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10 Inter-mining time Time-out interval 45 35 25 15 50 40 30 20 10 0 Fig. 9: Time to wait for a block to be mined in the second round Vs. the corresponding probability. instance, for a block to be mined with a probability between [0.7, 0.9] a network needs to wait for a time between [12, 23] minutes. Therefore, a typical time-out can be chosen from this interval. Note that having different hash power distribution will not affect the block generation time, as the defined difficulty Di2 in equation (4) ensures that a block is mined at a constant rate on the average (10 minutes in Bitcoin). 7 CONCLUSION In this paper, we have proposed a novel and energy- efficient consensus algorithm, called Green-PoW, for a pub- lic blockchain. In our algorithm, the overall energy con- sumption during mining is reduced by up to 50% compared to the original PoW. Green-PoW achieves its goal by taking advantage of the energy spent during one block mining to also elect a small number of miners that will exclusively mine the next block. In Green-PoW, time is divided into epochs that consist of two mining rounds. The first round is similar to mining in the original PoW with the exception that a small additional power is spent in order to qualify a subset of miners to exclusively contend in the second round. In the second round, where most of the mining power is saved, only the elected miners during the previous round have the right to participate and compete for forming a new block. To validate the performance of Green-PoW, extensive simulations have been conducted to mainly assess the energy saving compared to the original PoW. The results demonstrated the efficiency of the solution where up to 50% of the mining energy can be saved for a large network with equally distributed hashing power. We also have studied key security properties and shown the advantage of Green- PoW in reducing fork occurrences, the effect of censorship attack, and mining centralization. REFERENCES [1] S. Nakamoto, “Bitcoin: A peer-to-peer electronic cash system,” Tech. Rep., 2008. 2% 5% 10% 20% 50% Hash-power distribution Fig. 7: Energy saving ratio Vs. hash-power distribution 7 6 5 4 3 2 0.5 35 10 15 20 # second round miners Fig. 8: Average time (η) between the first and last considered runner-up to be include in Mi2. round, i.e., a function of |M2i |. To capture the effect of η, we plot in Fig. 8 the time needed in order to have a specific size of M2i . We consider the same simulation parameters as before, and we plot the time between the first and last considered runner-up, when having, 3, 5, 10 15, and 20 miners in the second round. We also consider different distributions of the hashing power in the network. In the case of uniformly distributed hash power among miners, the value of η does not increase much with the number of second round miners; however, when the distribution is not uniform, specifically, when 50% of the power is held by only 5% of the miners, η increases significantly. This is because more time is needed to wait for less-powerful nodes to mine a block and be able to join other miners in ρ2i . We also plot in Fig. 9 the required time for a block to be mined in the second round. As discussed previously, the inter block generation (mining) time follows Exponential distribution with the same rate parameter λ (1/600 in Bit- coin). Using equation (13) we plot the mining time between two consecutive blocks (time between the first round block and second round block) for different probability. A safe time-out can be chosen as the duration of time ensuring that a block will be mined with a high probability. For 0.6 0.8 0.99 0 0.2 0.4 block mining probability Uniform hash-power dist. Non-uniform hash-power dist. η (min.) Energy saving (%) Waiting time for block to be mined (min.)PDF Image | Efficient Blockchain Proof-of-Work Consensus Algorithm
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