**4. Proposed Protocol**

There are three types of blockchain, private, public and hybrid. A private blockchain (permissioned) operates in a restrictive environment, i.e., a closed network. In an authorized blockchain that is under the control of an entity, only authorized nodes with a revealed identity are allowed to enable basic functionalities such as consensus participation or data propagation [25]. Comparatively, in a public blockchain (permission-less/open access), if the node has a valid pseudonym (account address), it can freely join the network and activate any available network functionalities such as sending, receiving and validating transactions and blocks according to common rules. Therefore, there is usually such a blockchain network instance on a global scale that is subject to public governance. Specifically, anyone can participate in the blockchain consensus, although a person's voting power is generally proportional to its possession of network resources, such as computing power, wealth token and storage space [26]. A hybrid blockchain (consortium or federated)

is a creative approach to solving the needs of organizations which have a need for public and private blockchain functionality. Some aspects of organizations are made public, while others remain private. The consensus algorithms in a consortium blockchain are controlled by the predefined nodes. It is not open to the popular masses, it still has a decentralized character and there is not a single centralized force that controls it. Therefore, it offers all the functionalities of a private blockchain, including transparency, confidentiality, and efficiency, without a single party having to consolidate power. In this paper, we are concerned with the second type only, which is the public blockchain.

As shown in Figure 1, we divided the overall operation to reach consensus into several rounds (Supplementary Materials). At the start, a node launches the first round and looks for a solution for its own block, like the basic PoW algorithm, but with a much lower degree of difficulty than what is currently applied. Where the difficulty was *X* and the number of rounds was 1, in the proposed algorithm, the difficulty is *X* < *X* and the number of rounds is *Y* > 1. Once the solution is found, the node shares it and checks whether there are nine (9) other solutions found in the network for this round (for example, in a scenario of 10 solutions to find). If so, this node has the right to participate in the next round and to restart the PoW. If not, i.e., there are not ye<sup>t</sup> nine (9) solutions found by other nodes, this candidate node will wait until it receives the remaining nine (9) solutions. In the last round, the first node that will find the solution will be the miner, so that in the last round the protocol looks for a single solution. In the original PoW, the proof consists of finding the nonce according to the inequality: *Hash*(*Block* + *Nonce*) < *Target*. In the proposed protocol, the proof of round *i* is according to the following inequality:

$$IRash(Block + IDRound\_{i-1} + Nonce) $$

Initially, the identifier (ID) Round is equal to 1. After that, the *ID Round* is equal to the sum of nonces found in the previous round. Therefore, in each round, there is a new ID so that the nodes will work on it. If we have ten solutions to find in each round, we will obtain the following equation:

$$IDRound\_k = \sum\_{i=1}^{10} (none\_i \ of \ round\_{k-1}) \tag{3}$$

**Figure 1.** A Compute and Wait Consensus PoW Algorithm.

Let NbrR be the number of rounds and NbrS the number of solutions to find in each round. If two nodes succeed in finding the solution in the last round, then the other nodes will receive two solutions. In this case, the nodes must calculate the standard deviation of the solutions found in all the rounds for each of these two winners. The miner is the node with the smallest standard deviation. There is another parameter that we can introduce here, which is the consensus state. For the moment, in which round do the processes work? Assuming that a process decides to leave competition if the other processes exceed it by 5 rounds (or 4, for example), this will minimize the energy to be consumed. For a process, if the other competitors overtake him by two rounds, there is little hope of catching them. This process will lose energy unnecessarily if it continues the calculation.
