Agreement protocol

Agreement Protocol
Saif Ali Khan
31703213
Computer Engineering(Cyber Security)
Guided By:
Prof. A.K. Singh
Deptt of Computer Engineering
NIT KKR,CYBER SECURITY,1ST YEAR,SAIF ALI KHAN,31703213 1

Contents
1. What is agreement in distributed system and why agreement?
2. Synchronous and Asynchronous communication
3. Assumptions.
4. What is Agreement Problem(consensus problem) in Distributed
System?
5. Solutions to agreement problems in case of Synchronous system.
1.Lamport algo for crash failure
2.pease upper bound on faluty processes ‘f’
3. Lamport-Shostake –pease algo(oral message) OM(m).
4.Phase king Algorithm.(polynomial time message exachange)

content
6. Agreement solution in case of Asynchronous system
1. FLP impossibility of consensus in asynchronous system(1985)
2. Conversion of consensus into weaker version problem.
3. Terminating Reliable Broadcast
4.k-set Consensus
5. Approximate Agreement
7.Application of Agreement in Real life.

What is Agreement in DC(Basic Intro)
• A kind of co–operation or unity or accordance among processes.
• As we know that all the nodes in a distributed system are working
together in a cooperation to achieve a commom goals. Hence co-
operation among the process is very necessary .
• There are some standard agreement problem in DC. We will see each
problem and try to find find some protocol or algorithm to solve the
agreement problem.
• Agreement protocol is used to ensure that DS is able to achieve the
common goal even after occurance of various failures in Distributed
system.

Why agreement protocol in DC
• To achieve some common goal in Distributed system
• To deal with Various faulty processess which might produce wrong
results and send wrong information to other processes
• To achieve reliability of Distributed system

Problem which require Agreement
• Leader Election
• Distributed Transaction
• Mutual exclusion
• Any many more ….

When agreement is required?
• Agreement is always requird to achieve a common goal in distributed
system.
• When there are some types of faulty processes present in the
distributed system at that time we need to make sure that
performance of distributed system should not be affected at that time
we implement some agreement protocol (algo) ,so that output of
distributed should not be incorrect.or should not be affected
• Thres are some standard agreement problem we have, our job is to
study various agreement solution proposed by researchers to deal
with these agreement problem.
• Let’s Discuss some Assumptions used in Consensu Algorithm

Assumption Used in Areement protocol
• Failure models
• Synchronous/ Asynchronous communication
• Network connectivity
• Sender identication
• Channel reliability
• Authenticated vs. non-authenticatedmessages
• Agreement variable

Various Failures in Distributed System
A processor can fail in three modes:
• Crash fault : a processor stops functioning and never resumes
operation .
• Omission fault : a processor "omits" to send messages to some
processors.
• Malicious fault (Byzantine faults): most dangerous one
a processor behaves randomly and arbitarly. That means it does not
send correct information. It can be disloyal at any time we don’t know.
We cant trust on this .

We will find agreement solution in two mode
of communication under various failure
• Synchronous mode: Finite message delay(lockup step manner)
A process receives messages (1 round), performs a computation
(2 round), and send messages to other processes (3 round).
Message has not been sent can be recognized by intended recipient.
• Asynchronous mode: infinite message delay(non lockup step
manner)
The computation at processes does not proceed in lock steps. A
process can send and receive messages and perform computation at
any time.

Cont’d
Network Connectivity: The system is fully connected .Any process can
send message to any other processs.
Sender indetification:- That means a receiver is always aware about
idetitiy of sender.
Channel reliability: Channel is reliable. Only process can fail.
Aunthenticated vs Non Autheticated message:-
We will assume that message used in agreement protocol is
Unauthenticated message.
1)It can forge the message and claim that it has come from another
process.

Cont’d
• Agreement varibles:-
Varibales used in agreement can be Boolean or multivalued and need
not be an integer
But we generally used Boolean varibales….

Agreement protocol Inspiration .

