The notion that a quantum computer could crack a bitcoin private key in approximately nine minutes has sent shockwaves through the crypto community. To grasp the implications, it's essential to understand how bitcoin transactions work.
When a bitcoin transaction is initiated, the sender's wallet uses a private key to sign the transaction, which is then broadcast to the network and awaits confirmation by a miner. This process typically takes around 10 minutes. The private and public keys are linked 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, utilizing an algorithm like Shor's, could potentially reverse this math. The 'nine minutes' figure comes into play when considering that a quantum computer could be pre-programmed to solve parts of the problem 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, potentially allowing an attacker to redirect funds before the original transaction is confirmed.
This 'mempool attack' is alarming but requires a quantum computer that is not yet available. A more pressing concern is the approximately 6.9 million bitcoin that are already at risk due to exposed public keys.
These include early bitcoin addresses and wallets that have reused addresses, making them vulnerable to a potential quantum attack without the need for the nine-minute time constraint. The 2021 Taproot upgrade inadvertently increased the number of vulnerable wallets. While the bitcoin network would continue to function, the ability to derive private keys from public keys would undermine the security guarantees that make bitcoin valuable, potentially leading to widespread theft and a collapse of institutional trust. The solution lies in adopting post-quantum cryptography, which replaces vulnerable algorithms with quantum-resistant ones, a migration that Ethereum has been working towards for eight years but has not yet begun for bitcoin.