With the rapid evolution of the blockchain technologies, the interoperability of different blockchain systems is emerging as one of the essential features of blockchains. Sidechains, a mechanism providing communications between different blockchains, have been heralded as the crucial factor of blockchain interoperability. However, there are still issues that need to be addressed in terms of security and feasibility. In this article, for proof-of-stake (PoS) and proof-of-work (PoW) blockchains, we propose efficient sidechain constructions with fast cross-chain transfers and small proof size by novel cross-chain certificate generation process and committee selection methods. Moreover, we also provide an extra functionality of supporting instant cross-chain transfers, such that emergent cross-chain transactions can be processed immediately. Compared to prior sidechains, our PoS sidechain construction can achieve faster cross-chain transfers, which improves the promptness of cross-chain transfers. While our PoW sidechain construction is more efficient with smaller proof size, reducing the storage and bandwidth overhead. Furthermore, we formally prove our sidechain constructions satisfying the properties of atomicity and timeliness. Finally, we develop a proof-of-concept implementation of our sidechains, and the experimental results show our constructions is not only faster, but also efficient with low storage and bandwidth overhead.
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