ROBUST & SPECULATIVE BYZANTINE RANDOMIZED CONSENSUS WITH - PowerPoint PPT Presentation

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

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) Bruno Vavala, CMU-FCUL, Oct 2012 2 IEEE Symposium on Reliable and Distributed Systems 2012

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 Bruno Vavala, CMU-FCUL, Oct 2012 3 IEEE Symposium on Reliable and Distributed Systems 2012

BRACHA’S ALGORITHM (PODC 1984) • Seminal algorithm • Asynchronous • Byzantine resistant • Resilient-optimal (3f+1) • Correct under the 
 Strong Adversary model Bruno Vavala, CMU-FCUL, Oct 2012 4 IEEE Symposium on Reliable and Distributed Systems 2012

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

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

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

IN THEORY 1000000000000000000000000000000 1000000000000000000000000000 1000000000000000000000000 1000000000000000000000 1000000000000000000 Rounds 1000000000000000 1000000000000 1000000000 1000000 1000 1 4 28 52 76 100 Processes Potential problem: expected exponential time execution 
 under adverse conditions Bruno Vavala, CMU-FCUL, Oct 2012 8 IEEE Symposium on Reliable and Distributed Systems 2012

IN PRACTICE 10 Rounds 6 2 4 28 52 76 100 Processes In reality: it terminates in a constant number of rounds 
 under normal conditions Bruno Vavala, CMU-FCUL, Oct 2012 9 IEEE Symposium on Reliable and Distributed Systems 2012

RELIABILITY VS. PERFORMANCE WHAT’S THE MODEL? Bruno Vavala, CMU-FCUL, Oct 2012 IEEE Symposium on Reliable and Distributed Systems 2012

WHAT IS NORMAL? • Asynchrony? • Crash failures? • Byzantine failures? • Content-independent message scheduler? • Full information adversary? • Adversary message scheduler? Bruno Vavala, CMU-FCUL, Oct 2012 11 IEEE Symposium on Reliable and Distributed Systems 2012

AN EXPERIMENT Bruno Vavala, CMU-FCUL, Oct 2012 IEEE Symposium on Reliable and Distributed Systems 2012

FIRST ROUND first phase > < second phase third phase > toss a coin Bruno Vavala, CMU-FCUL, Oct 2012 13 IEEE Symposium on Reliable and Distributed Systems 2012

SECOND ROUND first phase > < second phase third phase > toss a coin Bruno Vavala, CMU-FCUL, Oct 2012 14 IEEE Symposium on Reliable and Distributed Systems 2012

THIRD ROUND first phase > < second phase third phase > decision Bruno Vavala, CMU-FCUL, Oct 2012 15 IEEE Symposium on Reliable and Distributed Systems 2012

PROBABILISTIC ANALYSIS Bruno Vavala, CMU-FCUL, Oct 2012 IEEE Symposium on Reliable and Distributed Systems 2012

INGREDIENTS • Hypergeometric distribution 
 H H ( n, k, n − f ) B • Binomial distribution 
 B ( n, p ) • Normal distribution 
 N ( np, np (1 − p )) • Some approximations ✓ ◆ i − np P ( B ( n, p ) ≤ i ) ≈ Φ √ np (1 − p ) Bruno Vavala, CMU-FCUL, Oct 2012 17 IEEE Symposium on Reliable and Distributed Systems 2012

KEY • Threshold of half plus 1/4 of procs 
 proposing v at the end of 2nd phase 
 1 ! 0.75 ! Proability ! All procs set v ( k>1/4 ) ! 0.5 ! A proc sets default ( k<1/4 ) ! 0.25 ! k < 1/4 k > 1/4 0 ! 1 ! 4 ! 7 ! 10 ! 13 ! 16 ! 19 ! Processes ! Bruno Vavala, CMU-FCUL, Oct 2012 18 IEEE Symposium on Reliable and Distributed Systems 2012

