Byzantine Agreement in the Presence of Mixed Faults on Processor and Links

1. Byzantine Agreement in the Presence of Mixed Faults on Processor and Links Hin-Sing Siu, Yeh-Hao Chin, Wei-Pang Yang Senior Member, IEEE Computer Society, April 1998 元智大學 資訊工程研究所 系統實驗室 陳桂慧 1999.03.31

2. Outline • Definition and conditions for an agreement • Basic concept and approaches • The basic approaches of GPBA • An example of GPBA • Conclusion

3. Definition and Conditions for an Agreement • GPBA ( generalized protocol for the BA problem) • in a general network • in a synchronous network • can solve BA problem with the following assumptions • 正常的 processor 不要求得知之前系統發生錯誤原因來源 • 不必是fully-connected • processors 和 links 都會是導致網路中存在的 fault 原因 • minimum the number of message exchange • in general network, processor requires t+1 rounds to exchange the message for reaching an agreement, t = 」(n-1)/3」 • maximum the number of tolerable faulty component

4. Definition and Conditions for an Agreement (2) • Goal of the GPBA • Agreement: all fault-free processor agree in the same common value v. • validity: the initial value of source is vs, vs = v • The BA can be achieved in a network if: • 1) n> 3Pa+Pd, and • 2) c> 2Pa+Pd+2(La+Ld)

5. Basic Concept and Approaches • Removing the influence of • step 1. faulty intermedium, FTVC • step 2. dormant faulty sender, absent rule (AR1)When Receives no message directory from S in the rth round, 1) if r=1, P will select the default value to replace the incoming message from S (the source), or 2) if r!=1, all messages received from S at the rth round and any subsequent rounds will be relayed to all processors as value RA1 (AR2)When R receives the value RAj, it will relay the value RAj+1 to all processors (if any). • step 3. arbitrary faulty sender, VOTE

6. A Network with Mixed Fault Fault-free processor dormant faulty processor arbitrary faulty processor Fault-free link arbitrary faulty link

7. The Basic Approaches of GPBA • The message under the influence of faulty sender ( both dormant and arbitrary fault) and intermedium. • The message under the influence of faulty sender ( both dormant and arbitrary fault) . • The message under the influence of arbitrary faulty sender. • The message free from the effect of a faulty component. Message Exchange Phase Decision Making Phase 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 FTVC 1 Absent rule FTVC Absent rule VOTE t t t t+1 t+1 t+1 FTVC Absent rule

8. An example of an IG-tree for the network model shown in Fig 1. N-2個 children N-1個 children No repeating processor identifier can avoid the recursive influences made by a faulty processor.

9. An example of GPBA (1) C=6 m, if S is fault-free. ψ, if S does not sent the message to R Arbitrary value, if S has an arbitrary fault MAJ := Majority function

10. An example of GPBA (2) Second round IG-tree After absent rule is applied It means a fault-free receiver doesn’t receive any message from G.

12. Conclusion

13. Conclusion (2) TABLE 4 The Constraints on failures for various protocol on both processor and link failures

14. Conclusion (3) • Solving BA problem in a general network, GPBA is optimal in • the number of rounds required • the number of message required • the number of faulty component allowable • GPMA does not require the faulty status of the system prior to the execution of the protocol. • GPMA is design for solving the BA problem with the most general assumptions. • The FTVC protocol can remove the influence of a faulty intermedium.