# Satellite-Aided Consensus Protocol for Scalable Blockchains
## 3 Patterns of Chain Evolution  
In this section, we show how such a satellite-aided blockchain extends and evolves. As shown in Figure 1(a), an honest winner \(w_{2}\), after being chosen by the oracle in round \(r_{2}\), would generate a valid block \(b_{2}\) on the top of the last block \(b_{1}\) and multicast it to the rest of the mining network. According to the oracle of \(r_{2}\), other miners can verify the identity of \(w_{2}\) and the validation of \(b_{2}\). Usually, the next winner \(w_{3}\) would propose a new block \(b_{3}\) on the top of \(b_{2}\). As such, the chain will grow and evolve.  
However, due to network delays or misbehaviors, exceptions may occur. As shown in Figure 1(b), it is possible that the chosen winner \(w_{2}\) misses the oracle due to the outage of satellite links, and thus does not generate any new block in round \(r_{2}\). As a result, the winner \(w_{3}\) of the next round will generate a block \(b_{3}\) on the top of \(b_{1}\) directly. While in Figure 1(c), \(w_{3}\) may not receive \(b_{2}\) in round \(r_{3}\) due to network delay. Since \(w_{3}\) has not been informed, it generates a new block \(b_{3}\) on the top of \(b_{1}\) directly. However,in this case, \(b_{2}\) exists at the same height, resulting in orphaned blocks. The future block extension will determine which block will be finally included in the main chain.  
In terms of misbehaviors, a winner \(w_{2}\) in Figure 2d may generate an invalid block, whereas, in Figure 2e, a miner \(w_{2}^{\prime}\) who has not been selected, may forge its identity and generate a block \(b_{2}^{\prime}\). In the above two cases, other miners can easily find that the block in Figure 2d is invalid and the block in Figure 2e is generated by an illegitimate winner by checking the block and oracle. Hence, these two \(b_{2}^{\prime}\) in Figure 2d,e will be ignored and excluded from the main chain. Furthermore, in Figure 2f, a malicious winner \(w_{2}\) may diverge the chain by publishing two or more valid blocks in one single round. As a rule of thumb, benign miners should discard all of them.  
Last but not least, the alternative history attack is likely to happen in a satellite-aided blockchain, and could bring disastrous effects to the blockchain systems. When an alternative history attack takes place, an adversary would create a fraudulent branch and secretly mine on it, as shown in Figure 2g. Until the adversarial branch is longer (or heavier) than the original benign one, the adversary will release it to alter a confirmed history. The probability of a successful alternative history attack, also known as the confirmation error probability [11], is thus used as a measure of chain security in this paper.  
In a nutshell, Figure 2a is the ideal pattern for blockchain extension, as one block is generated on the top of the chain in each round. Figure 2b,c are caused by the oracle multicast outage and block propagation delay and are thus inevitable in practice. Orphaned blocks may occur in these two cases and their combinations. The possible misbehaviors in Figure 2e,f can be effectively prevented by the proposed protocol. Essentially, the attack in Figure 2g poses an inherent risk of a distributed system, and hence the successful attack probability will be discussed in the following section to assess the resilience of the proposed protocol.