Byzatine General problem(inspired from
byzantine empire)
There was byzantine empire in middle ages ….there were some army
generals who were protecting the city. Now all general have to make an
agreement or some negotiation to invade the city . If any general is
found to be traitors they will not be able to protect the city .hence they
have to agree on some common terms and then only they can protect
the byzantine empire
Present part of byzantine empire is knowns Turkey (Istanbul)

1.Crash Free
2.Crash Failure
3.Byzatine failure
(Imp)Agreement problem=Byzantine problem+(Consensus
problem+ Interactive consistency )
Synchronous System Asynchronous System

Agreement problem(Byzantine problem)
Byzantine problem:
An arbitrarily chosen processor, called the source processor, broadcasts
its initial value to all other processors.
Agreement :All nonfaulty processors agree on the same value.
Validity:If the source processor is nonfaulty, then the common agreed
upon value by all nonfaulty processors must be same as the initial value
of the source.
Termination: Each non-faulty processor must eventually decide on a
value.
cont--NIT KKR,CYBER SECURITY,1ST YEAR,SAIF ALI KHAN,31703213 17

Agreement problem Types
• Byzantine agreement problem
• There are two flavoure of byzantine agrrement problem.
1.The consensus problem.
2.The interactive Consistency Problem.

Cont’d
If source is faulty then all non- faulty processes can agree on any
common value”.
“Value agreed upon by faulty processors is irrelevant

Threre are two variants of Byzantine problem
1. The consensus problem
2. The Interactive Consistency problem

The consensus problem
Here all process have some initial value they broadcast their initial
values to all others process and satisy the following condition:
Agreement:All non-faulty processes must agree on same single values
Validity: if all non faulty processes have the same initial value , then
the agreed value by all the non-faulty processes must be that same
value.
Termination: Each non-faulty process must eventually decide on a
value.
cont--

Cont’d
“If initial value of non-faulty processors are different then all non-
faulty processors can agree on any common value”.
“Value agreed upon by faulty processors is irrelevant”

The Interactive consistency problem
Every processor broadcasts its initial value to all other processors. The
initial values of the processors may be different .
A protocol for the interactive consistency problem should meet the
following conditions:
Agreement: All non-faulty processes must agree on the same array of
values A[v1 : : : vn].
Validity: If process i is non-faulty and its initial value is vi , then all non-
faulty processes agree on vi as the ith element of the array A. If process
j is faulty, then the non-faulty processes can agree on any value for A[j].
Termination: Each non-faulty process must eventually decide on the
array A.

This was all about agreement problem in
Distributed System
• Now we will discuss its solution in various failure model in
synchrounous mode and asynchronous mode.

Now lets Discuss the solution of agreement
problem in various failure model in synchronous
1.No failure
2. Crash failure
3.Byzantine failure

Agreement algorithm for No-failure
Agreement can easily achieved in constant no of message exchange
Both synchronous and asynchrounus mode will always achieve
agreement .Because when all process are working fine then they are
eventually satisfying the property of Distrubed system and with
constant no of message exchange we can achieve i.e all nodes in a
distributed system are working in a cooperation to achieve some
commone goal.

Agreement Protocol
Synchronous System Asynchronous System

Important notes: Please write everyone in
your notebook
• There are some solution that solve agreement problems by satisfying all
condition of agreement problem in case of synchronous system.
• But in case of asynchronous models , agrerment problem are not solvable.
However we can solve agreement problem in asynchronous System after
converting agreement problem in its weaker version. That means
agreement problem are reduce to some weaker verison .
Weaker version of agreement problem are:
1.k-set consensus
2.Approximate consensus
3.Renaming problem
4.Terminating reliable broadcast ( it is a kind of problem which require
consensus.)

*Agreement protocal in crash failure process
• This is the first algo given by Lamport to solve agreement problem.
• Source Broadcasts its initial value to all other processors.
• Processors send their values to other processors and also relay
received values to others.
• During Execution faulty processors may confuse by sending conflicting
values.
• However if faulty processors dominate in number, they can prevent
non-faulty processors from reaching an agreement.

Algorithm
• (global constants)
• integer: f ; // maximum number of crash failures tolerated
• (local variables)
• integer: x - local value;
• Process Pi (1 < i< n) executes the Consensus algorithm for up to f crash failures:
• for round from 1 to f + 1 do
• if the current value of x has not been broadcast then
• broadcast(x);
• yj  value (if any) received from process j in this round;
• x  min(x; yj );
• output x as the consensus value.

