Recently, blockchain has been applied in various fields to secure data exchanges and storage in decentralized systems. In a blockchain application where the task of the application which makes use of the data stored in a blockchain has to be accomplished by a time instant, the employed blockchain is essentially finitely-long. In this paper, we consider a general finitely-long blockchain model which is generalized from most existing works on finitely-long blockchain applications, and take the first step towards characterizing the vulnerability of finitely-long blockchains in securing data against double-spending attacks. For the first time, we develop a general closed-form expression for the probability of success in launching a double-spending attack on a finitely-long blockchain. This probability essentially characterizes the vulnerability of finitely-long blockchains. Then, we prove that the probability of success in launching a double-spending attack on a finitely-long blockchain is no greater than that on an infinitely-long blockchain, which implies that finitely-long blockchains are less vulnerable to double-spending attacks than infinitely-long blockchains. Moreover, we show that unlike infinitely-long blockchains which can be surely paralyzed by a 51% attack, finitely-long blockchains are more resistant to 51% attacks.

翻译：近年来，区块链已被广泛应用于去中心化系统中以保障数据交换与存储的安全性。在需要借助区块链存储数据完成特定任务的区块链应用中，由于任务必须在某个时刻前完成，所采用的区块链本质上是有限长度的。本文考虑了一种从现有大多数有限长区块链应用中泛化而来的通用有限长区块链模型，并首次系统刻画了有限长区块链在抵御双重支付攻击时保障数据安全的脆弱性。我们首次推导出了有限长区块链遭受双重支付攻击成功概率的通用闭式表达式——该概率本质上表征了有限长区块链的脆弱性。进而证明，有限长区块链上双重支付攻击的成功概率不高于无限长区块链，这意味着有限长区块链相比无限长区块链对双重支付攻击更具鲁棒性。此外，我们还发现，不同于无限长区块链可能被51%攻击彻底瘫痪，有限长区块链对这类攻击具有更强的抵抗力。