ROBUST & SPECULATIVE BYZANTINE RANDOMIZED CONSENSUS WITH CONSTANT TIME COMPLEXITY IN NORMAL CONDITIONS

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1 ROBUST & SPECULATIVE BYZANTINE RANDOMIZED CONSENSUS WITH CONSTANT TIME COMPLEXITY IN NORMAL CONDITIONS Bruno Vavala University of Lisbon, Portugal Carnegie Mellon University, U.S. Nuno Neves University of Lisbon, Portugal IEEE Symposium on Reliable and Distributed Systems 2012

2 CONSENSUS Fundamental problem in distributed computing Examples: SM Replication, Leader Election, Coordination, Group Membership, etc. Impossible to attain deterministically with crash-faults (partial correctness) Termination achievable with: weaker models (ev. synchrony assumption) randomization (almost-surely) 2

3 RANDOMIZED CONSENSUS Properties Validity: if all correct processes propose v, then v is the only possible decision Agreement: no two correct processes decide differently Probabilistic Termination: all correct processes eventually decide with probability 1 Assumptions Reliable channels Source-authenticated channels 3

4 BRACHA S ALGORITHM (PODC 1984) Seminal algorithm Asynchronous Byzantine resistant Resilient-optimal (3f+1) Correct under the Strong Adversary model 4

5 BRACHA S ALGORITHM (PODC 1984) Seminal algorithm Asynchronous Byzantine resistant Resilient-optimal (3f+1) Correct under the Strong Adversary model 1)RBcast value 2)Set majority value 1st phase (set majority) Bruno Vavala, CMU-FCUL, Oct IEEE Symposium on Reliable and Distributed Systems 2012

6 BRACHA S ALGORITHM (PODC 1984) Seminal algorithm Asynchronous Byzantine resistant Resilient-optimal (3f+1) Correct under the Strong Adversary model 1)RBcast value 2)Set majority value 4)RBcast value 5)Set quorum value (if any, or default v) 1st phase (set majority) 2nd phase (try-lock) Bruno Vavala, CMU-FCUL, Oct IEEE Symposium on Reliable and Distributed Systems 2012

7 BRACHA S ALGORITHM (PODC 1984) Seminal algorithm Asynchronous Byzantine resistant Resilient-optimal (3f+1) Correct under the Strong Adversary model 1)RBcast value 2)Set majority value 4)RBcast value 5)Set quorum value (if any, or default v) 7)RBcast value 8)Set decision value (if any, or majority) (if any, or flip coin) 10)start new round 1st phase (set majority) 2nd phase (try-lock) 3rd phase (try-decide) Bruno Vavala, CMU-FCUL, Oct IEEE Symposium on Reliable and Distributed Systems 2012

8 IN THEORY Rounds Processes Potential problem: expected exponential time execution under adverse conditions 8

9 IN PRACTICE 10 Rounds Processes In reality: it terminates in a constant number of rounds under normal conditions 9

10 RELIABILITY VS. PERFORMANCE WHAT S THE MODEL?

11 WHAT IS NORMAL? Asynchrony? Crash failures? Byzantine failures? Content-independent message scheduler? Full information adversary? Adversary message scheduler? 11

12 AN EXPERIMENT

13 FIRST ROUND first phase > < second phase third phase > toss a coin 13

14 SECOND ROUND first phase > < second phase third phase > toss a coin 14

15 THIRD ROUND first phase > < second phase third phase > decision 15

16 PROBABILISTIC ANALYSIS

17 INGREDIENTS Hypergeometric distribution H(n, k, n f) Binomial distribution B(n, p) Normal distribution N (np, np(1 Some approximations P (B(n, p) apple i) p)) p i np np(1 p) H B 17

18 KEY Threshold of half plus 1/4 of procs proposing v at the end of 2nd phase 1! 0.75! Proability! 0.5! 0.25! All procs set v ( k>1/4 )! A proc sets default ( k<1/4 )! k < 1/4 k > 1/4 0! 1! 4! 7! 10! 13! 16! 19! Processes! 18

