lec 10 agreementprotocols

7/31/2019 Lec 10 AgreementProtocols

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Agreement Agreement ProtocolsProtocols

CS60002:CS60002: DistributedDistributed SystemsSystems

PallaPalla bb DasguptaDasgupta

Dept.Dept. of of ComputerComputer Sc.Sc. && EngEng gg .,.,IndianIndian InstituteInstitute of of Technology Technology KharagpurKharagpur


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K K K

Dept. of CSE, IIT KGP


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ClassificationClassification of of FaultsFaults

BasedBased onon componentscomponents thatthat f f aa ilediled ProgramProgram // processprocess Processor Processor // machinemachine LinkLink StorageStorage

ClockClock

BasedBased onon behavior behavior of of faultyfaulty componentcomponent CrashCrash just just haltshalts FailstopFailstop crashcrash withwith additionaladditional conditionsconditions

OmissionOmission failsfails toto performperform somesome stepssteps ByzantineByzantine behavesbehaves arbitrarilyarbitrarily TimingTiming violatesviolates timingtiming constraintsconstraints



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ClassificationClassification of of ToleranceTolerance

TypesTypes of of tolerance:tolerance: MaskingMasking systemsystem alwaysalways behavesbehaves asas per per specificationsspecifications eveneven

inin presencepresence of of faultsfaults Non-maskingNon-masking systemsystem maymay violateviolate specificationsspecifications inin presencepresence of of

faults.faults. ShouldShould atat leastleast behavebehave inin aa welwel ll-defined-defined manner manner

FaultFault toleranttolerant systemsystem shouldshould specify:specify: ClassClass of of faultsfaults toleratedtolerated WhatWhat tolerancetolerance isis givengiven fromfrom eacheach classclass



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CoreCore problemsproblems

Agreement Agreement (multiple(multiple processesprocesses agreeagree onon somesome value)value) CC llockock syncsync hh ronizationronization StableStable storagestorage (data(data accessibleaccessible after after crash)crash) ReliableReliable communicationcommunication (point-t(point-t oo -point,-point, broadcast,broadcast, multicast)multicast)

Atomic Atomic



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OverviewOverview of of ConsensusConsensus ResultsResults

LetLet f f bebe thethe maximummaximum number number of of faultyfaulty pp r r ocessors.ocessors.

TightTight boundsbounds for for messagemessage passing:passing:

CrashCrash failuresfailures ByzantineByzantine failuresfailures

Number Number of of roundsrounds f f ++ 11 f f ++ 11

TotalTotal number number of of processorsprocessors

f f ++ 11 3f 3f ++ 11

MessageMessage sizesize polynomialpolynomial polynomialpolynomial



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OverviewOverview of of ConsensusConsensus ResultsResults

ImpossibleImpossible inin asynchronousasynchronous case.case. EvenEven if if wewe onlyonly wantwant toto toleratetolerate aa singlesingle crashcrash failure.failure. TrueTrue bothboth for for messagemessage passingpassing andand sharedshared read-writeread-write

memory.memory.



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ConsensusConsensus Algorithm Algorithm for for CrashCrash FailuresFailures

CodeCode

for for

eacheach

processor:processor:

v v :=:= mymy inputinputatat eacheach roundround 11 throughthrough f+1:f+1:

if if II havehave notnot yetyet sentsent v v thenthen sendsend v v ttoo allall waitwait toto receivereceive messagesmessages for for thisthis roundroundv v :=:= minimumminimum amongamong allall receivedreceived valuesvalues andand

currentcurrent valuevalue of of v v if if thisthis isis roundround f+f+11 thenthen decidedecide onon v v


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CorrectnessCorrectness of of CrashCrash ConsensusConsensus Algo Algo

Ter Ter mm ination:ination: ByBy thethe code,code, finishfinish inin roundround f f ++ 1.1.

Validity:Validity: HoldsHolds sincesince processorsprocessors dodo notnot introduceintroduce spuriousspurious messagesmessages

if if allall inputsinputs areare thethe same,same, thenthen thatthat isis thethe onlyonly valuevalue ever ever inin circulation.circulation.



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CorrectnessCorrectness of of CrashCrash ConsensusConsensus Algo Algo

Agreement: Agreement: SupposeSuppose inin contradictioncontradiction pp j j decidesdecides onon aa smaller smaller value,value, x x ,,

thanthan doesdoes pp ii.. ThenThen x x waswas hiddenhidden fromfrom pp ii byby aa chainchain of of faultyfaulty

pp r r ocessors:ocessors:

round round roundf

roundf+1

q 1 1 q2 2 q f q f+1 p j

p i

ThereThere areare f f ++ 11 faultyfaulty processorsprocessors inin thisthis chain,chain, aa contradiction.contradiction.


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ccc



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PerformancePerformance of of CrashCrash ConsensusConsensus Algo Algo

Number Number of of processorsprocessors nn >> f f f f ++ 11 roundsrounds nn 2 2 |V||V| messages,messages, eacheach of of sizesize lologg |V||V| bits,bits, wherewhere

V V iiss thth ee inpuinpu tt set.set.



