Cryptocurrencies including Bitcoin are known to be vulnerable to so-called ‘double-spending’ attacks, where the same digital currency is used to execute multiple different transactions simultaneously. Little is known, however, about the underlying reasons for this vulnerability. Here we develop an agent-based model to study how features of cryptocurrency networks contribute to their vulnerability to double-spending attacks. Perhaps surprisingly, we find neither the number of network nodes nor its path length seem to influence the probability of successful attacks. We find robust evidence that the network's clustering coefficient has substantial influence. In particular, scale-free networks, with their small clustering coefficients, are more than twice as likely to succumb to double-spending attacks than are networks with larger coefficients, such as regular networks. The implication is that cryptocurrency networks, which are scale-free, may be uniquely susceptible to double-spending attacks.

众所周知，包括比特币在内的加密货币容易受到所谓的“双花”攻击，即使用同一种数字货币同时执行多项不同的交易。然而，关于此漏洞的根本原因知之甚少。在这里，我们开发了一个基于代理的模型来研究加密货币网络的特征如何导致其易受双花攻击。也许令人惊讶的是，我们发现网络节点的数量及其路径长度似乎都不会影响成功攻击的概率。我们发现有力的证据表明网络的聚类系数具有重大影响。特别是，具有较小聚类系数的无标度网络比具有较大系数的网络屈服于双花攻击的可能性高出两倍以上，比如常规网络。这意味着无标度的加密货币网络可能特别容易受到双花攻击。