19 GOING BACKWARDS decision on v message exchange 3rd Phase Linear bias of constant 1/4 of procs proposing v message exchange 2nd Phase Procs have constant probability of setting v Linear bias of (just) positive constant beyond the average message exchange 1st Phase Square root bias beyond the average of procs proposing v Back to coin tossing, this is a... Basic property of the Normal Distribution: p=2/5 (or 2.5 rounds ) 19

20 EVALUATION

21 PERFORMANCE 2.5 rounds Rounds! 3.5! 3! 2.5! 2! 1.5! 1! 0.5!? 0! 4! 16! 28! 40! 52! 64! 76! 88! 100! Processes! Cluster of 6 nodes Up to 100 processes n = 3f + 1 Divergent initial configuration 21

22 PERFORMANCE 3.5! 2.5 rounds baseline Rounds! 3! 2.5! 2! 1.5! 1! 0.5! 0! 4! 16! 28! 40! 52! 64! 76! 88! 100! Processes! Analysis says 2.5 rounds after coin flipping Baseline at 1 round Theoretically satisfactory, but practically not precise, constant complexity 22

23 LOOK AT THE CONSTANTS Approximations are theoretically good Loss of precision when computing constant values P (H(n, k, n f) apple i) ours apple i µb A better approximation is available P (H(n, k, n f) apple i) Feller 23 i µh A multiplicative constant impacts noticeably just on constants i µh H = i µb B p 3 B H

24 PERFORMANCE 1.59 rounds baseline Rounds! 3.5! 3! 2.5! 2! 1.5! 1! 0.5! 0! 4! 16! 28! 40! 52! 64! 76! 88! 100! Processes! Analysis says 1.59 rounds after coin flipping Baseline at 1 round Theoretically satisfactory and practically rather precise constant complexity 24

25 HIGH LEVEL VIEW Model Complexity SA O(2 n ) WA SMO O(1) 1 round 25

26 HIGH LEVEL VIEW strong adversary Model Complexity SA O(2 n ) WA SMO O(1) 1 round 26

27 HIGH LEVEL VIEW strong adversary Model Complexity SA O(2 n ) synchronous msg order WA O(1) SMO 1 round 27

28 HIGH LEVEL VIEW strong adversary oblivious adversary Model Complexity SA O(2 n ) synchronous msg order OA O(1) SMO 1 round Complexity values are all relative to the Bracha s algorithm 28

29 LET S GO BEYOND

30 OVERVIEW Termination in 1-2 rounds (good) 3-6 phases (bad) Objective: can we improve phase complexity in normal conditions while maintaining reliability? (oblivious) crash-failures may happen Decision in 1 phase possible in a weaker model Focus on the set of ( n-f ) received messages 30

31 SPECULATION 1st Phase broadcast and set majority decision quorum reached 2nd Phase broadcast and try lock value no decision speculate v is locked 3rd Phase broadcast and try decide v broadcast (3s) try decide v 31

32 PERFORMANCE 10! 8! 6! Phases! Rounds! 4! 2! 0! 0! 20! 40! 60! 80! 100! Procs with proposal v! 32

33 PERFORMANCE 10! 8! 6! Phases! Rounds! 4! 2! 0! 0! 20! 40! 60! 80! 100! Procs with proposal v! 2-phase termination more frequent with more msgs 33

34 BENEFITS AND DRAWBACKS PROs CONs 2 phases/round in the best case Algorithm complexity increased due to speculation 3 phases/round if speculation fails Fragile for near divergent proposals Does not compromise original algorithm s properties 34

35 SUMMARIZING Bracha s algorithm (PODC 1984) terminates in constant time (1.59 expected rounds) in normal conditions First cross-model (non-trivial) analysis Enhanced detection of anomalous/malicious behavior (Almost) matching upper-bound with respect to Attiya-Censor s lower bound (PODC 2008) Improved algorithm through inexpensive Speculation 35

36 THANK YOU!