**4. Experimental Results**

During the implementation phase, we set the simulation in such a way that the hash output is uniformly distributed between miners and stakes. The difficulty was adjusted to α = 0.01, the stacker power was set to S = [80, 40, 20, 15, 10, 5, 5, 5, 5, 5] and the miner power was set to M = [32, 16, 8, 6, 4, 2, 2, 2, 2, 2, 2]. Numbers have already been set to show the linearity of the exponential rise in computational power. To begin with, the block time was set to 20 s in *t*, with a duration of 90 days per entire chain.

During the simulation, a total of 385,479 blocks were generated, out of which 192,688 were stake blocks and 192,791 were mining blocks. As shown in Figure 6, the rewards were proportional to computing power (stake/mining), which was considered a fair outcome.The target block time was 20 s, resulting in a stake block time of 40 s and a mining block time of 40 s with an average rate of P*s*∈*S s/ds*, P *m*∈*M m/dm* and P*s*∈*S s/ds* + P *m*∈*M m/dm.*

**Figure 6.** Experimental results of (**a**) stake power vs. block rewards distribution and (**b**) hash power vs. block rewards distribution.

During the experiment, which we ran on the Google Colab platform, we determined that the initial simulation would consume not more than 200 MB of RAM, as shown in Table 4.

**Table 4.** Machine computational power.


Figure 6a,b illustrate the stake and hash power results over the block rewards distribution. The mean and standard deviation of time are presented in Table 5.

**Table 5.** Mean and standard deviation of time.


According to the simulation results, the attacker side that dominates the network with more than 51% computation power cannot easily launch the attack because the fork mechanism has a split rule between PoW and PoS implementations. Hence, to take over this network and launch an attack, the attacker needs to command over 100% of the system, which is impossible on a consensus blockchain node. Figure 7 shows that the chain power is demonstrated over the block time generation and distribution, and Figure 8 shows the proposed hybrid model computational power over PoW and PoS block time distributions.

We began the simulation experiment and based on previous data, we set the computational power for mining to 76, which is the same block size. The results are shown in Table 6.

Additionally, we discovered that the combined PoW and PoS protocol limits the effective computational power to 52.31. The results of the miner computational power needed for the hybrid mechanism are presented in Table 7.

**Figure 7.** Power vs. block time distribution.

**Figure 8.** Experimental results of (**a**) computational power vs. PoS block time distribution and (**b**) computational power vs. PoW block time distribution.


**Table 6.** Miners' computational power before implementing the proposed hybrid mechanism.

**Table 7.** Miners' computational power with the proposed hybrid mechanism (PoW and PoS).


Mining power and actively minting coins may also be used to calculate the attack's cost. They may be used as a rough estimate of the cost of mining power because they are closely related to miner earnings (fees and coin base incentives). The active stake can be determined because the amount of Satoshi released every second is inversely proportional to the stake difficulty. By dividing the amount of Satoshi issued into equal parts for each PoS block, we can estimate the total amount of Satoshi currently being mined. To compute the income per block required to sustain the attack cost, these measures may be used to determine an attack–cost objective (e.g., a particular number of Bitcoins or a certain percentage of the total number of Bitcoins mined to date). In turn, this information can be used to dynamically alter the block size and ensure that the block income continues to support the set attack cost goal. Therefore, mining earnings will be increasingly predictable, a certain degree of security will be maintained, and costs will be reduced.

The majority of honest minters make the mistake of making coins on a chain that they believe will last the longest, only to have their efforts thwarted by a competitor's longer chain. This situation means that several law-abiding minters are penalised for minting. If the fine does not exceed the revenue from minting one block, the expected revenue from the effort to mint should exceed zero. A small fee is likely to have a substantial impact, so the projected revenue from minting should be equal to the overall revenue from minting. Ultimately, this depends on whether dishonest minting on a short chain benefits the dishonest minter. Therefore, how much of a penalty should be imposed is debatable.

Given that PoS blocks have little influence on whether an attacker will be successful in performing an orphan-based mining monopoly attack unless the attacker controls a substantial portion of the coins actively being mined, punishing minters who minted over another PoS block would double the collateral damage. Consequently, minter punishment proofs will be invalid if the most recent PoW block is shared by the minted block and the current block. Further research is needed to determine how much stake an attacker needs to possess in order to perform a mining monopoly attack effectively.

If a PoW block has more than one option (e.g., a collision leaving one orphaned), minters may refuse to mint so as to avoid the penalty. If they do so, they will miss out on the most probable benefit of their actions (which would be much greater). Therefore, the likelihood of this behaviour occurring is very low because the predicted benefits exceed 0 by a factor of two.
