3.The framework of This Study:
To analyze the security and performance implications of different consensus and network layer protocol author has prepared a quantitative framework to carry out this study. Author’s framework is a combination of two key elements.

Figure:6 Components of Study Framework
** Pictures taken from ETH Zurich Research Report.

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They are (i) POW Blockchain and (ii) Security Model. A blackchin instance is a proof of work blockchain instantiated by consensus layer and network layer parameter. As discussed earlier a consensus mechanism is what all the blocks in the network follow to validate a transaction. For example, Bitcoin uses a POW consensus layer mechanism which searches for a nonce value such that the current target value should be lesser than the hash value. In network layer two most important parameters for POW blockchain is
Block size: This defines how many transactions can be put into each block. If the block size is bigger then block propagation speed decreases. On the other side, it increases the stale block rate.

Information Propagation mechanism: This shows how information is delivered in peer to peer network. There are four types of standard information propagation mechanism:
Send Headers: Peers can directly issue a send header to directly receive block headers from its peer in future.

Unsolicited Block Push: A mechanism of broadcasting blocks by the miners without advertisement.
Relay Networks: It enhances the synchronization of miners of the common pool of transaction.
Hybrid Push/Advertisement System: A system which combines the use of push and advertisement system.

In the left-hand side, POW blockchain takes consensus and network parameters as input and gives output like block propagation time, throughput. To realistically capture the output of this POW based blockchain authors have put this blockchain on the simulators they have developed. These simulators take input parameter such as block interval, mining power as well as block size, propagation protocol, the location of miner’s etc. Stale block rate is an important output from this POW based blockchain because it gives the efficiency of peer to peer connection of an honest network. This Stale block rate is taken as an input to Security model. This model also takes different security parameters as input such as adversarial mining power, mining cost, number of required confirmation. The main objective of this model is to holistically compare the security and performance of different POW blockchain with different parameters as input. This security model is based on Markov decision Process and provides an optimal adversarial strategy for double spending and selfish mining as an output.
3.1Security Model:
Parameters for the Security Model:
Stale Block Rate: Stale block rate captures information propagation mechanism.

Mining Power: This is typically used in the study model to capture the fraction of the total mining power possessed by the adversary.
Block Confirmation Number: Total number of blocks required to confirm a transaction.

Impact of Eclipse Attack: This study model accounts for eclipse attack as well.

3.2 Markov Decision Process: (MDP)
The right tool for a problem which deals with “states” and “discrete events” with a certain probability is a Markov Decision Process (MDP). MDPs are a mathematical model which decides the best policy means in what sequence the actions should be implemented to maximize a goal. An MDP model has multiple states and actions. Actions are the transitions between states. In MDP each transition can happen with some probability. In this model, some actions might provide a reward or loss to occur. Figure 7 shows a graphical depiction of a Markov Decision Process. In the intended security and performance of POW study, MDP is based on four tuples. It is represented as follows M:=<S, A, P, R>. Where S represents state space, A is for representing actions, P is the stochastic transition matrix and R is the reward matrix.

Figure 7: A graphical depiction of MDP with states s_0, s_1, S_2 and action a_0, a_1.The two rewards are -1 and +5. (Figure created by MistWiz on WikiCommons).

In this model an adversary can perform the below actions:
Adopt: If an adversary thinks it can never win over an honest miner then it performs this action.

Override: If adversaries chain is longer than the honest miner then it overrides the honest mining chain.

Match: if the length of adversarial chain and honest chain are same then adversary perform this action.

Wait: If an adversary has not yet found a block then it continues mining until it finds one.

Exit: This action is performed during the double-spending attack.
Now state space S also has four-tuple namely length of honest chain, length of adversarial chain, blocks mined by eclipsed victim and fork. In the research, paper MDPs were built such a way which could provide justification when a rational attacker successfully double-spend or selfish mine.

Selfish Mining vs Double Spending: Main goal in selfish mining is to increase the relative share of the adversarial block in the main chain. In double spending, the adversary is more focused on earning maximum revenue. It is also found in the study that selfish mining is not always rational. Following an adversarial strategy for mining 1000 blocks with 30% hash power, an adversary can mine 209 blocks, but an honest miner can mine 300 blocks. In honest mining, an adversary can earn by mining a block. It also loses it’s reward if a block is adopted by the main chain. As the main chain poses maximum hash power, the probability is always high for an adversary to lose the competition.
Eclipse Attack: In this type of attack attacker takes control of peer to peer network and obscure target node’s view of the blockchain. The researcher has found attacker can saturate the connection to a target victim. It means all the connection to the victim would be bottlenecked and passed through attacker nodes so that it can manipulate the connections. Following eclipse attack scenarios are captured by our model:
No Eclipse Attack: This study model captures this case.