Agreement algorithm for crash failure process
• f=no of crash failure process out total ‘n’ process
• Up to f (< n) crash failures possible.
• In f + 1 rounds, at least one round has no failures.
• Now justify: agreement, validity, termination conditions are satised.
• Complexity: O(f + 1)n2 messages
• f + 1 is lower bound on number of rounds

Pease Algorithm for upper bound on faulty
processor .
• Pease basically discuss that there is limit on the no of faulty processor
That means if f= no of faulty processor out of ‘n’ process
Then
f less than or equal to ( n - 1) / 3
That means pease want to say that for f=1 and n=3 we can’t achieve
agreement in
This is very very important for exam point of view.
Let’s see prove on the next page

(Imp) Let us study two majority Based algorithm
to solve Consensus Problem
1. Lamport -Shostake -Pease (in the textebook it is mentioned as
Byzantine agreement tree algorithm : exponential Synschronous
algorithm )
2.Phase King Algorithm: polynomial (synchronous system)

Lamport-Shostak-Pease Algorithm (Majority)
• The Oral Message (OM(m)) algorithm with m > 0 (some faulty
processor(s)) solves the Byzantine agreement problem for 3m + 1
processors with at most m faulty processors
• The initiator sends n - 1 messages to everyone else to start the
algorithm
• Everyone else begins OM( m - 1) activity, sending messages to n - 2
processors
• Each of these messages causes OM (m - 2) activity, etc., until
OM(0) is reached when the algorithm stops
• When the algorithm stops each processor has input from all others
and chooses the majority value as its value

B
Coor
dina
tor
A

Cont’d
At the end we have to take majority.
Fox example if process p have (1,0,0,0,0) as you can see that zero is in
the majority. Hence when algorithm terminates each process and they
will eventually agreed on majority values.
Ex (1,1,1,1,1,0,0,0)

Cont’d
Round Aim to tolerate failure Each message get sent to total message excahneg
1 f n-1 n-1
2 f-1 n-1 (n-1)(n-2)
F+1 0 n-f-1 (n-1)(n-2)(n-f-1)

Complexity analysis
• Total message exachange n+ (n-1)(n-2)+ (n-1)(n-2)……………..+(n-1)(n-
2)…….(n-f-1).
• O(n^f). This is exponential time. Hence this is not very feasible.

In the red book
• In the red book, this algorithm has implemented in two ways
1. Iterative
2. Recursion

Cont’d
• The algorithm has O(nm) message complexity, with m + 1 rounds of
message exchange, where n  (3m + 1)
• Recursion unfolding:- process acts as a source and sends its values to
each other process.
• Recursion folding:-Each process uses the values it receives from the
other sources ,and uses that values as the agreement value. If no
values is received , a default values is Assumed.

Phase King Algorithm for Agreement protocol
• Algorithm was by proposed by berman and garay
• Problem of previous algo is that it required exponential number of
message exchange with (f+1) round of message exchange.
• But in case of phase king algo, it required (f+1) phase with
polynomial number of message exchange that is the main advantage
of using phase king algo.
• It can tolerate only f< ceal of (n4), where n it total no of nodes
and f is no of faulty node.

Cont’d
• Each phase has 2 rounds
– Round 1:
• Each process broadcasts its estimate of the consensus to all others
and awaits the values broadcast by others
• Counts the number of 1 votes and 0 votes
• If either number > n/2, then it sets majority to that value and sets
mult to the number of votes received for the majority value
• If neither number of votes is greater than n/2, a default value is used
for majority value. It will occur in case of malicious process.

Round 2:
• The phase king for phase k is Pk
• Pk broadcasts its majority value which serves as a tiebreaker for
those which have a mult value less than n/2+ f
• When a process receives the tie‐breaker from the king,
– If mult > n/2 + f then it updates its estimate of the decision variable v
to its majority value
– Otherwise it updates its estimate of the decision variable v to the
tie‐breaker value

Complexity
• This algo take two round for every phase and total no of message
exchange is (f+1)[(n-1)(n+1)] message.

A comparision b/w LSP and King Algorithm
LSP Algorithm Phase King Algorithm
1. Exponetial message complexity 1.Polynomial Message complexity
O(n^f)
(f+1)(n-1)(n+1)
2.F<= floor of (n-1)3 2. F < Ceal of (n4)
1. Take f+1 phase total 3.it takes f+1 phases with each
take takes two 2 round.

