Byzantine consensus is Θ(n2): the Dolev-Reischuk bound is tight even in partial synchrony
The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with n processes and at most f < n / 3 failures, any solution to Byzantine consensus exchanges Ω ( n 2...
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| Veröffentlicht in: | Distributed computing 2024-06, Vol.37 (2), p.89-119 |
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| creator | Civit, Pierre Dzulfikar, Muhammad Ayaz Gilbert, Seth Gramoli, Vincent Guerraoui, Rachid Komatovic, Jovan Vidigueira, Manuel |
| description | The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with
n
processes and at most
f
<
n
/
3
failures, any solution to Byzantine consensus exchanges
Ω
(
n
2
)
words, where a word contains a constant number of values and signatures. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony where the network alternates between (1) asynchronous periods, with unbounded message delays, and (2) synchronous periods, with
δ
-bounded message delays. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing
SQuad
, a partially synchronous Byzantine consensus protocol with
O
(
n
2
)
worst-case communication complexity. In addition,
SQuad
is optimally-resilient (tolerating up to
f
<
n
/
3
failures) and achieves
O
(
f
·
δ
)
worst-case latency complexity. The key technical contribution underlying
SQuad
lies in the way we solve
view synchronization
, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present
RareSync
, a view synchronization protocol with
O
(
n
2
)
communication complexity and
O
(
f
·
δ
)
latency complexity, which we utilize in order to obtain
SQuad
. |
| doi_str_mv | 10.1007/s00446-023-00458-w |
| format | Article |
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n
processes and at most
f
<
n
/
3
failures, any solution to Byzantine consensus exchanges
Ω
(
n
2
)
words, where a word contains a constant number of values and signatures. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony where the network alternates between (1) asynchronous periods, with unbounded message delays, and (2) synchronous periods, with
δ
-bounded message delays. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing
SQuad
, a partially synchronous Byzantine consensus protocol with
O
(
n
2
)
worst-case communication complexity. In addition,
SQuad
is optimally-resilient (tolerating up to
f
<
n
/
3
failures) and achieves
O
(
f
·
δ
)
worst-case latency complexity. The key technical contribution underlying
SQuad
lies in the way we solve
view synchronization
, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present
RareSync
, a view synchronization protocol with
O
(
n
2
)
communication complexity and
O
(
f
·
δ
)
latency complexity, which we utilize in order to obtain
SQuad
.</description><identifier>ISSN: 0178-2770</identifier><identifier>EISSN: 1432-0452</identifier><identifier>DOI: 10.1007/s00446-023-00458-w</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Communication ; Complexity ; Computer Communication Networks ; Computer Hardware ; Computer Science ; Computer Systems Organization and Communication Networks ; Messages ; Software Engineering/Programming and Operating Systems ; Synchronism ; Theory of Computation</subject><ispartof>Distributed computing, 2024-06, Vol.37 (2), p.89-119</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-268f6353c38f12a4269530cab231011d343b94e09cbc888ac29447b6fd496c213</citedby><cites>FETCH-LOGICAL-c363t-268f6353c38f12a4269530cab231011d343b94e09cbc888ac29447b6fd496c213</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00446-023-00458-w$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00446-023-00458-w$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Civit, Pierre</creatorcontrib><creatorcontrib>Dzulfikar, Muhammad Ayaz</creatorcontrib><creatorcontrib>Gilbert, Seth</creatorcontrib><creatorcontrib>Gramoli, Vincent</creatorcontrib><creatorcontrib>Guerraoui, Rachid</creatorcontrib><creatorcontrib>Komatovic, Jovan</creatorcontrib><creatorcontrib>Vidigueira, Manuel</creatorcontrib><title>Byzantine consensus is Θ(n2): the Dolev-Reischuk bound is tight even in partial synchrony</title><title>Distributed computing</title><addtitle>Distrib. Comput</addtitle><description>The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with
n
processes and at most
f
<
n
/
3
failures, any solution to Byzantine consensus exchanges
Ω
(
n
2
)
words, where a word contains a constant number of values and signatures. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony where the network alternates between (1) asynchronous periods, with unbounded message delays, and (2) synchronous periods, with
δ
-bounded message delays. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing
SQuad
, a partially synchronous Byzantine consensus protocol with
O
(
n
2
)
worst-case communication complexity. In addition,
SQuad
is optimally-resilient (tolerating up to
f
<
n
/
3
failures) and achieves
O
(
f
·
δ
)
worst-case latency complexity. The key technical contribution underlying
SQuad
lies in the way we solve
