EEC 688/788 Secure and Dependable Computing Lecture 8 Wenbing Zhao Department of Electrical and Computer Engineering Cleveland State University wenbing@ieee.org

EEC688/788: Secure & Dependable Computing Outline Reminder Deadline for lab report: Tuesday 7/5 in class (hardcopy) Deadline for project proposal submission: Thursday 6/30 midnight Distributed consensus and Paxos algorithms Distributed consensus problem Classic Paxos Multi-Paxos Dynamic Paxos Cheap Paxos Fast Paxos 2/24/2019 EEC688/788: Secure & Dependable Computing

Distributed Consensus Distributed consensus is a fundamental problem in distributed computing Ensure replica consistency Asynchronous distributed system No upper bound on processing time No upper bound on clock drift rate No upper bound on networking delay In an asynchronous distributed system, you cannot tell a crashed process from a slow one, even if you can assume that messages are sequenced and retransmitted (arbitrary numbers of times), so they eventually get through 2/24/2019 EEC688/788: Secure & Dependable Computing

FLP Impossibility Results FLP (Fischer, Lynch and Paterson) Impossibility result A single faulty process can prevent consensus Because a slow process is indistinguishable from a crashed one Chandra/Toueg Showed that FLP Impossibility applies to many problems, not just consensus In particular, they show that FLP applies to group membership, reliable multicast So these practical problems are impossible to solve in asynchronous systems They also look at the weakest condition under which consensus can be solved Ways to bypass the impossibility result Use unreliable failure detector Use a randomized consensus algorithm 2/24/2019 EEC688/788: Secure & Dependable Computing

Distributed Consensus Older generation of consensus algorithms rely on the use of an unreliable failure detector to exclude failed processes from the consensus consideration Difficult to understand and harder to prove for correctness The Paxos algorithm introduced by Lamport Separate safety and liveness properties “Paxos is among the simplest and most obvious of distributed algorithm” by Lamport Consensus can be reached during periods of synchrony No consensus is possible if system very asynchronous, but guarantees no disagreement 2/24/2019 EEC688/788: Secure & Dependable Computing

EEC688/788: Secure & Dependable Computing Consensus Problem Safety: Only a value that has been proposed may be chosen If a value is chosen by a process, then the same value must be chosen by any other process that has chosen a value If a process learns a value, then the value must have been chosen by some process Liveness: Some proposed value is eventually chosen and, if a value has been chosen, then a process can eventually learn the value 2/24/2019 EEC688/788: Secure & Dependable Computing

The Paxos Algorithm – Consensus for Asynchronous Distributed Systems Contribution: separately consider safety and liveness issues. Safety can be guaranteed and liveness is ensured during period of synchrony Participants of the algorithm are divided into three categories Proposers: those who propose values Accepters: those who decide which value to choose Learners: those who are interested in learning the value chosen 2/24/2019 EEC688/788: Secure & Dependable Computing

EEC688/788: Secure & Dependable Computing The Paxos Algorithm How to choose a value Use a single acceptor: straightforward but not fault tolerant Use a number of acceptors: a value is chosen if the majority of the acceptors have accepted it Accepted does not mean chosen. However, if a value has been chosen, it must have been accepted first 2/24/2019 EEC688/788: Secure & Dependable Computing

EEC688/788: Secure & Dependable Computing The Paxos Algorithm Requirements for choosing a value P1. An acceptor must accept the first proposal that it receives P2. If a proposal with value v is chosen, then every higher-numbered proposal that is chosen has value v The proposal numbers are totally ordered => P2 guarantees the safety property 2/24/2019 EEC688/788: Secure & Dependable Computing

The Paxos Algorithm How to guarantee P2? P2a: If a proposal with value v is chosen, then every higher-numbered proposal accepted by any acceptor has value v But what if an acceptor that has never accepted v accepted a proposal with v’? P2b: if a proposal with value v is chosen, then every higher-numbered proposal issued by any proposer has value v P2b implies P2a, which implies P2 P2b P2a P2 V is chosen by some acceptor Newer proposal Must propose v Only v could Have been accepted Only v could Have been chosen by other acceptors 2/24/2019 EEC688/788: Secure & Dependable Computing