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 ) Bruno Vavala, CMU-FCUL, Oct 2012 19 IEEE Symposium on Reliable and Distributed Systems 2012

EVALUATION Bruno Vavala, CMU-FCUL, Oct 2012 IEEE Symposium on Reliable and Distributed Systems 2012

PERFORMANCE 3.5 ! 3 ! ? 2.5 rounds 2.5 ! Rounds ! 2 ! 1.5 ! 1 ! 0.5 ! 0 ! 4 ! 16 ! 28 ! 40 ! 52 ! 64 ! 76 ! 88 ! 100 ! Processes ! • Cluster of 6 nodes • n = 3f + 1 • Up to 100 processes • Divergent initial configuration Bruno Vavala, CMU-FCUL, Oct 2012 21 IEEE Symposium on Reliable and Distributed Systems 2012

PERFORMANCE 3.5 ! 3 ! 2.5 rounds 2.5 ! Rounds ! 2 ! 1.5 ! baseline 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 Bruno Vavala, CMU-FCUL, Oct 2012 22 IEEE Symposium on Reliable and Distributed Systems 2012


 
 LOOK AT THE CONSTANTS • Approximations are theoretically good • Loss of precision when computing constant values 
 ours ⇣ ⌘ i µ B P ( H ( n, k, n − f ) ≤ i ) ≤ Φ − σ B • A better approximation is available 
 Feller ⇣ ⌘ i µ H P ( H ( n, k, n − f ) ≤ i ) Φ ≈ − σ H • A multiplicative constant impacts noticeably just on constants 
 ⇣ ⌘ ⇣ ⌘ i µ H i µ B √ Φ = Φ − − 3 σ H σ B Bruno Vavala, CMU-FCUL, Oct 2012 23 IEEE Symposium on Reliable and Distributed Systems 2012

PERFORMANCE 3.5 ! 3 ! 2.5 ! Rounds ! 2 ! 1.59 rounds 1.5 ! baseline 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 Bruno Vavala, CMU-FCUL, Oct 2012 24 IEEE Symposium on Reliable and Distributed Systems 2012

HIGH LEVEL VIEW Model Complexity SA O(2 n ) WA O(1) SMO 1 round Bruno Vavala, CMU-FCUL, Oct 2012 25 IEEE Symposium on Reliable and Distributed Systems 2012

HIGH LEVEL VIEW strong adversary Model Complexity SA O(2 n ) WA O(1) SMO 1 round Bruno Vavala, CMU-FCUL, Oct 2012 26 IEEE Symposium on Reliable and Distributed Systems 2012

HIGH LEVEL VIEW strong adversary Model Complexity SA O(2 n ) s y n c h r o n o u s m s g o r d e r WA O(1) SMO 1 round Bruno Vavala, CMU-FCUL, Oct 2012 27 IEEE Symposium on Reliable and Distributed Systems 2012

HIGH LEVEL VIEW strong adversary Model Complexity y r a s r e v d a s u o i v i l b o SA O(2 n ) s y n c h r o n o u s m s g o r d e r OA O(1) SMO 1 round Complexity values are all relative to the Bracha’s algorithm Bruno Vavala, CMU-FCUL, Oct 2012 28 IEEE Symposium on Reliable and Distributed Systems 2012

LET’S GO BEYOND Bruno Vavala, CMU-FCUL, Oct 2012 IEEE Symposium on Reliable and Distributed Systems 2012

｛ OVERVIEW 1-2 rounds (good) Termination in 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 Bruno Vavala, CMU-FCUL, Oct 2012 30 IEEE Symposium on Reliable and Distributed Systems 2012

SPECULATION broadcast and decision 1st Phase set majority quorum reached speculate broadcast and 2nd Phase try lock value v is locked no decision broadcast and broadcast (3s) 3rd Phase try decide v try decide v Bruno Vavala, CMU-FCUL, Oct 2012 31 IEEE Symposium on Reliable and Distributed Systems 2012