The claim that a quantum computer could derive a bitcoin private key from a public key in approximately 9 minutes has sent shockwaves through the crypto community. To understand the implications, it's essential to grasp how bitcoin transactions work. When a bitcoin transaction is made, the sender's wallet uses a private key to sign the transaction, which is then broadcast to the network. The private key is linked to a public key through a complex mathematical problem known as the elliptic curve discrete logarithm problem.
Classical computers are incapable of reversing this math in a reasonable timeframe, but a sufficiently powerful quantum computer could potentially do so using an algorithm called Shor's. The 9-minute timeframe 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 can finish the job and derive the private key in about 9 minutes, giving the attacker a roughly 41% chance of redirecting funds before the original transaction confirms. This mempool attack, although alarming, requires a quantum computer that doesn't yet exist.
A more pressing concern is the 6.9 million bitcoins that are already vulnerable due to exposed public keys. These coins are at risk of being cracked by a sufficiently powerful quantum computer without any time pressure. The bitcoin network would continue to function, but the ability to derive private keys from public keys would undermine the ownership guarantees that make bitcoin valuable, potentially leading to a collapse of institutional trust in the network's security model.
The solution lies in post-quantum cryptography, which would replace the vulnerable math with algorithms that quantum computers can't crack.