Isolate the Victim: This captures those cases where total mining power decreases. In return, it increases the fraction of mining power possessed by an adversary.

Exploit the eclipsed victim: Adversary uses victims mining power to expand its own chain.

3.3 Selfish Mining MDP:
As discussed previously the main goal of a selfish miner is to increase the relative number of adversary block in the main chain. In this study, the model author has captured that by optimizing the relative revenue. But there is a problem of applying single player MDP in this particular case because selfish miner deals with relative revenue. To overcome this problem the author has applied Sapirshtein el. Sapirshtein el proposes that an adversary with less than 33% of total hash power can make a profit from the network. This model captures various parameter such as block propagation time, block generation interval, block size and eclipse attack.

3.3.1 Optimal Strategies For Selfish Mining :
Authors have used MDP solver for finite state space MDP’s. The output author received from the model is below. Here the author tries to find the impact of stale block rate on selfish mining.

Figure 8: Selfish mining (Relative revenue vs Adversarial mining power)
** Pictures taken from ETH Zurich Research Report.

In Figure 8 author tries to understand how adversarial mining power influences the relative revenue of an attacker. For this he has put the adversarial mining power is in X-axis and relative revenue in the Y axis. The graph is drawn for a stale block rate of 1% and 10%. It is seen from this diagram that relative revenue increase with the increase of adversarial mining power. An upper bound is also taken in this diagram to understand the cases when the relative revenue of a selfish miner maximized by overriding a block of an honest chain. Figure 8 shows the upper bound exceeded when network delays and parameters are captured.

Figure 9: Relative revenue vs Stale rate
** Pictures taken from ETH Zurich Research Report.

In Figure 9 author tries to understand the relationship between stale block rate and relative revenue. He compares relative revenue in Y axis with stale block rate in X-axis for a mining power ? of .1 and .3 respectively. This diagram suggests a nonlinear relationship between relative revenue and stale block rate.

Author has also studied the impact of the eclipse attack in selfish mining. Figure 9 explains the relationship between eclipsed mining power ? and adversarial mining power ?. In this study the cases considered are
1. where adversary uses victims mining power ?
2. When an adversary uses honest miners blocks to advance its own chain.

It is seen for higher ? values selfish mining capability also increases. In this graph, an exceptional case is also observed for ?=.3 and ?=.38. For this situation, it is more profitable for an adversary not to include some of the victim’s blocks. Here victim’s blocks are accounted as a reward for the honest chain. This, in turn, reduces the block share of an adversary.

Figure 10: Eclipsed mining power vs Adversarial mining power
** Pictures taken from ETH Zurich Research Report.

3.4 Double Spending MDP: As discussed earlier in the double-spending rational adversary tries to maximize its profit. In double spending, it is assumed that loss in operational cost is less because the adversary can earn some goods or money in exchange for a transaction. In double spending, exit state can only be reached if the length of an adversarial chain is at least a block longer than the honest chain (la ; lh ) after k block confirmation for an honest chain with 1?? mining power. This is described in the below table 2. A question can arise during this study as the adversary is rational it is hard to reach an exit state. But it is found that in exit state adversary can earn a reward of

blocks.

** Pictures taken from ETH Zurich Research Report.

3.4.1 Optimal Strategies for Double Spending: To create optimal strategies author has used the pymdtoolbox library and applied PolicyIteration algorithm. By this block confirmation value, k is received which is sufficient to make a safe transaction in presence of rational adversary in the network. To decide in a certain scenario if a rational adversary would do double spend or selfish mining, a minimum value of double spend vd must be determined. For achieving that author start with high double spending value so that exit state is reachable in optimal double spending strategy. Author has done this because the presence of exit state in policy ensures double spending is highly profitable. In this below Table -3 an example is shown for optimal strategy.

Table 3: Optimal Strategies for double spending.

