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the relation between the previous average block time and the difficulty level, where F is the factor used to recalculate the difficulty of the next two weeks. It represents the ratio of the expected average block time of the network TE to the actual recorded average block time TAvg. Based on how the difficulty adjustment works, Bitcoin pushes miners to invest in more powerful mining rigs, to be qualified for competing with other miners under the incriminating mining difficulty. Despite the operation cost, miners continue to spend more because of the expected remuneration when winning the mining race. This feature makes PoW based blockchain a power-hungry system that burns energy indefinitely as long as the network of miners is growing. of each step of the algorithm is given in the remaining of this section. Algorithm 1 Green-PoW Consensus Algorithm. 4 F = TE (1) TAvg D(i+1) = D(i) × F (2) 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: init: b=1;ρ=1{b:block number,b:ρ:round} runnerUp = false {I am a runner-up} loop if ρ == 1 then nonce =FindBlockNonce(b) if nonce then {nonce found} AppendNewBlock(b) AnnounceBlock(b) b=b+1 ρ = 2 {Enter power-save mode} else if ValidBlockReceived(b) then AppendNewBlock(b) b=b+1 ρ=2 ContinueFindBlockNonce(b) if nonce then runnerUp = true AnnounceRunnerUpBlock(b) else if RunnerUpBlockReceived(b) then 3.1.3 Chain forks Blockchain may witness inconsistencies that cause branch- ing in the chain, this phenomenon is called forks, where more than one valid block is broadcasted to the network si- multaneously [19]. Consequently, nodes get confused when updating the chain and each will end up adopting different blocks as the chain head. Network propagation delays are mostly the reason for fork occurrence, which has been vali- dated empirically in [19], [20]. Other factors also play a role in causing forks such as the time needed to generate a block, network bandwidth, and the number of connections each node establishes with the network. Blockchain nodes resolve a fork in the next block period by adopting the longest chain, which is identified by calculating the cumulative number of expected hashes performed to generate each block in the chain. The frequent occurrence of forks allows adversaries to conduct various attacks (discussed further in section 5) that could degrade the security of the blockchain network. 4 ENERGY-EFFICIENT CONSENSUS ALGORITHM Green-PoW is an energy-efficient consensus algorithm that reduces the computation load to nearly 50% compared to the original Bitcoin’s PoW algorithm, without affecting the other properties of the system. The algorithm divides time into epochs, where each epoch consists of two consecutive mining rounds. Let τi denote the epoch of time correspond- ingtothecreationofblocksnumber2iand2i+1,andρ1i and ρ2i denote the first and second mining round, respectively, within the epoch τi. During ρ1i , the mining process to create a new block follows the same Bitcoin mining steps, where the set of all miners, which is denoted as M, can participate. In addition, a very small subset of miners, denoted as M2i , is elected during this same mining round to be the only eli- gible participants for mining the next block in ρ2i . Note that M1i , which refers to the set of miners that can participate in ρ1i , is equal to M and both are used interchangeably. All the other miners M\M2i , during ρ2i , pause until the considered block gets appended before starting a new mining epoch (τi+1). An illustrative example of the mining process during one epoch of time is given in Fig. 2. The detailed description AbortMining(b) mode} end if end if end if {Enter power-save end if else {second round: ρ = 2} runnerUp then nonce =FindBlockNonce(b) if nonce then AppendNewBlock(b) AnnounceBlock(b) else if ValidBlockReceived(b) then AppendNewBlock(b) AbortMining(b) end if end if b=b+1 ρ=1 runnerUp = false else {not a runner-up} if ValidBlockReceived(b) then AppendNewBlock(b) b=b+1 ρ = 1 {Exit power-save mode} end if end if end if endloop ifPDF Image | Efficient Blockchain Proof-of-Work Consensus Algorithm
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