**7. Analysis**

To increase the level of security, PoW is based on the degree of difficulty. However, it remains weak against 51% attacks [27]. Regarding domination, when the difficulty is equal to *D*, there will be only one candidate (*N*1) who has the greatest computing power. We have already done a test and reduced the difficulty to 50% to obtain 10 candidates, so the probability that *N*1 wins is 10% instead of 100%, because no process controls the standard deviation of its solutions. Therefore, the dominance has been reduced.

As for the 51% attack, when dominance is reduced, the 51% attack will also be reduced. On the other hand, the pool can not work freely to find a single solution, it has to go through several rounds. After each round, the node must share the identifier of this round (*idround*) which is calculated from the solutions trounced in the previous round, from which the protocol implies to introduce this *idround* in the next proof of round (Equation (3)). These steps will slow down the operation of producing another longer chain (branch) for use in double-spending.

Speaking of the Sybil attack, it is in principle impracticable unless the attacker has more than 50% of the network's computing resources. Also, the consensus mechanism does not prevent an attacker from disrupting the network by creating a number of malicious nodes (false identities). The proposed protocol combines two techniques, multi-rounds and standard deviation. In comparison to the basic PoW, it is difficult for these two techniques and for a false identity to be the final winner. These false identities must create a chain longer than the chain known in the network. The first technique (multi-rounds) will slow down their work, the second (standard deviation) will decrease their chances.

#### **8. Conclusions and Future Work**

In this work, we have proposed an effective and applicable consensus algorithm, and shown that, in blockchain or in any setting where we need an agreement, it is adaptable. We have studied its validity according to the four known conditions of the agreement. We have shown the energy gain achieved by this protocol to reach a drop of 15.63% with five rounds and to reach a drop of 19.91% with ten rounds. We have set up several scenarios establishing in each one several tests, with the manipulation of three factors (number of rounds, number of processes and number of solutions in each round). We have studied separately the influence of each factor on the energy consumed, and also, the influence of introducing these factors in comparison to the basic PoW. We have seen the robustness of the algorithm against the most famous attacks (51% and Sybil attack). In the future, we intend to implement this algorithm in other sectors such as healthcare, for instance.

**Supplementary Materials:** Compute and Wait Proof o Work (CW-PoW) Video is available online at https://mmutube.mmu.ac.uk/media/POW\_Demonstration/1\_zrjr8fqq.

**Author Contributions:** Formal analysis, A.B.; Methodology, M.K., A.L. and R.E.; Software, M.H.; Supervision, A.A.; Validation, M.A. and B.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
