## 1 Introduction
In this paper, the three categories of ACDs are supported by N-version programming (NVP) [22] and virtual machine (VM) migration [23; 24; 26]. An adaptive cloud network for blockchain consisting of multiple ACD nodes is taken as the application scenario. Adversaries join the network as outsiders towards a specific target. According to the attacking purposes, such a specific target can be either the node with the most computing power or the node existing at a crucial location in the network. The ACD blockchain cloud is built in two-layer with VM migration in the upper layer and NVP in the lower layer. Then we propose a hierarchical model named SPM based on Stochastic Reward net (SRN) [27], Poisson process [28], Maringale theory [29] and Markov chain [28] accordingly. This three-layer model describes the different stages of an attack spreading through the network. In the first layer, an SRN-based model is built to capture details of a single-step attack with fine granularity, then initially evaluate the NVP approach. In the second layer, adding a description of the time factor, the Poisson process is adopted to quantify the defensive effectiveness of a single NVP node against repetitive attacks. The first two layers evaluate the security of an ACD node, i.e., a blockchain node, which lays a foundation for the following abstracted computations. Focused on VM migration, the third layer describes adversaries' movements along with the topology of blockchain and calculates the attack success rate and time. Furthermore, the simulations explore the relationship between resource consumption and security. The obtained results indicate the effectiveness of each ACD technology and the synergy effect of combining ACDs, which helps optimize configurations accordingly. It should be indicated that an earlier version of this paper has been published in [30]. So, in this paper, we extend our previous investigations as follows. 1. The research objective is extended from improved MTD networks to more complex ACD networks integrating multiple ACD techniques. 2. The first two layers of the early model are reconstructed to describe the defensive process adequately. The SRN is introduced for analyzing the security of each blockchain node and enhancing the extensibility of SPM. 3. We elaborate on the Markov chain and Martingale theory, then we obtain the relation between system failure rate and configuration and hence verify the result of each. To the best of our knowledge, the proposed SPM model is the first work that evaluates the security of a combination of ACDs that partially uses the Martingale theory. The main contributions of this paper are three folds:  
1. Hierarchical. The hierarchical structure of SPM improves the flexibility and scalability of modeling. The three layers of SPM can be used either combined altogether to obtain the security of the entire ACD network, or independently to evaluate the effectiveness of each ACD method. 2. Thorough. Multiple metrics are set to describe the effectiveness of ACDs, including each ACD node being compromised probability, the probability of the target being compromised, mean time to attack, and mean time to repair. This thorough assessment describes the effect of ACD technologies adopted at different network layers, improving the evaluation scope. 3. Integrated. Incorporating the synergy of multiple ACD mechanisms in the evaluation, we analyze the complete attacking process in an integrated ACD network. Further, we compare the effectiveness of various defensive strategies to optimize the configurations. The rest of this paper is organized as follows. Section 2 discusses some related works. We provide background information on ACD structures in Section 3. The three-layer security analysis model is explained in Section 4. The simulations and analysis are presented in Section 5. Finally, conclusions and future works are drawn in Section 6.