The concept of a quantum computer 'cracking' bitcoin in a matter of minutes has been making headlines, but what does it truly imply? To grasp this, it's essential to understand how bitcoin transactions function. When a bitcoin transaction is made, the sender's wallet uses a private key to sign the transaction, which is then linked to a public key.
This public key is shared with the network and is temporarily stored in the mempool before being added to a block by a miner, 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 cannot solve efficiently. However, a sufficiently powerful quantum computer could potentially solve this problem using Shor's algorithm.
The recent study found that a quantum computer could be pre-programmed to simplify the attack, requiring only about nine minutes to derive a private key once the corresponding public key appears in the mempool. This timeframe gives an attacker a roughly 41% chance of stealing funds before the original transaction is confirmed. It's worth noting that such a powerful quantum computer does not yet exist, with estimates suggesting it would require fewer than 500,000 physical qubits, far beyond the capabilities of current quantum processors.
A more pressing concern is the approximately 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 quantum computer without the need for the nine-minute race, as the public keys are already visible. The 2021 Taproot upgrade inadvertently expanded the pool of vulnerable wallets. While the bitcoin network itself would continue to function, as mining uses a different algorithm, the ability to derive private keys from public keys would undermine the security guarantees that make bitcoin valuable, potentially leading to a collapse of institutional trust.
The solution to this issue lies in post-quantum cryptography, which would replace the vulnerable mathematical algorithms with ones that are resistant to quantum computer attacks.