The notion that a quantum computer can derive a bitcoin private key from a public key in approximately nine minutes has sparked widespread concern. To grasp the practical implications, it's essential to understand how bitcoin transactions function. When a bitcoin transaction is initiated, the wallet uses a private key to sign the transaction, which is then linked to a public key. This public key is broadcast to the network and remains in a waiting area until a miner includes it in a block, a process that typically takes around 10 minutes.
The connection between the private and public keys is based on a complex mathematical problem known as the elliptic curve discrete logarithm problem, which classical computers are unable to reverse within a reasonable timeframe. However, a sufficiently powerful quantum computer could potentially solve this problem. The recent study found that a quantum computer can be pre-programmed to perform the parts of the attack that don't depend on a specific public key, allowing it to derive the private key in about nine minutes once the public key appears in the mempool.
This gives the attacker a roughly 41% chance of redirecting the funds before the original transaction is confirmed. A more pressing concern is the approximately 6.9 million bitcoin that are already vulnerable due to exposed public keys. These coins are at risk of being cracked by a powerful quantum computer without any time pressure.
The bitcoin network would continue to function, but the security guarantees that make it valuable would be compromised. To address this issue, the implementation of post-quantum cryptography is necessary, which would replace the vulnerable mathematical algorithms with ones that quantum computers cannot crack.