** Pictures taken from ETH Zurich Research Report.

Here ? = 0.3,? = 0,rs = 0.41%,cm = ?,? = 0 and vd = 19.5. Length of adversary chain is la, taken as rows. Length of honest chain is lh. Three values of each entry are irrelevant, relevant and active. * means unreachable and w, a, e represents wait, adopt and exit respectively. In this example cut off value for honest chain and adversarial is taken as 20. This suggests both this chain length cannot be greater than the defined cut-off value. So what is the main goal of this analysis? The attacker must overcome a threshold if it wants to double spend with profit for a fixed number of confirmed block k. In the other cases it is more profitable to do honest mining. This result is illustrated in Figure 10. The x-axis shows how the adversarial mining power is influencing the threshold. Different values of k (the desired number of confirmations) lead to different curves.

The y-axis in Figure 10 shows how many successive blocks are needed to be mined before a double spending attack to be successful. For an adversary, around 30% mining power needs 6 block confirmation and the expected number of blocks is roughly 100.

An adversary with mining power of more than .25 needed less than 1000 blocks to successfully carry out double-spending attack.

Figure:10 Expected blocks for double spending rs = 0.41%, ? = 0, cm = ? and ? = 0.

** Pictures taken from ETH Zurich Research Report.

Here stale block rate is represented by rs. ?, cm represents the propagation parameter and maximum mining costs respectively.

Impact of Propagation Parameter: Propagation parameter signifies the connectivity efficiency in an adversarial chain. It suggests if connectivity increases in the adversarial network then adversarial mining power also increases. Author has put adversarial mining power in the X-axis and shown double spending transaction should have a threshold value. If transaction value is more than the threshold value, then only double spending is profitable. It can also be seen from Figure 11 that higher the propagation parameter ? lower the transaction value an adversary expects to double spend.

Figure:11 Impact of propagation parameter ? with respect to double spending transaction value.

** Pictures taken from ETH Zurich Research Report.

In this graph double spending value(vd) is taken in Y-axis and adversarial mining power(?) in the X-axis. If ? increase vd decreases.

Impact of mining costs: From the study, it is found that mining cost has a negligible impact on adversarial strategy. It is shown by the below Figure 12.

Figure 12: Impact of mining cost.

** Pictures taken from ETH Zurich Research Report.

Value of double spend (Vd) is in the Y-axis and adversarial mining power(?) in the X-axis. rs = 0.41%, ? = 0, ? = 0 Cm represents maximum mining cost ?vd is the difference in costs.

Impact of Stale Block Rate: In Figure 13 impact of stale block rate is explained for double spending. This below experiment is carried out for a mining power of .1 and .3 respectively. It can be seen if stale block rate grows the value of double spend decreases. Author has found double spending value of an adversary decreases from 9.2 to 6.4 block reward with mining power .3 and a stale block rate of 10% and 20 %.

Figure:13 Impact of stale block rate.

** Pictures taken from ETH Zurich Research Report.

Here Vd is the value of double spend in the Y-axis, Stale block rate in X-axis and adversarial mining power is represented by ?.

Impact of Eclipse Attack: The impact of eclipse attack is represented by Figure 14. It is assumed that an adversary attacks an honest block with ? eclipsed mining power. It can be observed eclipsed mining power increases with the increase of adversarial mining power. So eclipse attack is beneficial for an adversary. For example, an adversary with an adversary with ?=.025 and ? =.1 reduces the double spending value (vd) from 880 block reward to .75 block.

Figure 14: Full eclipse attack
** Pictures taken from ETH Zurich Research Report.

In Figure 14 eclipse mining power ? is in Y axis and adversarial mining power is in X axis and , rs = 0.41%, ? = 0 and cm = 0.

Bitcoin vs Ethereum: Figure 15 shows the reward required for a double spending attack to make a profit. The y-axes show the reward required from fraudulent behavior as multiples of the block reward, i.e. multiples of the reward of non-fraudulent behavior.
The figure also contrasts between Ethereum and Bitcoin. As a consensus algorithm both this chain uses proof of work, but the key difference is the block time. i.e. the duration between the generation of two blocks. Stale block rate increases because of shorter block times. It means the time gap between finding two blocks is much shorter in Ethereum. Thus, participant blocks more often return finding the same block which increases the stale block rate in the network.

Below points are observed by the author in the study.
First: Figure 15 shows 6 Bitcoin block confirmation is more resilient to double spending than that of 12 Ethereum block.

Second: Ethereum’s double spending resilience is better only for an adversary with less than 11% hash power.

Third: If block reward goes up blockchain is more resilient to double spending attack.

Figure 15: Double spending resistance of Ethereum vs Bitcoin
** Pictures taken from ETH Zurich Research Report.

Block reward is in the Y-axis and Adversarial mining power in the X-axis. Ethereum (k ?{6,12}) vs. Bitcoin (k = 6).