Now lets Disscus agreement solution in case of
Asynchrounous models
• IN 1985 ,THREE Scientist FLP(fisher ,lynch and patterrson exaplained
in their research paper that impossibility of Agreement in
asynchronous system)
• That’s it is also called FLP impossibility.
• Fisher has explained that there is impossibility of reaching agreement
In an asynchrounous (message passing system). Even if a single process
Is allowed to have a crash failure.

Cont’d
• Because of time constrain I am not explaining proof of FLP impossblity
Plesase refer to research paper of FLP impossibility published in 1985,I
am leaving for you as an exercise.

Theses are the problem requires Agreement
protocol but are not solvable in asyn
• The leader Election Problem
• Terminating Reliable Broadcost
• Atomic Broadcost.

Terminating Reliable Broadcast problem
This is problem wich state that a correct process always gets a
messages even if the sender process get crashes while sending the
message.
Formal description
Validity: If the sender of a broadcast message m is non-faulty, then all
correct processes eventually deliver m.
Agreement: If a correct process delivers a message m, then all correct
processes deliver m.
Integrity: Each correct process delivers at most one message. Further, if
it delivers a message dierent from the null message, then the sender
must have broadcast m.
Termination: Every correct process eventually delivers some message.

Not Solvable
• There exists no algorithm that can solve TRB

Reduction from Agreement to TRB
• Commander sends its value using TRB.
• Receiver decides on 0 or 1 based on value it receives. If it receives a
"null"
• message, it decides on default value.
• But, as consensus is not solvable, hence there exist no algorithm to
implement TRB.

Weaker version of RTB
• Reliable Broadcast is RTB without terminating condition.
• RTB requires eventual delivery of messages, even if sender fails
before sending. In this case, a null message needs to get sent.
• In RB, this condition is not there.
• RTB requires recognition of a failure, even if no msg is sent
• Crux: RTB is required to distinguish between a failed process and a
slow process.
• RB is solvable under crashfailures; O(n2) messages

solution
• Process P0 initiates Reliable Broadcast:
• (1a) broadcast message M to all processes.
• (2) A process Pi ,1 <=i <=n, receives message M:
• (2a) if M was not received earlier then
• (2b) broadcast M to all processes;
• (2c) deliver M to the application.

K-Set consensus( A weaker version of Agrrement
• AS we have already explained that agreement (consensus) is not
solvable in asynchronous system ,However we will solve a weaker
version of Agreement problem called K- set consensus will be solvable
provided that no of crash falure ‘f’is less than parameter k .
• K- parameter:-it indicate that the non-faulty agree on the different
values ,as long as size of the the set of the values agreed upon is
bounded by k.

cont’d
k-Agreement: All non-faulty processes must make a decision, and the
set of values that the processes decide on can contain up to k (> f )
values.
Validity: If a non-faulty process decides on some value, then that value
must have been proposed by some process.
value.

Example from Red Book
Let n=10,f=2,k=3 then 3-set is (8,9,10).
Algo.(Solution)
• (variables)
• integer: v  initial value;
• A process Pi , 1 <= i<= n, initiates k-set consensus:
• broadcast v to all processes.
• await values from |N| -f processes and add them to set V;
• ( decide on max(V).

Asynchronous Renaming
• The renaming problem assigns to each process Pi , a name mi from a
domain M, and is formally specied as follows.
Agreement: For non-faulty processes Pi and Pj , mi not equal mj .
Termination: Each non-faulty process is eventually assigned a name mi
Validity: The name mi belongs to M.
Anonymity: The code executed by any process must not depend on its
initial identifier.

Approximate agreement(epsilon consensus)
Another weaker version to solve consensus problem in async system
under crash failure is approximate algo.
epsilon-Agreement: All non-faulty processes must make a decision and
the values decided upon by any two non-faulty processes must be
within range of each other.
Validity: If a non-faulty process Pi decides on some value vi , then that
value must be within the range of values initially proposed by the
processes.
value.

Application of Agreement protocol
• It is used in fault tolerance clock synchronization which you will study
in chapter 15 of Red Book.
• It is also very frequently used in Atomic distributed database commit.
• Control of UAV(drone)
• Smart power grid

References
• “Distribute Computing” Ajay D.Kshemkalyani And Mukesh Singhal.
• Slides of Prof. Mayank Jain

Agreement protocol

More Related Content

What's hot (20)

Similar to Agreement protocol (20)

Recently uploaded (20)

Agreement protocol