We consider the execution of smart contracts on Bitcoin. There, every contract step corresponds to appending to the blockchain a new transaction that spends the output representing the old contract state, creating a new one for the updated state. This standard procedure requires the contract participants to pay transaction fees for every execution step. In this paper, we introduce a protocol that moves most of the execution of a Bitcoin contract off-chain. When all participants follow this protocol, they are able to save on transaction fees, drastically reducing them. By contrast, whenever adversaries try to disrupt the off-chain execution, any honest participant is still able to enforce the correct contract behaviour, by continuing its execution on-chain.

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