Paper 2023/1130

Asynchronous Agreement on a Core Set in Constant Expected Time and More Efficient Asynchronous VSS and MPC

Ittai Abraham, Intel Labs
Gilad Asharov, Bar-Ilan University
Arpita Patra, Indian Institute of Science Bangalore
Gilad Stern, Tel Aviv University
Abstract

A major challenge of any asynchronous MPC protocol is the need to reach an agreement on the set of private inputs to be used as input for the MPC functionality. Ben-Or, Canetti and Goldreich [STOC 93] call this problem Agreement on a Core Set (ACS) and solve it by running $n$ parallel instances of asynchronous binary Byzantine agreements. To the best of our knowledge, all results in the perfect and statistical security setting used this same paradigm for solving ACS. Using all known asynchronous binary Byzantine agreement protocols, this type of ACS has $\Omega(\log n)$ expected round complexity, which results in such a bound on the round complexity of asynchronous MPC protocols as well (even for constant depth circuits). We provide a new solution for Agreement on a Core Set that runs in expected $O(1)$ rounds. Our perfectly secure variant is optimally resilient ($t<n/4$) and requires just $O(n^4\log n)$ expected communication complexity. We show a similar result with statistical security for $t<n/3$. Our ACS is based on a new notion of Asynchronously Validated Asynchronous Byzantine Agreement (AVABA) and new information-theoretic analogs to techniques used in the authenticated model. Along the way, we also construct a new perfectly secure packed asynchronous verifiable secret sharing (AVSS) protocol with just $O(n^3\log n)$ communication complexity, improving the state of the art by a factor of $O(n)$. This leads to a more efficient asynchronous MPC that matches the state-of-the-art synchronous MPC.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
A major revision of an IACR publication in TCC 2024
DOI
10.1007/978-3-031-78023-3_15
Keywords
consensusagreement on a core setverifiable secret sharingasynchrony
Contact author(s)
ittai abraham @ intel com
gilad asharov @ biu ac il
arpita @ iisc ac in
gilad stern @ mail huji ac il
History
2024-12-05: last of 3 revisions
2023-07-20: received
See all versions
Short URL
https://ia.cr/2023/1130
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2023/1130,
      author = {Ittai Abraham and Gilad Asharov and Arpita Patra and Gilad Stern},
      title = {Asynchronous Agreement on a Core Set in Constant Expected Time and More Efficient Asynchronous {VSS} and {MPC}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1130},
      year = {2023},
      doi = {10.1007/978-3-031-78023-3_15},
      url = {https://eprint.iacr.org/2023/1130}
}
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