A quantum computer could potentially derive a bitcoin private key from a public key in approximately nine minutes, according to Google's Quantum AI team. This timeline has raised concerns and sparked debate about the security of the bitcoin network. To understand the implications, it's essential to grasp how bitcoin transactions work. When a bitcoin transaction is sent, the wallet uses a private key to sign the transaction, while the public key is shared publicly.
The public key is linked to the private key through a complex mathematical problem known as the elliptic curve discrete logarithm problem, which classical computers cannot solve efficiently. However, a sufficiently powerful quantum computer using Shor's algorithm could potentially reverse this math. The nine-minute timeline comes into play when a quantum computer is 'primed' in advance by pre-computing parts of the attack that don't depend on a specific public key. Once a public key appears in the mempool, the quantum computer would only need about nine minutes to derive the private key, giving it a roughly 41% chance of redirecting funds before the original transaction is confirmed.
This 'mempool attack' is alarming but requires a quantum computer that does not yet exist. A more pressing concern is the 6.9 million bitcoin that are already vulnerable due to exposed public keys, either from early bitcoin addresses or wallets that have reused addresses.
These coins can be cracked by a sufficiently powerful quantum computer without any time pressure. The 2021 Taproot upgrade inadvertently expanded the pool of vulnerable wallets. While the bitcoin network would continue to function, the ability to derive private keys from public keys would undermine the ownership guarantees that make bitcoin valuable, putting anyone with exposed keys at risk of theft and eroding institutional trust in the network's security. The solution lies in post-quantum cryptography, which would replace the vulnerable math with algorithms that quantum computers cannot crack.