How Does a Double-Spend Attack Leverage a 51 Percent Network Control?

In a double-spend attack, the attacker first makes a legitimate transaction, such as sending coins to an exchange, and receives goods or services. Simultaneously, they use their 51 percent control to secretly mine a private version of the blockchain where the original transaction is reversed or never included.

Once the attacker's private chain is longer than the public chain, they broadcast it, forcing the network to accept the new history. This effectively allows the attacker to spend the same coins twice: once on the public chain and once on the private chain.