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6 Append Block Continue Mining mining- save mode Accept Block Mining start new Block Update M2 List End 1st Round Append Block Is in M2 List? • A malicious node that is not eligible to participate in ρ2i , may try to start the mining before the time- out in order to get an advantage (receive a reward) over other non-participating nodes. However, this is very risky for the attacker as the success of such manipulation depends on the probability that no block will be received from eligible nodes (M2i ); in such a case the attacker could be wasting a lot of energy if it does not win. • Due to network asynchronicity, it is possible that some nodes will receive a valid block from an honest ineligible participant while their time-out is not yet ended. In this situation, these nodes will initially reject the block, but because the majority will accept it, the block will appear in the longest chain and the minority will end up accepting it. It is worth noting that both the time-out and η help in defining a good balance between system liveness and energy-efficiency. Growing η improves system liveness by increasing |M2i |, yet it diminishes energy-efficiency as more miners will participate in ρ2i . By using the time-out, Green- PoW can ensure liveness, but it may also increase the energy consumption if |M2i | is very small, i.e., η is very short, as timing-out ρ2i is likely to happen frequently. Therefore, a careful selection of η is crucial for Green-PoW to ensure the desired energy-efficiency. More hints about the typical choice of the time-out and η parameters are given in Section 6. 4.3 Second Round Mining Difficulty d Announce block Mining next Block First round (ρ1) Fig. 3: The state diagram of a miner in Green-PoW. Second round (ρ2) As presented in Section 3.1.2, given that the total mining power of the network can change over time, the mining difficulty is dynamically adjusted to ensure that blocks are generated at a nearly constant rate. In Green-PoW, because the total hash power decreases drastically in each second round mining, compared to the first round, a new difficulty level defined specifically for the second round is required. Let D1 and D2 denote the difficulty level to consider during ρ1 and ρ2, respectively. A block is considered as valid only if its hash value respects the target hash (e.g., in the block header), which is calculated based on the difficulty level of the corresponding mining round. The difficulty level is initially set to the minimum value and updated every T period of time (every 2 weeks in Bitcoin). Using equation (1) and (2) presented in Section 3.1.2, the new difficulties Dj1 and Dj2 for the jth Tj period can be calculated as follow: D1=D1 TE (3) j j−1 TAvg1 D2=D2 TE (4) j j−1 TAvg2 Where TE is the expected average block time (10 minutes in Bitcoin), and TAvg1 and TAvg2 are the actual average block-time calculated over the last Tj, for blocks generated in ρ1 and ρ2, respectively. Note that because it may happen that some blocks in the second round are generated with the participation of all network miners, in case of timing out, these blocks will be considered for the adjustment of A b u o k o r 2nd ( . t v i c e m r n n d k c i c o l n b l e i c B A n n v u g n o n n o n A n n o e b g o n c i k m r o A d n b u o f t e c o N n u o f e . c v n c s e B o r e l k d c o u Y o N l c B k r r e c v . ) o N N o l n c c e f o u n . c e r B l o c kPDF Image | Efficient Blockchain Proof-of-Work Consensus Algorithm
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