Decentralized cryptocurrency systems, known as blockchains, have shown promise as infrastructure for mutually distrustful parties to agree on transactions safely. However, Bitcoin-derived blockchains and their variants suffer from the limitations of the CAP Trilemma, which is difficult to be solved through optimizing consensus protocols. Moreover, the P2P network of blockchains have problems in efficiency and reliability without considering the matching of physical and logical topologies. For the CAP Trilemma in consortium blockchains, we propose a physical topology based on the multi-dimensional hypercube with excellent partition tolerance in probability. On the other hand, the general hypercube has advantages in solving the mismatch problems in P2P networks. The general topology is further extended to a hierarchical recursive topology with more medium links or short links to balance the reliability requirements and the costs of physical network. We prove that the hypercube topology has better partition tolerance than the regular rooted tree topology and the ring lattice topology, and effectively fits the upper-layer protocols. As a result, blockchains constructed by the proposed topology can reach the CAP guarantee bound through adopting the proper transmission and the consensus protocols protocols that have strong consistency and availability.
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