Author has also tried to compare both this block chains by equalling their stale block rate. It is observed that Ethereum’s security is lower in caparison to bitcoin Figure 16 explains the following.

Figure 16: Comparison between Ethereum and Bitcoin.

** Pictures taken from ETH Zurich Research Report.

Value of double spend is on the Y-axis and Adversarial mining power is in the X-axis. Here k is 6, rs = 6.8% and their difference is ?vd.

3.Framework of This Study:
To analyse the security and performance implications of different consensus and network layer protocol author has prepared a quantitative framework to carry out this study. Author’s framework is a combination of two key elements.

Figure:6 Components of Study Framework
They are (i) POW Blockchain and (ii) Security Model. A blackchin instance is a proof of work blockchain instantiated by consensus layer and network layer parameter. As discussed earlier a consensus mechanism is what all the blocks in the network follows to validate a transaction. For example Bitcoin uses a POW consensus layer mechanism which search for a nonce value such that current target value should be lesser than hash value. In network layer two most important parameters for POW blockchain is
Block size: This defines how many transaction can be put into each block. If block size is bigger then block propagation speed decreases. On the other side it increases stale block rate.

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Information Propagation mechanism: This shows how information is delivered in peer to peer network. There are four types of standard information propagation mechanism:
Send Headers: Peers can directly issue a send header to directly receive block headers from it’s peer in future.

Unsolicited Block Push: A mechanism of broadcasting blocks by the miners without advertisement.
Relay Networks: It enhances the synchronization of miners of common pool of transaction.

Hybrid Push/Advertisement System: A system which combine use of push and advertisement system.

In the left-hand side POW blockchain takes consensus and network parameters as input and gives output like block propagation time, throughput. To realistically capture the output of this POW based blockchain authors have put this blockchain on the simulators they have developed. These simulator’s takes input parameter such as block interval, mining power as well as block size, propagation protocol, location of miner’s etc. Stale block rate is an important output from this POW based blockchain because it gives the efficiency of peer to peer connection of an honest network. This Stale block rate is taken as an input to Security model. This model also takes different security parameters as input such as adversarial mining power, mining cost, number of required confirmation. This security model is based on Markov decision Process and provide optimal adversarial strategy for double spending and selfish mining as an output.
3.1Security Model:
Parameters for the Security Model:
Stale Block Rate: Stale block rate captures information propagation mechanism.

Mining Power: This is typically used in the study model to capture the fraction of total mining power possessed by adversary.

Block Confirmation Number: Total number of blocks required to confirm a transaction.

Impact of Eclipse Attack: This study model accounts for eclipse attack as well.

3.2 Markov Decision Process: (MDP)
The right tool for a problem which deals with “states” and “discrete events” with a certain probability is a Markov Decision Process (MDP). MDPs are a mathematical model which decides the best policy means in what sequence the actions should be implemented to maximize a goal. An MDP model has multiple states and actions. Actions are the transitions between states. In MDP each transition can happen with some probability. In this model some actions might provide a reward or loss to occur. Figure 7 shows a graphical depiction of a Markov Decision Process. In the intended security and performance of POW study MDP is based on four tuples. It is represented as follows M:=<S,A,P,R>. Where S represents state space, A is for representing actions, P is stochastic transition matrix and R is reward matrix.

Figure 7: A graphical depiction of MDP with states s_0, s_1, S_2 and action a_0, a_1 .The two rewards are -1 and +5. (Figure created by MistWiz on WikiCommons).

In this model an adversary can perform the below actions:
Adopt: If an adversary thinks it can never win over an honest miner then it performs this action.

Override: If adversaries chain is longer than the honest miner then it overrides the honest mining chain.

Match: if the length of adversarial chain and honest chain are same then adversary perform this action.

Wait: If an adversary has not yet found a block then it continues mining until it finds one.

Exit: This action is performed during double spending attack.

Now state space S also has four tuple namely length of honest chain, length of adversarial chain, blocks mined by eclipsed victim and fork. In the research paper authors built MDPs for a rational attacker and asked what the attacker should do to successfully double-spend or selfish mine.Selfish Mining vs Double Spending: Main goal in selfish mining is to increase the relative share of adversarial block in the main chain. In double spending adversary is more focused on earning maximum revenue. It is also found in the study that selfish mining is not always rational. Following an adversarial strategy for mining 1000 blocks with 30% hash power, an adversary can mine 209 blocks, but an honest miner can mine 300 blocks. In honest mining an adversary can earn by mining a block. It also loses it’s reward if a block is adopted by the main chain. As the main chain poses maximum hash power, probability is always high for an adversary to lose the competition.