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Lower Lower BoundBound onon RoundsRounds

Assumptions: Assumptions: nn >> f f ++ 11 everyevery processor processor isis supposedsupposed toto sendsend aa

messagemessage toto everyevery other other processor processor inin everyevery roundround

InputInput setset isis {0,1}{0,1}



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ByzantineByzantine Agreement Agreement ProblemsProblems

ModeMode ll :: TotalTotal of of nn processes,processes, atat mostmost mm of of whichwhich cancan bebe faultyfaulty ReliableReliable communicationcommunication mediummedium FullyFully connectedconnected Receiver Receiver alwaysalways knowsknows thethe identityidentity of of thethe sender sender of of aa

messagemessage ByzantineByzantine faultsfaults SynchronousSynchronous systemsystem

InIn eacheach round,round, aa processprocess receivesreceives messages,messages, performsperforms computation,computation, andand sendssends messages.messages.



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ByzantineByzantine Agreement Agreement

Also Also knownknown asas ByzantineByzantine GeneralsGenerals pp r r oblemoblem OneOne processprocess x x broadcastsbroadcasts aa valuevalue v v

Agreement Agreement Condition:Condition: All All non-faultynon-faulty processesprocesses mustmust

agreeagree onon aa commoncommon value.value. ValidityValidity Condition:Condition: TheThe agreedagreed uponupon valuevalue mustmust bebe v v if if x x isis nonnon --faulty.faulty.



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VariantsVariants

ConsensusConsensus EachEach pp r r ocessocess broadcastsbroadcasts itsits initialinitial valuevalue

SatisfySatisfy agreementagreement conditioncondition If If initialinitial valuevalue of of allall non-faultynon-faulty processesprocesses isis v v ,, thenthen thethe

agreedagreed uponupon valuevalue mustmust bebe v v

InteractiveInteractive ConsistencyConsistency EachEach pp r r ocessocess k k broadcastsbroadcasts itsits ownown valuevalue v v k k

All All nono nn -faulty-faulty processesprocesses agreeagree onon aa commoncommon vector vector ((v v 11 ,v ,v 2 2 ,,,, v v nn ))

If If thethe k k thth processprocess isis non-faulty,non-faulty, thenthen thethe k k thth valuevalue inin thethe

vector vector agreedagreed uponupon byby nono nn -faultyprocesses-faultyprocesses mustmust bebe v v k k

SolutionSolution toto ByzantineByzantine agreeagree mm ent ent problem problem impliesimplies solutionsolution toto other other twotwo



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ByzantineByzantine Agreement Agreement ProblemProblem

NoNo solutionsolution possiblepossible iif f :: asynchronousasynchronous system,system, or or nn


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S

T U

S

T U

S

T UUUUUUUU

Proof Proof

Theorem:Theorem: ThereThere isis nono t-Byzantine-robust t-Byzantine-robust broadcast broadcast protocol protocol for for t t N/3N/3

S S0 0 1 1

0 0 1 10 0T U T U1 1

Scenario-0:Scenario-0: TT mustmust decidedecide 00 Scenario-1:Scenario-1: UU mustmust decidedecide 00

S Scenario-2:Scenario-2:0 1 ---- similar similar toto ScenariScenari oo -0-0 fofor r TT

0 1 ---- similar similar toto ScenariScenari oo -1-1 fofor r UU0 ---- TT decidesdecides 00 andand UU decidesdecides 11T U1



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Lampor Lampor t-t-ShostaShosta k-k-PeasePease Algorithm Algorithm contd..contd..

For For t t >> 0,0, Broadcast Broadcast (( N,N, t t ):):

PulsePulse11 TheThe generalgeneral sendssends valval uuee ,, x x g g toto

allall processes,processes, thethe lieutenantslieutenantsdodo notnot send.send.

ReceiveReceive messagesmessages of of pulsepulse 1.1.

LieutenantLieutenant p p actsacts asas follows:follows:if if aa messagemessage valval uuee ,, x x waswas

receivedreceived fromfrom g g inin pulse-1pulse-1thenthen x x p p == x x elseelse x x p p == udef udef ;;

Announc Announc ee x x p p toto thethe other other

lieutenantslieutenants byby actingacting asasaa generalgeneral ininBroadcast Broadcast p p (( N N 11 ,, t t 11 )) inin thethe nextnext pulsepulse

PulsePulset t ++11 ReceiveReceive messagesmessages of of ppulseulse t t ++11 ..

TheThe generalgeneral decidesdecides onon x x g g .. For For lieutenantlieutenant p p ::

A A decisiondecision occursoccurs inin Broadcast Broadcast qq ((

N N 11 ,, t t 11 )) for for eacheach lieutenantlieutenant qq

WWpp [[qq ]] == decisidecisi oo nn ininBroadcast Broadcast qq (( N N 11 ,, t t 11 ))

y y p p == max max (W(Wpp ))



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FeaturesFeatures

Ter Ter mm ination:ination: IIf f Broadcast Broadcast (( N N ,, t t )) isis startedstarted inin pulsepulse 1,1, everyevery processprocess decidesdecides inin pulsepulse t t ++ 11

DependenceDependence :: If If thethe generalgeneral isis correct,correct, if if therethere areare f f faultyfaulty pp r r ocesses,ocesses, andand if if N N >> 2 2 f f ++ t t ,, thenthen allall correctcorrect processesprocesses

decidedecide onon thethe inputinput of of thethe generalgeneral Agreement: Agreement: All All correctcorrect processprocess ee ss decidedecide onon thethe samesame

valuevalue

TheThe Broadcast Broadcast (( N N ,, t t )) protocol protocol isis aa t t --Byzantine-robust Byzantine-robust broadcast broadcast proto proto c c oo l l fofor r t t

lec 10 agreementprotocols

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