The notion that a quantum computer could potentially 'crack' bitcoin in nine minutes has generated significant attention and apprehension. To comprehend the implications of this claim, it is essential to understand the underlying mechanics of bitcoin transactions.
When a bitcoin transaction is initiated, the sender's wallet utilizes a private key to sign the transaction, thereby verifying ownership of the coins. This private key is mathematically linked to a public key, which is broadcast to the network and temporarily stored in the mempool before being included in a block by a miner. The average time for confirmation is 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 practical timeframe.
However, a sufficiently powerful quantum computer could potentially solve this problem using Shor's algorithm. The recent study by Google's Quantum AI team discovered that a quantum computer could be pre-programmed to perform the parts of the attack that do not depend on a specific public key, allowing it to derive a private key from a public key in approximately nine minutes once the public key appears in the mempool. This timeframe is shorter than the average confirmation time for a bitcoin transaction, giving an attacker a roughly 41% chance of redirecting funds before the original transaction is confirmed.
This vulnerability is often referred to as the 'mempool attack.' Although this attack is alarming, it requires a quantum computer that does not yet exist. A more pressing concern is the approximately 6.9 million bitcoins that are already at risk due to exposed public keys. This includes older bitcoin addresses that use a format called pay-to-public-key, where the public key is visible on the blockchain by default, as well as any wallet that has reused an address.
These coins are vulnerable to attack by a sufficiently powerful quantum computer without any time pressure. The 2021 Taproot upgrade inadvertently expanded the pool of wallets that would be vulnerable to a future quantum attack.
While the bitcoin network would continue to function, the ability to derive private keys from public keys would compromise the ownership guarantees that underpin the value of bitcoin. The solution to this vulnerability lies in the implementation of post-quantum cryptography, which would replace the vulnerable mathematical algorithms with ones that are resistant to quantum computer attacks. Ethereum has been working towards this migration for eight years, while bitcoin has yet to initiate the process.