Eclipse Attack: Following eclipse attack scenarios are captured by our model:
No Eclipse Attack: This study model captures this case.

Isolate the Victim: This captures those cases where total mining power decreases. In return it increases the fraction of mining power possess by adversary.

Exploit the eclipsed victim: Adversary uses victims mining power to expand it’s own chain.

3.3 Selfish Mining MDP:
As discussed previously the main goal of a selfish miner is to increase the relative number of adversary block in the main chain. In this study model author has captured that by optimizing the relative revenue. But there is a problem of applying single player MDP in this particular case because selfish miner deals with relative revenue. To overcome this problem author has applied Sapirshtein el. Sapirshtein el proposes that an adversary with less than 33% of total hash power can make profit from the network. This model captures various parameter such as block propagation time, block generation interval, block size and eclipse attack.

3.3.1 Optimal Strategies For Selfish Mining :
Authors have used MDP solver for finite state space MDP’s. The output author received from the model is below:

Figure:7 Selfish mining (Relative revenue vs Adversarial mining power)
In Figure 7 Adversarial mining power is in X axis and Relative revenue in Y axis. Here author is comparing selfish mining under a stale block rate of 1% and 10%. It is seen from this diagram that relative revenue increase with the increase of adversarial mining power.

Figure: 8 Relative revenue vs Stale rate
In another graph author compares relative revenue in Y axis with stale block rate in X axis for a mining power ? of .1 and .3 respectively. From Figure 8 suggests a nonlinear relationship between relative revenue and stale block rate.

Author has also studied the impact of eclipse attack in selfish mining. Figure 9 explains relationship between eclipsed mining power ? and adversarial mining power ?. It is seen for higher ? values selfish mining capability also increases. In this graph an exceptional case is also observed for ?=.3 and ?=.38. For this situation it is more profitable for an adversary not to include some of victims blocks. Here victim’s blocks are accounted as a reward for honest chain. This in turn reduce the block share of an adversary.

Figure:9 Eclipsed mining power vs Adversarial mining power
3.4 Double Spending MDP: As discussed earlier in double spending rational adversary tries to maximize it’s profit. In double spending it is assumed that loss in operational cost is less because adversary can earn some goods or money in exchange of transaction. In double spending exit state can only be reached if length of an adversarial chain is at least a block longer than the honest chain (la ; lh ) after k block confirmation for an honest chain with 1?? mining power. This is described in the below table 2. A question can arise during this study as adversary is rational it is hard to reach an exit state. But it is found that in exit state adversary can earn a reward of

blocks.

3.4.1 Optimal Strategies for Double Spending : To create optimal strategies author has used pymdtoolbox library and applied PolicyIteration algorithm. By this block confirmation value k is received which is sufficient to make a safe transaction in presence of rational adversary in the network. To decide in a certain scenario if a rational adversary would do double spend or selfish mining, minimum value of double spend vd must be determined. For achieving that author start with high double spending value so that exit state is reachable in optimal double spending strategy. Author has done this because the presence of exit state in policy ensures high profitability for doubles spending strategy otherwise honest mining is more profitable. In this below Table -3 an example is shown for optimal strategy.

Table 3: Optimal Strategies for double spending.

Here ? = 0.3,? = 0,rs = 0.41%,cm = ?,? = 0 and vd = 19.5. Length of adversary chain is la, taken as rows. Length of honest chain is lh. Three values of each entry are irrelevant, relevant and active. * means unreachable and w, a, e represents wait, adopt and exit respectively. In this example cut off value for honest chain and adversarial is taken as 20. This suggest both this chain length cannot be greater than defined cut-off value. Author has also plotted a graph to explain the number of blocks required for a successful double spending attack. It is also observed in the study that an adversary with mining power of more than .25 needed less than 1000 blocks to successfully carry out double spending attack. Let’s look at Figure 10.

Figure:10 Expected blocks for double spending rs = 0.41%, ? = 0, cm = ? and ? = 0.

In this graph expected number of blocks is in Y axis and adversarial mining power in X axis . Here stale block rate is represented by rs. ? , cm represent propagation parameter and maximum mining costs respectively.