EEC688/788: Secure & Dependable Computing The Paxos Algorithm How to ensure P2b? P2c: For any v and n, if a proposal with value v and number n is issued, then there is a set S consisting of a majority of acceptors such that either (a) no acceptor in S has accepted any proposal numbered less than n, or (b) v is the value of the highest-numbered proposal among all proposals numbered less than n accepted by the acceptors in S 2/24/2019 EEC688/788: Secure & Dependable Computing

EEC688/788: Secure & Dependable Computing The Paxos Algorithm To ensure P2c, an acceptor must promise: It will not accept any more proposals numbered less than n, once it has accepted a proposal n Rules on both acceptors and proposers 2/24/2019 EEC688/788: Secure & Dependable Computing

EEC688/788: Secure & Dependable Computing The Paxos Algorithm Phase 1. (a) A proposer selects a proposal number n and sends a prepare request with number n to a majority of acceptors. (b) If an acceptor receives a prepare request with number n greater than that of any prepare request to which it has already responded, then it responds to the request with a promise not to accept any more proposals numbered less than n and with the highest-numbered proposal (if any) that it has accepted. 2/24/2019 EEC688/788: Secure & Dependable Computing

EEC688/788: Secure & Dependable Computing The Paxos Algorithm Phase 2. (a) If the proposer receives a response to its prepare requests (numbered n) from a majority of acceptors, then it sends an accept request to each of those acceptors for a proposal numbered n with a value v, where v is the value of the highest-numbered proposal among the responses, or is any value if the responses reported no proposals. (b) If an acceptor receives an accept request for a proposal numbered n, it accepts the proposal unless it has already responded to a prepare request having a number greater than n. 2/24/2019 EEC688/788: Secure & Dependable Computing

EEC688/788: Secure & Dependable Computing The Paxos Algorithm 2/24/2019 EEC688/788: Secure & Dependable Computing

Importance of Keeping Promises (for not accepting older proposal) Not a problem if a value has been chosen 2/24/2019 EEC688/788: Secure & Dependable Computing

Importance of Keeping Promises (for not accepting older proposal) Safety violated without promise with competing proposers 2/24/2019 EEC688/788: Secure & Dependable Computing

Importance of Keeping Promises (for not accepting older proposal) Safety is ensured by the promise with competing proposers 2/24/2019 EEC688/788: Secure & Dependable Computing

Multi-Paxos: Paxos for State Machine Replication Client: partially assumes the role of a proposer Server replicas: acceptors Value to be agreed on: total ordering of requests sent by clients Total ordering accomplished by running a sequence of instances of Paxos Each instance is assigned a sequence number, representing the total ordering of the request that is chosen Value to be chosen: the request chosen for the instance

Multi-Paxos: Paxos for State Machine Replication Client: partially assumes the role of a proposer Only propose a value (i.e., request it sends) without the corresponding proposal number A server replica, the primary, decides on the proposal number Primary: essentially the proposer in Paxos Propose a sequence number – request binding Propagate value chosen (i.e., total ordering info) to other replicas (i.e., learners) Initial membership is known with a sole primary First phase can be omitted during normal operation When the primary is suspected, a new primary is elected (view change)

Multi-Paxos: Paxos for State Machine Replication Normal operation of Multi-Paxos

Multi-Paxos: Checkpointing and Garbage Collection Paxos is open-ended: it never terminates A proposer is allowed to initiate a new proposal even if every acceptor has accepted a proposal An acceptor must remember the last proposal that it has accepted and the latest proposal number it has accepted In Multi-Paxos, every replica must remember such info for every instance of Paxos: Need infinite memory Solution: periodic checkpointing, e.g., once for every n requests Garbage collect logs after taking each checkpoint Request or control msg needed by a slow replica may not be available anymore after a checkpoint => state transfer

