Decentralized cryptocurrency systems, known as blockchains, have shown promise as an infrastructure for mutually distrustful parties to securely agree on transactions. Nevertheless, blockchain systems are constrained by the CAP Trilemma. Due to performance degradation, it is impossible to address this issue by improving simply the consensus layer or the network layer. To alleviate the CAP constraint in consortium blockchains, we propose a topological construction method to optimize the physical layer based on multi-dimensional hypercubes with excellent partition tolerance in probability. The basic topology has the advantage of solving the mismatch problem between the overlay network and the underlying network. It is further extended to hierarchical recursive topologies with more intermediate links or short links to balance the reliability requirement with the cost of building the physical network. We prove that the proposed hypercube topology has better partition tolerance than the regular rooted tree and ring lattice topologies, and effectively fits the upper-layer protocols at the consensus and network layers. As a result, combined with suitable transmission and consensus protocols that satisfy strong consistency and availability, the proposed topology-constructed blockchain can reach the CAP guarantee bound.