Impact of Propagation Parameter: Propagation parameter signifies the connectivity efficiency in an adversarial chain. Author has tried to put up a relationship between double spending transaction value with adversarial mining power in the following diagrams. It can also be seen from Figure 11 that higher the propagation parameter ? lower the transaction value an adversary expects to double spend.

Figure:11 Impact of propagation parameter ? with respect to double spending transaction value.

In this graph double spending value(vd) is taken in Y axis and adversarial mining power(?) in X axis. If ? increase vd decreases.

Impact of mining costs: From the study it is found that mining cost has negligible impact on adversarial strategy. It is shown by the below Figure 12.

Figure 12: Impact of mining cost.

Value of double spend (Vd) is in Y axis and adversarial mining power(?) in X axis. rs = 0.41%, ? = 0, ? = 0 Cm represents maximum mining cost ?vd is the difference in costs.

Impact of Stale Block Rate: In Figure 13 impact of stale block rate is explained for double spending. This below experiment is carried out for a mining power of .1 and .3 respectively. It can be seen if stale block rate grows value of double spend decreases.

Figure:13 Impact of stale block rate
Here Vd is value of double spend in Y axis, Stale block rate in X axis and adversarial mining power is represented by ?.

Impact of Eclipse Attcak: The impact of eclipse attack is represented by Figure 14. It is assumed that an adversary attacks an honest block with ? eclipsed mining power. It can be observed eclipsed mining power increases with the increase of adversarial mining power. So eclipse attack is beneficial for adversary.

Figure 14: Full eclipse attack
In Figure 14 eclipse mining power ? is in Y axis and adversarial mining power is in X axis and , rs = 0.41%, ? = 0 and cm = 0.

Bitcoin vs Ethereum: Below points are observed by author in the study.
First: Figure 15 shows 6 Bitcoin block confirmation is more resilient to double spending than that of 12 Ethereum block.

Second: Ethereum’s double spending resilience is better only for adversary with less than 11% hash power.

Third: If block reward goes up block chain is more resilient to double spending attack.

Figure 15: Double spending resistance of Ethereum vs Bitcoin
Block reward is in Y axis and Adversarial mining power in X axis. Ethereum (k ?{6,12}) vs. Bitcoin (k = 6).

Author has also tried to compare both this block chains by equalling their stale block rate. It is observed that Ethereum’s security is lower in caparison to bitcoin Figure 16 explains the following.

Figure 16: Comparison between Ethereum and Bitcoin.

Value of double spend is in Y axis and Adversarial mining power is in X axis. Here k is 6, rs = 6.8% and their difference is ?vd.

4.Blockchain Simulator and Results: The simulator author has developed for this study capture parameter’s like block size, block interval, propagation mechanism by measuring stale block rate, block propagation times. In this simulator point to point connections are established between nodes. Global IT latency statistics of Varizon are used to capture latency in the network. Regular nodes and miners are distinguished in this network. Bitnode’s geographical node location is adopted and used for the nodes in this simulator. Author has also used blockchain.info’s mining pool distribution and used it in this simulator. In Table 4 all the parameters which are captured by the simulator is listed.

Table -4 Parameters of Simulator
4.1 Evaluated Result:
Simulator Validation: In order to validate the performance of this study simulator author has adjusted the parameters of table 4 with the real world deployed blockchain. For determining the stale block rate author has crawled 24000 Bitcoin,1000,000 Litecoin and 240,000 Dogecoin blocks. The performance achieved from this model is quite like the real world blockchain. Stale block rates of Dogecoin and Litecoin are particularly close and Bitcoin’s stale block rate falls in some cases like where relay network and unsolicited block push is not used by miner.

Figure 17: Geographical Location of Bitcoin miner’s in study simulator.

Block Interval: Author has tested block interval with a range of .5 sec to 25 minutes in the simulator. It is tested for four different block request management system namely 1. Standard block request management 2. Standard block request management enhanced by unsolicited block push from miners 3. Former component with relay network 4. Send header mechanism with unsolicited block push and relay network.

For standard block request management system with 10 minutes block interval study simulator produces stale block rate 1.85 % in compare to 1.69 % reported by Wattenhoffer.

Stale block rate reduces significantly after introduction of unsolicited block push for miner because of two main reason—a. miners profit most out of unsolicited block push because they are interconnected b. propagation method is crucial to reach the majority of the network rapidly. To measure the impact of the block interval author has feed the resulting stale block into MDP models. It is found for an adversary with 30% of total mining power relative revenue is inversely proportional to consensus time.

