Byzantine Problems

1
Byzantine Problems

• Quick Intro
• Jochen Liedtke

2
Byzantine Generals Problem
3
Byzantine Problem (a)
4
Byzantine Problem (b)
server
client
5
Byzantine Problem (b)
S4
S3
S2
S5
S1
client
6
Byzantine Solution
S4
S3
S2
S5
S1

• Assume
• all non-faulty replicas are in the same state
• all non-faulty replicas are deterministic
• all non-faulty replicas reply identically
• (if all non-faulty replicas execute requests in
  the same order)

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Byzantine Solution (1/2)
S4
S3
S2
S5
S1
2f1 server replicas at most f faulty replicas
f1 identical replies x ? x is correct
reply !
8
Byzantine Solution (1/2)
S4
S3
S2
S5
S1

• BUT
• replicas must first establish agreement and
  commit
• then they can reply
• which quorum for agreement ?

9
Byzantine Solution (1/2)
S4
S3
S2
S5
S1

• BUT
• replicas must first establish agreement and
  commit
• then they can reply
• which quorum for agreement ?

f1 quorum ?
10
Byzantine Solution (1/2)
S4
S3
S2
S5
S1

• ERGO
• quorum must include at least f1 non-faulty
  replicas

2 f 1 quorum !
11
Byzantine Solution (1/3)
S4
S3
S2
S5
S1
S6
3f 1 server replicas at most f faulty replicas
S7
Client replies f1 identical replies
required Server quorum 2f1 identical replies
required