A “double spend” attack — one of the key technical challenges that bitcoin was cleverly designed to avoid through the use of proof-of-work — is also known as the Byzantine Generals Problem in computer science. In this attack, the attacker first submits a valid bitcoin transaction; suppose this first transaction is a large purchase of software (it must be something that the seller delivers instantly, so the attacker’s first transaction couldn’t be a large purchase of furniture from overstock.com, which famously takes bitcoin as a payment method, since it would take a minimum of hours to days before the furniture was delivered) from a company online in return for bitcoin.

​​Immediately after receiving the goods for the first purchase, the attacker then attempts to spend the very same bitcoins spent in the first transaction, but this time using them to make another purchase from a different seller (say, in return for the second seller sending the attacker some amount of fiat money or some other crypto-currency). The attacker then races to mine a bitcoin block containing the second transaction, but not the first transaction, which would invalidate the second transaction. Because the attacker by assumption has at least 51% of the network hash rate, they are more likely than not to mine the next block, though this is not guaranteed given the probabilistic nature of mining. If the attacker is then able to quickly mine more blocks and stick these to the end of the block chain, the attacker’s version of the blockchain will become the canonical one that all other miners and nodes defer to, since it is the longest valid chain.

​​That’s about all the attacker can do with a 51% attack; note that no one’s bitcoins that were safely stored in a secure wallet were stolen or destroyed; rather, a couple merchants got scammed — not the end of the world, and certainly not worth the costs the attacker would incur in implementing the attack!