Impact of Block Size: From the study it is found block propagation time has linear relationship with block size. But this linear relationship is valid up to 4 MB block size. From 4 MB to 8 MB stale block rate increases exponentially with propagation times. If block size increases relative revenue of selfish miner also increase but double spending value decreases. Author has also found efficient block propagation mechanism increases the security of the block chain. The results of this study for four previously discussed block request management system is shown in the below table 5.

Table 5: Impact of the block size on the median block propagation time (tMBP) in seconds
The stale block rate is rs, vd and rrel, given the current Bitcoin block generation interval and an adversary with ? = 0.3 and k = 6.

Throughput: Author has varied block size (.1 MB-8 MB) and block interval (.5 second-25 Minutes) to capture different blockchain throughput. Throughput is calculated in transaction per second (tps). Stale block rate and infer are represented with vd and rrel. The result author has got is shown in the below table -6.

Table 6: Impact of throughput for K=6 and 16 mining pool with 30% adversarial mining power.

From this table it can be seen 60tps throughput can be achieved with existing security in the bitcoin by changing the input parameters like block size and block interval.
5. Conclusion: In this study author has proposed a quantative framework to measure the security and performance of different POW based blockchains. The impact of network lavel parameters on the security of blockchain is evaluated in this study. From study it is found 37 Ethereum block confirmation equals 6 Bitcoin block confirmation. It means bitcoin blocks are more secured than Ethereum’s. It is also proved that 60 tps of bitcoin throughput can be achieved without sacrificing the existing security by varying input the parameters.

6.Reference:
1. On the Security and Performance of Proof of Work Blockchains by Arthur Gervais, Ghassan O. Karame, Karl Wüst, Vasileios Glykantzis, Hubert Ritzdorf, Srdjan ?Capkun.

2. Shai Rubin What is blockchain –youtube3. steemit.com
4. cryptocompare.com

3.1 Introduction
This chapter presents the systematic procedure of the activities taken in the study. The chapter describes the participants of the study (students/teachers) and provides a complete description of the instruments used for collecting data (test/questionnaire).

They include the following:
The research design and the population used for the study.
The sample size and sample procedure chosen for the research.
The method of data collection and data analysis.

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They are discussed under the following sub-headings.
3.2 Research design

The research method employed in this study is a quantitative design. Richards et al. (1992) refer to quantitative research as “research that uses procedures which gather data in numerical form” (p.302). The present study (pre test) is to check the knowledge of punctuation marks. After that, they will be given instructions on the same lesson (punctuation marks) to measure the effectiveness of learner performances a post-test will be done.
After identifying the errors, the researcher statistically analyzed the collected data using SPSS program, frequencies and percentages. Additionally, a test was administered to the students and a questionnaire to teachers of English language to assess their students’ as they use punctuation marks.

This research belonged qualitative as well as quantitative data. Therefore it is a mix method of data analyzing. The students’ test marks and second part of the teachers’ questionnaire belong to quantitative data analysis, because statistically the researcher had presented the result of them and the researcher had presented the idea of the teachers’ questionnaire first part in words. Therefore, it belonged to qualitative method.

The pre and post test have helped to achieve the first and second objectives of this research. It helped to identify the knowledge of using punctuation marks in writing and to find out the errors that the students are making in different marks in writing. The questionnaires also helped to identify the students’ knowledge of using punctuation mark in their school worked.

3.3 The Subjects of the Study
3.3.1 Students
Population means the larger group of the research. In this research, the population was the students at the College of Technology- Galle. Academic year 2017 which consisted of about 2000 students. The course DCS was selected since it was a single, because which is conducted at the end of the running in three months.
The course in the English medium the students’ number came to about 120 of whole population. This course was preferred to the National Certificate in professional English, Diploma in English and Education. These three courses have a teaching component in English which should require formal teaching of punctuation as required by their syllabus content.
The researcher’s objective was to examine the extent to which punctuation is picked up or not pick up through general teaching.

A sample is a small population selected for observation and analysis. The sample of this research was the students at the first semester of the DCS students at College of Technology – Galle 2017. The student of DCS students’ pre education requirement was GCE Advanced Level (any stream). Their subjects were Grammar, Advanced reading and writing, working cohesively with others, and Communication skills
The researcher conducted the study of punctuation errors made by the students. These students were studying English language as the main subject. They study the “Developing Career Skills” textbook.

