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The rise of smart contract systems such as Ethereum has resulted in a proliferation of blockchain-based decentralized applications including applications that store and manage a wide range of data. Current smart contracts are designed to be executed solely by miners and are revealed entirely on-chain, resulting in reduced scalability and privacy. In this paper, we discuss that scalability and privacy of smart contracts can be enhanced by splitting a given contract into an off-chain contract and an on-chain contract. Specifically, functions of the contract that involve high-cost computation or sensitive information can be split and included as the off-chain contract, that is signed and executed by only the interested participants. The proposed approach allows the participants to reach unanimous agreement off-chain when all of them are honest, allowing computing resources of miners to be saved and content of the off-chain contract to be hidden from the public. In case of a dispute caused by any dishonest participants, a signed copy of the off-chain contract can be revealed so that a verified instance can be created to make miners enforce the true execution result. Thus, honest participants have the ability to redress and penalize any fraudulent or dishonest behavior, which incentivizes all participants to honestly follow the agreed off-chain contract. We discuss techniques for splitting a contract into a pair of on/off-chain contracts and propose a mechanism to address the challenges of handling dishonest participants in the system. Our implementation and evaluation of the proposed approach using an example smart contract demonstrate the effectiveness of the proposed approach in Ethereum.