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Reaching consensus for asynchronous distributed key generation

Reaching consensus for asynchronous distributed key generation We give a protocol for Asynchronous Distributed Key Generation (A-DKG) that is optimally resilient (can withstand f<n3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\varvec{f}}}<\frac{{{\varvec{n}}}}{{{\varvec{3}}}}$$\end{document} faulty parties), has a constant expected number of rounds, has O(λn3)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\varvec{O}}}({\varvec{\lambda }} {{\varvec{n}}}^{{\varvec{3}}})$$\end{document} expected communication complexity, and assumes only the existence of a PKI. Prior to our work, the best A-DKG protocols required Ω(n)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\varvec{\Omega }}({{\varvec{n}}})$$\end{document} expected number of rounds, and Ω(n4)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\varvec{\Omega }}({{\varvec{n}}}^4)$$\end{document} expected communication. Our A-DKG protocol relies on several building blocks that are of independent interest. We define and design a Proposal Election (PE) protocol that allows parties to retrospectively agree on a valid proposal after enough proposals have been sent from different parties. With constant probability the elected proposal was proposed by a nonfaulty party. In building our PE protocol, we design a Verifiable Gather protocol which allows parties to communicate which proposals they have and have not seen in a verifiable manner. The final building block to our A-DKG is a Validated Asynchronous Byzantine Agreement (VABA) protocol. We use our PE protocol to construct a VABA protocol that does not require leaders or an asynchronous DKG setup. Our VABA protocol can be used more generally when it is not possible to use threshold signatures. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Distributed Computing Springer Journals

Reaching consensus for asynchronous distributed key generation

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0178-2770
eISSN
1432-0452
DOI
10.1007/s00446-022-00436-8
Publisher site
See Article on Publisher Site

Abstract

We give a protocol for Asynchronous Distributed Key Generation (A-DKG) that is optimally resilient (can withstand f<n3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\varvec{f}}}<\frac{{{\varvec{n}}}}{{{\varvec{3}}}}$$\end{document} faulty parties), has a constant expected number of rounds, has O(λn3)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\varvec{O}}}({\varvec{\lambda }} {{\varvec{n}}}^{{\varvec{3}}})$$\end{document} expected communication complexity, and assumes only the existence of a PKI. Prior to our work, the best A-DKG protocols required Ω(n)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\varvec{\Omega }}({{\varvec{n}}})$$\end{document} expected number of rounds, and Ω(n4)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\varvec{\Omega }}({{\varvec{n}}}^4)$$\end{document} expected communication. Our A-DKG protocol relies on several building blocks that are of independent interest. We define and design a Proposal Election (PE) protocol that allows parties to retrospectively agree on a valid proposal after enough proposals have been sent from different parties. With constant probability the elected proposal was proposed by a nonfaulty party. In building our PE protocol, we design a Verifiable Gather protocol which allows parties to communicate which proposals they have and have not seen in a verifiable manner. The final building block to our A-DKG is a Validated Asynchronous Byzantine Agreement (VABA) protocol. We use our PE protocol to construct a VABA protocol that does not require leaders or an asynchronous DKG setup. Our VABA protocol can be used more generally when it is not possible to use threshold signatures.

Journal

Distributed ComputingSpringer Journals

Published: Sep 8, 2022

Keywords: Distributed computing; Distributed key generation; Consensus; Byzantine adversary; Asynchrony

References