view synchronization
, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present
RareSync
, a view synchronization protocol with
O
(
n
2
)
communication complexity and
O
(
f
·
δ
)
latency complexity, which we utilize in order to obtain
SQuad
.</description><subject>Communication</subject><subject>Complexity</subject><subject>Computer Communication Networks</subject><subject>Computer Hardware</subject><subject>Computer Science</subject><subject>Computer Systems Organization and Communication Networks</subject><subject>Messages</subject><subject>Software Engineering/Programming and Operating Systems</subject><subject>Synchronism</subject><subject>Theory of Computation</subject><issn>0178-2770</issn><issn>1432-0452</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kMtOwzAQRS0EEqXwA6wssYGFYfyo47CD8pQqISHYsLEc12lSilPspFX4Er6KbyIlSOxYzYx07h3pIHRI4ZQCJGcRQAhJgHHSbSNF1ltoQAVnpLvYNhoATRRhSQK7aC_GOQBwStkAvVy2H8bXpXfYVj46H5uIy4i_Po89OznHdeHwVbVwK_LoymiL5hVnVeOnG6YuZ0WN3cp5XHq8NKEuzQLH1tsiVL7dRzu5WUR38DuH6Pnm-ml8RyYPt_fjiwmxXPKaMKlyyUfccpVTZgST6YiDNRnjFCidcsGzVDhIbWaVUsayVIgkk_lUpNIyyofoqO9dhuq9cbHW86oJvnupOUiVJlwK6CjWUzZUMQaX62Uo30xoNQW9cah7h7pzqH8c6nUX4n0odrCfufBX_U_qG-aAdEQ</recordid><startdate>20240601</startdate><enddate>20240601</enddate><creator>Civit, Pierre</creator><creator>Dzulfikar, Muhammad Ayaz</creator><creator>Gilbert, Seth</creator><creator>Gramoli, Vincent</creator><creator>Guerraoui, Rachid</creator><creator>Komatovic, Jovan</creator><creator>Vidigueira, Manuel</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>U9A</scope></search><sort><creationdate>20240601</creationdate><title>Byzantine consensus is Θ(n2): the Dolev-Reischuk bound is tight even in partial synchrony</title><author>Civit, Pierre ; Dzulfikar, Muhammad Ayaz ; Gilbert, Seth ; Gramoli, Vincent ; Guerraoui, Rachid ; Komatovic, Jovan ; Vidigueira, Manuel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-268f6353c38f12a4269530cab231011d343b94e09cbc888ac29447b6fd496c213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Communication</topic><topic>Complexity</topic><topic>Computer Communication Networks</topic><topic>Computer Hardware</topic><topic>Computer Science</topic><topic>Computer Systems Organization and Communication Networks</topic><topic>Messages</topic><topic>Software Engineering/Programming and Operating Systems</topic><topic>Synchronism</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Civit, Pierre</creatorcontrib><creatorcontrib>Dzulfikar, Muhammad Ayaz</creatorcontrib><creatorcontrib>Gilbert, Seth</creatorcontrib><creatorcontrib>Gramoli, Vincent</creatorcontrib><creatorcontrib>Guerraoui, Rachid</creatorcontrib><creatorcontrib>Komatovic, Jovan</creatorcontrib><creatorcontrib>Vidigueira, Manuel</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Distributed computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Civit, Pierre</au><au>Dzulfikar, Muhammad Ayaz</au><au>Gilbert, Seth</au><au>Gramoli, Vincent</au><au>Guerraoui, Rachid</au><au>Komatovic, Jovan</au><au>Vidigueira, Manuel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Byzantine consensus is Θ(n2): the Dolev-Reischuk bound is tight even in partial synchrony</atitle><jtitle>Distributed computing</jtitle><stitle>Distrib. Comput</stitle><date>2024-06-01</date><risdate>2024</risdate><volume>37</volume><issue>2</issue><spage>89</spage><epage>119</epage><pages>89-119</pages><issn>0178-2770</issn><eissn>1432-0452</eissn><abstract>The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with
n
processes and at most
f
<
n
/
3
failures, any solution to Byzantine consensus exchanges
Ω
(
n
2
)
words, where a word contains a constant number of values and signatures. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony where the network alternates between (1) asynchronous periods, with unbounded message delays, and (2) synchronous periods, with
δ
-bounded message delays. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing
SQuad
, a partially synchronous Byzantine consensus protocol with
O
(
n
2
)
worst-case communication complexity. In addition,
SQuad
is optimally-resilient (tolerating up to
f
<
n
/
3
failures) and achieves
O
(
f
·
δ
)
worst-case latency complexity. The key technical contribution underlying
SQuad
lies in the way we solve
view synchronization
, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present
RareSync
, a view synchronization protocol with
O
(
n
2
)
communication complexity and
O
(
f
·
δ
)
latency complexity, which we utilize in order to obtain
SQuad
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00446-023-00458-w</doi><tpages>31</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | Communication Complexity Computer Communication Networks Computer Hardware Computer Science Computer Systems Organization and Communication Networks Messages Software Engineering/Programming and Operating Systems Synchronism Theory of Computation |
| title | Byzantine consensus is Θ(n2): the Dolev-Reischuk bound is tight even in partial synchrony |
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