Nicaea: A Byzantine Fault Tolerant Consensus Under Unpredictable Message Delivery Failures for Parallel and Distributed Computing

Byzantine fault-tolerant (BFT) consensus is a critical problem in parallel and distributed computing systems, particularly with potential adversaries. Most prior work on BFT consensus assumes reliable message delivery and tolerates arbitrary failures of up to <inline-formula><tex-math notat...

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Vydané v:IEEE transactions on computers Ročník 74; číslo 3; s. 915 - 928
Hlavní autori: Jing, Guanlin, Zou, Yifei, Xu, Minghui, Zhang, Yanqiang, Yu, Dongxiao, Shan, Zhiguang, Cheng, Xiuzhen, Ranjan, Rajiv
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: IEEE 01.03.2025
Predmet:
Byzantine fault-tolerance
Computational modeling
Computers
Consensus algorithm
Consensus protocol
Distributed computing
Electronic mail
Fault tolerance
Fault tolerant systems
message delivery failure
parallel and distributed computing
Protocols
Reliability
ISSN:0018-9340, 1557-9956
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Abstract Byzantine fault-tolerant (BFT) consensus is a critical problem in parallel and distributed computing systems, particularly with potential adversaries. Most prior work on BFT consensus assumes reliable message delivery and tolerates arbitrary failures of up to <inline-formula><tex-math notation="LaTeX">\frac{n}{3}</tex-math> <mml:math><mml:mfrac><mml:mi>n</mml:mi><mml:mn>3</mml:mn></mml:mfrac></mml:math><inline-graphic xlink:href="jing-ieq1-3506856.gif"/> </inline-formula> nodes out of <inline-formula><tex-math notation="LaTeX">n</tex-math> <mml:math><mml:mi>n</mml:mi></mml:math><inline-graphic xlink:href="jing-ieq2-3506856.gif"/> </inline-formula> total nodes. However, many systems face unpredictable message delivery failures. This paper investigates the impact of unpredictable message delivery failures on the BFT consensus problem. We propose Nicaea, a novel protocol enabling consensus among loyal nodes when the number of Byzantine nodes is below a new threshold, given by: <inline-formula><tex-math notation="LaTeX">\frac{\left(2-\rho\right)\left(1-\rho\right)^{2n-2}-1}{\left(2-\rho\right) \left(1-\rho\right)^{2n-2}+1}n</tex-math> <mml:math><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfrac><mml:mi>n</mml:mi></mml:math><inline-graphic xlink:href="jing-ieq3-3506856.gif"/> </inline-formula>, where <inline-formula><tex-math notation="LaTeX">\rho</tex-math> <mml:math><mml:mi>ρ</mml:mi></mml:math><inline-graphic xlink:href="jing-ieq4-3506856.gif"/> </inline-formula> denotes the message failure rate. Theoretical proofs and experimental results validate Nicaea's Byzantine resilience. Our findings reveal a fundamental trade-off: as message delivery instability increases, a system's tolerance to Byzantine failures decreases. The well-known <inline-formula><tex-math notation="LaTeX">\frac{n}{3}</tex-math> <mml:math><mml:mfrac><mml:mi>n</mml:mi><mml:mn>3</mml:mn></mml:mfrac></mml:math><inline-graphic xlink:href="jing-ieq5-3506856.gif"/> </inline-formula> threshold under reliable message delivery is a special case of our generalized threshold when <inline-formula><tex-math notation="LaTeX">\rho=0</tex-math> <mml:math><mml:mi>ρ</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math><inline-graphic xlink:href="jing-ieq6-3506856.gif"/> </inline-formula>. To the best of our knowledge, this work presents the first quantitative characterization of unpredictable message delivery failures' impact on Byzantine fault tolerance in parallel and distributed computing.
AbstractList Byzantine fault-tolerant (BFT) consensus is a critical problem in parallel and distributed computing systems, particularly with potential adversaries. Most prior work on BFT consensus assumes reliable message delivery and tolerates arbitrary failures of up to <inline-formula><tex-math notation="LaTeX">\frac{n}{3}</tex-math> <mml:math><mml:mfrac><mml:mi>n</mml:mi><mml:mn>3</mml:mn></mml:mfrac></mml:math><inline-graphic xlink:href="jing-ieq1-3506856.gif"/> </inline-formula> nodes out of <inline-formula><tex-math notation="LaTeX">n</tex-math> <mml:math><mml:mi>n</mml:mi></mml:math><inline-graphic xlink:href="jing-ieq2-3506856.gif"/> </inline-formula> total nodes. However, many systems face unpredictable message delivery failures. This paper investigates the impact of unpredictable message delivery failures on the BFT consensus problem. We propose Nicaea, a novel protocol enabling consensus among loyal nodes when the number of Byzantine nodes is below a new threshold, given by: <inline-formula><tex-math notation="LaTeX">\frac{\left(2-\rho\right)\left(1-\rho\right)^{2n-2}-1}{\left(2-\rho\right) \left(1-\rho\right)^{2n-2}+1}n</tex-math> <mml:math><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfrac><mml:mi>n</mml:mi></mml:math><inline-graphic xlink:href="jing-ieq3-3506856.gif"/> </inline-formula>, where <inline-formula><tex-math notation="LaTeX">\rho</tex-math> <mml:math><mml:mi>ρ</mml:mi></mml:math><inline-graphic xlink:href="jing-ieq4-3506856.gif"/> </inline-formula> denotes the message failure rate. Theoretical proofs and experimental results validate Nicaea's Byzantine resilience. Our findings reveal a fundamental trade-off: as message delivery instability increases, a system's tolerance to Byzantine failures decreases. The well-known <inline-formula><tex-math notation="LaTeX">\frac{n}{3}</tex-math> <mml:math><mml:mfrac><mml:mi>n</mml:mi><mml:mn>3</mml:mn></mml:mfrac></mml:math><inline-graphic xlink:href="jing-ieq5-3506856.gif"/> </inline-formula> threshold under reliable message delivery is a special case of our generalized threshold when <inline-formula><tex-math notation="LaTeX">\rho=0</tex-math> <mml:math><mml:mi>ρ</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math><inline-graphic xlink:href="jing-ieq6-3506856.gif"/> </inline-formula>. To the best of our knowledge, this work presents the first quantitative characterization of unpredictable message delivery failures' impact on Byzantine fault tolerance in parallel and distributed computing.
Author Zhang, Yanqiang
Yu, Dongxiao
Shan, Zhiguang
Xu, Minghui
Jing, Guanlin
Zou, Yifei
Cheng, Xiuzhen
Ranjan, Rajiv
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Snippet Byzantine fault-tolerant (BFT) consensus is a critical problem in parallel and distributed computing systems, particularly with potential adversaries. Most...
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SubjectTerms Byzantine fault-tolerance
Computational modeling
Computers
Consensus algorithm
Consensus protocol
Distributed computing
Electronic mail
Fault tolerance
Fault tolerant systems
message delivery failure
parallel and distributed computing
Protocols
Reliability
Title Nicaea: A Byzantine Fault Tolerant Consensus Under Unpredictable Message Delivery Failures for Parallel and Distributed Computing
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