Multi-Paxos: Leader Election and View Change Leader election: can be done using a full Paxos instance New primary needs to determine if a value has been chosen in each incomplete instance of Paxos Leader election and history determination can be done in a simple full paxos: view change

Multi-Paxos: View Change A set of 2f+1 replicas, replica id: 0,1,…,2f History of system: a sequence of views Each view: one and only one primary Initially replica 0 assumes the primary role for v=0 Subsequently, replicas take the primary role in a round-robin fashion To ensure liveness A replica starts a view change timer on the initiation of each instance of Paxos If the replica does not learn the request chosen before timer expires => suspect the primary

View Change On suspecting the primary, a replica broadcasts a view change message to all Current primary, if it is wrongly suspected, joins the view change anyway (i.e., it steps down from primary role) A replica joins the view change even if it’s view change timer has not expired yet On joining view change, a replica stops accepting normal control msgs and respond to only checkpointing and view change msgs

View change View change msg contains New view # Seq# of last stable checkpoint A set of accepted records since last stable checkpoint Each record consists of view#, seq#, request msg On receiving f+1 view change msgs, new primary sends new view msg Include a set of accept msgs Include all accepted msgs as part of view change msg When a gap in seq# is detected, create an accept request with no op A replica accepts new view msg if it has not installed a newer view

Dynamic Paxos Designed to accommodate reconfiguration Extension majority concept to quorum Classic Paxos => uses static quorum Dynamic quorum: quorum size may change dynamically Cheap Paxos uses dynamic quorum

Dynamic Paxos Fewer replicas are required by using spare replicas and reconfiguration provided no other fault during reconfiguration Without reconfiguration, 3f+1 replicas can only tolerate up to 3f/2 faulty replicas 2f+1 active replicas, plus f spares can tolerate up to 3f-1 faulty replicas via substitution and reconfiguration As long as 1 active replica and 1 spare are operating

Dynamic Paxos Reconfiguration request must be totally ordered with respect to regular application requests A reconf request includes both new membership and quorum definition Replicas in the new membership should not accept msgs unrelated to reconf from replicas that have been excluded from the membership External replicas should not be allowed to participate the consensus step Replica mistakenly excluded can join via reconfiguration

Cheap Paxos Cheap Paxos is a special instance of Dynamic Paxos Aims to minimize involvement of spare replicas Enable the use of f+1 active replicas to tolerate f faults, provided that sufficient spares are available (f or more) Active replicas are referred to as main replicas Spare replicas are referred to as auxiliary replicas

Cheap Paxos Primary quorum Secondary quorum Consists of all active replicas Secondary quorum Must be formed by the majority of combined replicas Consists of at least one main replica => Ensures intersection between primary and secondary quorums Question: what if only one active replica is alive?

Cheap Paxos Upon detection of the failure of an active replica, a reconfiguration request is issued New primary quorum still consists of all surviving active replicas When reconfig request is executed, switch to new configuration Auxiliary replicas are not bothered unless a reconfiguration is necessary What if the primary fails => view change

Cheap Paxos: View Change For history information: new primary must collect info from every active replica except the old primary For approval of the primary role, the new primary must collect votes from all surviving active replicas plus one or more auxiliary replica => a secondary quorum The secondary quorum is used to complete all Paxos instances started by old primary but not yet completed

Cheap Paxos Replicas in secondary quorum must propagate their knowledge to all replicas prior to moving back to primary quorum So that auxiliary replicas do not have to keep all requests and control msgs How to achieve this Primary notifies its latest state to all replicas not in secondary quorum Main replica (if it is not in secondary quorum) requests for retransmission of missing msgs Auxiliary replica keeps new info from primary and purge old data, and ack to the primary Primary resumes ordering requests after it receives ack from every replica

