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Brief presentation on the Byzantine agreement problem

Brief presentation on the Byzantine agreement problem

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Transcript

  • 1. Network-Aware Distributed Algorithm
    Guanfeng Liang & NitinVaidya
  • 2. A Classic Distributed Algorithm Problem
    Byzantine Agreement (BA): source S wants to send message to n-1 peers
    Fault-free peers must agree
    S fault-free agree on its message
    Up to f failures
    2
  • 3. Message Passing Model
    Point-to-point private links
    3
    S
    A
    C
    B
  • 4. From a Networking Perspective
    Q: What are the link capacities?
    A: ∞ bits/second (implicitly)
    Q: Is it realistic?
    A: ......
    4
    How does link capacityaffect performance of BA?
  • 5. Message Passing with Capacity
    Point-to-point private links
    Each link has its own fixed capacity
    5
    S
    1
    3
    1
    4
    2
    2
    A
    C
    1
    3
    4
    2
    B
    2
    5
  • 6. Capacity of Agreement
    Borrow notions from communications literature
    6
    Number of bit agreed on [0,t]
    t
    Throughput = lim
    t->∞
    Capacity = sup{Throughput}
  • 7. Traditional vs. Ours
    Traditional BA alg’s
    Send the whole message over each link
    Agree on the whole message all at once
    Proposed BA alg
    Send a fraction of the message over each link using coding
    Reach agreement incrementally
    Adapts to the location of failures
    7
  • 8. Data = a, b
    S
    a
    a+b
    b
    3
    1
    2
    a, b non-binary
    Generation 1 - Step 1
    8
  • 9. Generation 1 - Step 2
    Data = a, b
    S
    a
    a+b
    b
    3
    1
    b
    2
    b
    a+b
    9
    a
  • 10. A Bad Peer
    Data = a, b
    S
    a
    a+b
    b
    a
    b
    a+b
    a
    b’
    a+b
    3
    1
    b
    2
    b’
    1 detects error
    a
    a+b
    10
  • 11. Which is bad?
    11
    S
    S
    Look the same to 1
    a
    a
    a+b
    a+b
    b
    b’
    b
    b’
    3
    3
    1
    1
    2
    2
    b’
    b’
    a
    a
    a+b
    a+b
  • 12. Generation 1 – Extra Broadcast
    a
    b
    a+b
    S
    a
    b
    a+b
    a
    b’
    a+b
    3
    1
    2
    12
    a
    b
    a+b
  • 13. Generation 1 – Conflict Found
    a
    b
    a+b
    S
    a
    b
    a+b
    a
    b’
    a+b
    3
    1
    2
    13
    a
    b
    a+b
  • 14. Data = c, d
    S
    c
    c+d
    d
    3
    1
    2
    Generation 2 - Step 1
    14
    1 knows 2 is bad
  • 15. Generation 2 – Step 2
    Data = c, d
    S
    c
    c+d
    d
    c
    d’
    c+d
    c
    c+d
    3
    1
    d’
    2
    1 knows 2 is bad
    3 detects error
    c
    c+d
    15
  • 16. Generation 2 – Extra Broadcast
    c
    d
    c+d
    S
    c
    d’
    c+d
    c
    c+d
    3
    1
    2
    16
    d’
    c+d
  • 17. Generation 2 – Failure Identified
    c
    d
    c+d
    S
    c
    d’
    c+d
    c
    c+d
    3
    1
    2
    17
    d’
    c+d
  • 18. Improvement over Traditional BA Algorithms
    Traditional ≤ min(link) = ε
    Proposed-> min(2 links) = R + ε
    18
    S
    R
    R
    ε
    3
    1
    2
  • 19. Summary
    Capacity of BA given link capacity
    Other capacity constraints
    Framework for efficient BA
    Coding
    Incremental agreement
    Can be used for multicast with node failure
    19
  • 20. Thanks you!
  • 21. Adversary Model
    Byzantine adversary
    Omniscient – no secret hidden
    Arbitrary behavior – worst case analysis
    Computationally unbounded – cryptography won’t help
    21