Mobile Byzantine Agreement Problem in Arbitrary Networks International

Mobile Byzantine Agreement Problem in Arbitrary Networks International Conference On Principles Of Distributed Systems December 16 th , 2013 Toru Sasaki, Yukiko Yamauchi, Shuji Kijima, and Masafumi Yamashita Kyushu University, Japan 2020/9/29 1

Agreement problem ØMake processes agree on a same value • Initial : each process is given a value of 0 or 1 • Goal : all processes agree on a same value • Simple case for cooperative operation on distributed system 1 0 0 1 2020/9/29 0 0 0 2

Byzantine agreement problem ØByzantine faults : take any actions regardless of an algorithm (Static) Byzantine agreement problem[3] • Static Byzantine faults • Gets reliable information from the messages relayed through many processes • Algorithm : complete network, arbitrary network • Impossibility results Mobile Byzantine agreement problem • Mobile Byzantine faults : move to different processes at regular time interval • More processes are corrupted as we spend many time • Algorithm : complete network Our results • Impossibility results • Algorithms on arbitrary network [3] L. Lamport, R. Shostak, M. Pease, The Byzantine generals problem，ACM Transactions on Programming Languages and Systems, 4, 382 -401, 1982. 2020/9/29 3

Table of Contents 1. Problem definition and previous results Ø Model Ø Mobile Byzantine agreement problem 2. Our results Ø Impossibility results Ø Two mobile Byzantine agreement algorithms 3. Conclusion and future work 2020/9/29 4

Table of Contents 1. Problem definition and previous results Ø Model Ø Mobile Byzantine agreement problem 2. Our results Ø Impossibility results Ø Two mobile Byzantine agreement algorithms 3. Conclusion and future work 2020/9/29 5

Network model Ø process 2020/9/29 Communication link vertex edge 6

Synchronous model ØExecution consists of a sequence of rounds ØA round consists of three steps（send, receive, computation） Each process sends messages receives the messages computes the local state Round 1 S R Round 2 C S R C ・・・ time All processes have sent the messages All processes have received the messages ØEvery step is synchronous (no communication delay) 2020/9/29 7

Fault model Ø agent 2020/9/29 Round 1 move Round 2 faulty correct move [1] J．A．Garay，Reaching (and maintaining) agreement in the presence of mobile faults，In Proceedings of Workshop on Distributed Algorithms，pp. 253 -264, 1994． time 8

Recovery Ø Sends malicious message S Round 1 R C S corrupted Round 2 R C S R ・・・ recover corrupted recover 2020/9/29 corrupted 9

Mobile Byzantine Agreement Problem (MBA) [1] Ø Decide Input 0 0 2020/9/29 1 1 10

Mobile Byzantine Agreement Problem (MBA) [1] Ø Decide Input 0 a 0 0 b 0 c d 2020/9/29 Preserve 0 a b c 0 d 0 0 0 a b c d 11

Difficulty of MBA Ø Mobile Byzantine agreement problem Same algorithm as BA is unapplicable because: • The paths are too long • Faults move many times → many processes are corrupted [3] L. Lamport, R. Shostak, M. Pease, The Byzantine generals problem，ACM Transactions on Programming Languages and Systems, 4, 382 -401, 1982. 2020/9/29 12

Previous results Ø optimal 2020/9/29 13

Previous results ØByzantine agreement problem (BA) Algorithm Impossibility Complete network Arbitrary network ØMobile Byzantine agreement problem (MBA) Algorithm Impossibility Complete network ? ? ? Arbitrary network 2020/9/29 ? ? ? 14

Table of Contents 1. Problem definition and previous results Ø Model Ø Mobile Byzantine agreement problem 2. Our results Ø Impossibility results Ø Two mobile Byzantine agreement algorithms 3. Conclusion and future work 2020/9/29 15

Impossibility results on MBA Ø Mobile Byzantine agreement Derive impossibility results on MBA from that on BA mobile static Same behavior 2020/9/29 16

Impossibility results on MBA ØByzantine agreement problem (BA) Algorithm Impossibility Complete network Arbitrary network ØMobile Byzantine agreement problem (MBA) Algorithm Complete network optimal Arbitrary network 2020/9/29 ? ? ? Impossibility ? ? ? 17

Table of Contents 1. Problem definition and previous results Ø Model Ø Mobile Byzantine agreement problem 2. Our results Ø Impossibility results Ø Two mobile Byzantine agreement algorithms 3. Conclusion and future work 2020/9/29 18

How to solve MBA on arbitrary network ? ØIdea of Dolev’s algorithm (BA on arbitrary network) • Simulate complete network by realizing reliable transmission • Execute Byzantine agreement algorithm on virtual complete network Reliable transmission • Transmit a message between any two processes even if these processes are not connected Reliable transmission ØWe also consider the reliable transmission on MBA [5] R. Diestel, “Graph Theory”, Springer-Verlag, 1997. 2020/9/29 19

Algorithm for reliable transmission Outline of the algorithm for reliable transmission on MBA 3 6 4 2 5 2 4 3 6 5 Ø 2020/9/29 20

Algorithm DP-Byz Ø [2] N. Banu, S. Souissi, T. Izumi and K. Wada, Internayional Journal of Computer Applications, 43, No. 21, 2011. 2020/9/29 21

DPT : Disjoint Path Transmission Ø corrupt 2020/9/29 corrupt Gets five copies (two of them are corrupted) 22

DPT : Disjoint Path Transmission Hold the copy Take the majority Ø 2020/9/29 23

DP-Byz 2020/9/29 24

Algorithm KP-Byz Ø 2020/9/29 25

Per. T – Permeate Transmission Ø 2020/9/29 26

Per. T – Permeate Transmission Ø Round 1 Send the received value to the neighbor Send the majority value to the neighbor Round 4 Round 3 Round 2 Take the majority of the received values 27

KP-Byz 2020/9/29 28

Table of Contents 1. Problem definition and previous results Ø Model Ø Mobile Byzantine agreement problem 2. Our results Ø Impossibility results Ø Two mobile Byzantine agreement algorithms 3. Conclusion and future work 2020/9/29 29

Conclusion ØMobile Byzantine agreement problem (MBA) Algorithm Impossibility Complete network Arbitrary network 2020/9/29 30

Future work ØGap between the sufficient condition and the necessary condition ØDiscover a new impossibility results ØDiscover algorithms on more arbitrary network 2020/9/29 31