Abstract: Double-spending attacks are also called “double-spending” attacks, which use the digital characteristics of Bitcoin to complete two or more payments with “the same money”. Firstly, the types of double expenditures?are summarized, and the existing double spending models are compared, and their advantages and disadvantages are analyzed. Then a pre-excavation double spending model is constructed, ?and it has a block advantage when it comes to double spending attacks?because of having considered?that the nodes have been excavated for a period of time before the attack. The applicable conditions of the model are set and the model?is solved. Based on the experimental data, the correctness of the constructed model is verified by comparison with the existing model. Finally, based on the research on the double spending in the blockchain, two methods for resisting the double spending attack in the blockchain are given, which provides a certain reference value for the blockchain-based virtual currency to resist the double spending attack.

Key words: double spending attack, Bitcoin, blockchain, pre-excavation double spending model

摘要： 双重花费攻击又被称为“双花”攻击，即利用比特币的数字特性用“同一笔钱”完成两次或者多次支付。首先总结了双重花费的类型，并对现有的双重花费模型进行对比，分析其具有的优缺点，然后构造了一个预挖掘双重花费模型，考虑节点在进行攻击之前就已经挖掘了一段时间，从而在进行双重花费攻击时具有块数优势。对模型的适用条件进行设置，并对模型进行求解。基于实验得到的数据，与现有模型进行对比验证所构造模型的正确性。最后基于对区块链中双重花费的研究，给出了两个抵御区块链中双重花费攻击的方法，为基于区块链的虚拟货币抵御双重花费攻击提供了一定的参考价值。

关键词: 双重花费攻击, 比特币, 区块链, 预挖掘双重花费模型