Example

Example

Example

Example

Fast Paxos Multi-Paxos: use one round of P1 for all instances of Paxos Fast Paxos: aims to further reduce the cost of consensus by running one P2a for all instances of Paxos Enables an acceptor to select a value (provide by a client) unilaterally and sends P2b to the primary However, there is no free lunch => we need more replicas to tolerate f faulty nodes (> 2f+1 for sure) We will also have to deal with collision recovery

Fast Paxos: Basic Steps Fast Paxos runs in rounds and each round has up to two phases In each round, 1st phase: prepare phase to enable the coordinator to solicit the status and promises 2nd phase for the coordinator to select a value to be voted on When an acceptor responded to P1a in round i, it has participated the round I When an acceptor sent P2b in response to P2a, it has casted its vote

Fast Paxos: Basic Steps Start from an initial membership, phase 1 will always enable the coordinator to select any value for P2b Need to run P1 once for all rounds Need to run P2a once for all rounds => eliminate another communication step Classic round is used only when a consensus is not reached in the fast round Due to coordinator failure Due to a collision

Fast Paxos: Normal Operation

Fast Paxos: Collision Recovery In the presence of multiple clients, acceptors may chose different requests (values) The coordinator must collect from a quorum of replicas on their values and select the right value On detecting a collision, i.e., the presence of multiple values, the coordinator initiates a Classic round Phase 1 can be omitted in Classic round because the coordinator already collected enough info

Fast Paxos: Quorum Requirement Quorum based on majority will not work Coordinator cannot rule out any value in the presence of collision Any value could have been chosen The coordinator must select a value that have been chosen or might have been chosen Intuition: coordinator selects a value only if it is present in the majority of the votes collected Need to make sure that a value in the minority could not have been chosen

Fast Paxos: Quorum Requirement How to ensure that a value in the minority could not have been chosen First, it cannot be chosen in the same fast round => the majority value makes it impossible Second, make sure two fast quorums (Rf) intersect in more than half of |Rf| acceptors Third, make sure any fast quorum Rf, and any classic quorum Rc intersect in more than half of |Rc| acceptors

Fast Paxos: Quorum Requirement Let total number of acceptors be n, number of faults tolerated in a fast round e, and # of faults tolerated in a classic round f Derive inequalities (n-f)+(n-f)-n>0 (n-e)+(n-e)-n>(n-e)/2 (n-e)+(n-f)-n>(n-f)/2 Reduce to n > 2f and n > 2e+f

Fast Paxos: Quorum Requirement First quorum formation: maximize e => e=f, n> 3f => |Rc| = n-f > 2f => n = 3f+1 Second quorum formation: maximize f f < n/2 e <= n/4 If e=1, n=4; |Rf| = |Rc| = 3

Fast Quorum: Coordinator Value Selection Rule If no acceptor has casted any vote, the coordinator gets to select any value for P2b If only a single value in the votes, select that value If multiple values, select that one that is in the majority, if one is present. Otherwise, select any value

Exercise 1: Classific Paxos There are 2 proposers p1 and p2, 3 acceptors a1, a2, a3. Proposer p1 sends a prepare request to a1 and a2 with (p#=1). Proposer p2 sends a prepare request to a2 and a3 with (p#=2). a1 and a2 reply to proposer p1 that they received the proposal p1(p#=1). Similarly a2 and a3 reply to proposer p2 that they received the proposal p2(p#=2). If p1 then sends an accept request to a1 and a2 with (p#=1, v#=2), what happens at a1 and a2? If proposer p2 sends a accept request to a2 and a3 with (p#=2, v3#=3), what happens at a2 and a3? If proposer 1 again sends a new proposal and accept request, say p3, to a1 and a2 with (p#=3), does a 1 and a2 accept the proposal? Assume that the value is already chosen in question b, what is the final value chosen for this new proposal?

Exercise 2: Fast Paxos Given the number of faulty acceptors that can be tolerated in fast round e=5 Find out the following: The minimum number of acceptors needed (n) The faulty acceptors that can be tolerated in a classic round (f) The size of classic quorum The size of fast quorum