Table 3.2
Students of DCS (Developing Career Students)
Sample of the research
2017

Courses Age Gender Total
Female Male
DCS Between 21 – 23 38 26 64
Sample 28 22 50

3.3.2 Teachers
The teachers of English language in government schools in the Galle district were chosen as the required subjects for the study. 10 teachers were selected randomly. They were given a questionnaire to assess their students’ writing skills in the use of punctuation marks by responding to its questions. Therefore, the researcher wanted to follow up the background to this sample. Consequently teachers from the catchment area were taken for the initial study. The reason for giving the teacher questionnaire is to know whether they have taught punctuation marks at the school properly and to whether they have given their attention on students’ error in using punctuation marks in writing.

3.4 Research Instruments
An instrument is a device to get data. It is one of the important tasks to keep the quality of the research result.
For collecting data, the researcher used two types of research instruments. They were test and questionnaire. The elaboration of the two research instruments are described below:

3.4.1 Students’ Test
The test was an instrument for collecting data. It was used to compare the errors committed by students with the teachers’ experienced feedback on students’ punctuation writing problems.
This test contains a series of questions used to measure skill, knowledge, intelligence, capability or talent of the students. Thus, the researcher used it as a tool to identify the errors made by students and used this tool to collect data about the students’ ability or knowledge regarding punctuation marks.
The researcher prepared the test paper for students to realize the objectives of the research. Thus, it consisted of sixty sentences for six types of punctuation marks. Students had to apply proper punctuation marks in the sentences. The total marks of the test were 60.
Pre-Test
The students of the experimental groups were given a pre-test to test their knowledge of punctuation marks. It was done to find out the standards of students in punctuation before receiving punctuation instructions. The test consisted of sixty sentences which represent six punctuation marks. The students were required to put the correct marks in their correct places.
Post Test
The post-test was administered to determine students’ performance in the use of punctuation marks. Then, within six weeks the particular students received punctuation instruction regarding selected punctuation marks. After six weeks they faced the post test. Its purpose is to find out whether or not the students have made progress on punctuation marks as usual.

3.4.2 Teachers’ Questionnaire
To collect the data, a questionnaire was given to the teachers of English Language. Questionnaire is a data collection instrument in scientific research. Its purpose was to collect data on teachers’ perception of the students’ punctuation errors. The teachers were asked to evaluate their students’ use of punctuation marks and also to check whether the syllabus provides punctuation marks as well. This tool was used because it is suitable for collecting reliable and valid data from a high proportion of population within a reasonable period of time at a minimum cost.
The questionnaire consisted of two sections, section one, five open ended questions and section two, ten statements. The options are designed as Liker-scales of the variables structured (always, sometimes, often, rarely, never). The whole questionnaire contains fifteen questions.

3.5 Sample Size and Sampling Procedure.
Out of the total number of sixty four students following this course at the Technical College- Galle in 2017, fifty were selected for the research study. This was because it was an experimental study. Out of sixty four, fifty students were selected as the sample. The population of the students was sampled randomly. This was done by tossing folded papers which contained number one and two. The students who got number one belonged to the research sample.

3.6 Data Collection Procedures
To collect the data, a questionnaire was given to teachers of English language. Its purpose was to collect data on teachers’ perception of the students’ punctuation errors. The teachers were asked to evaluate their students’ use of punctuation marks and whether the syllabus provides punctuation marks as well.

A written test was administered to the students in order to understand how far the students were able to place punctuation marks correctly. The test was developed to check students’ punctuation errors. First, the researcher got permission to hold the test. After that, the researcher explained to the students about the test and gave instructions how to insert punctuation marks in the given sentences in the test paper. Within 60 minutes the students did the test in the classroom. Finally, the researcher collected the test papers, marked, analyzed and discussed them with the students. I felt it was necessary that sample should understand the aim of the experiment and response positively.

3.7 Methods of Data Analysis
In order to have a proper analysis of the data in this research provided, one hundred marks were allotted for the six punctuation marks (full stop, comma, apostrophe, question mark, colon and semi-colon), sixty marks for the test.
The research questions were analyzed using the mean. Questions were analyzed item by item including the correct and wrong answers. This was by giving one mark for the correct answer and no mark given for the wrong answer.
For the questionnaire and test, the researcher tabulated the responses in tables of frequencies and percentages so as to be discussed by using SPSS program.

3.8 Summary of the Chapter
This chapter presents the methodology of the research. The chapter clearly indicates the way the researcher collected the data and the instruments employed for collecting data, which are the participants of the research (students/teachers), and the techniques followed in analyzing.

The next chapter discusses how the collected data is analyzed and interpreted.

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