of-tau" setup protocol for pairing-based polynomial commitments and zk-SNARKs, and certain verifiable mixnets.

Due to their round-robin structure, protocols of this class inherently require $n$ sequential broadcast rounds, where $n$ is the number of participants.

We describe how to compile them generically into protocols that require only $O(\sqrt{n})$ broadcast rounds. Our compiled protocols guarantee output delivery against any dishonest majority. This stands in contrast to prior techniques, which require $\Omega(n)$ sequential broadcasts in most cases (and sometimes many more). Our compiled protocols permit a certain amount of adversarial bias in the output, as all sampling protocols with guaranteed output must, due to Cleve's impossibility result (STOC'86). We show that in the context of the aforementioned applications, this bias is harmless.

Category / Keywords: cryptographic protocols / multiparty computation, guaranteed output delivery, round compression, distributed sampling, setup ceremonies, powers of tau, SNARKs, mixnets

Original Publication (with major differences): IACR-EUROCRYPT-2022

Date: received 26 Feb 2022, last revised 28 Feb 2022

Contact author: j at ckdoerner net

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2022/257

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