  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.
