The notion that a quantum computer could potentially 'crack' bitcoin in a matter of minutes has been making headlines, but what does this actually mean in practical terms? To understand the implications, it's essential to delve into the mechanics of bitcoin transactions. When a bitcoin transaction is initiated, the sender's wallet utilizes a private key to sign the transaction, which is then linked to a public key.
This public key is broadcast to the network and is temporarily stored in the mempool before being confirmed 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. While classical computers are unable to reverse this math in a feasible timeframe, a sufficiently powerful quantum computer could potentially do so using an algorithm known as Shor's.
The recent study by Google found that a quantum computer could be pre-programmed to accelerate the process, allowing it to derive a private key from a public key in approximately nine minutes once the public key appears in the mempool. This gives the attacker a roughly 41% chance of succeeding in redirecting the funds before the original transaction is confirmed. The concept can be likened to a thief developing a universal safe-cracking machine, which, although requiring hours to build, can crack any safe with just a few final adjustments that take around nine minutes.
This 'mempool attack' is alarming but requires a quantum computer that is not yet in existence. However, a more pressing concern is the estimated 6.9 million bitcoins that are already vulnerable due to exposed public keys.
This includes early bitcoin addresses and wallets that have reused addresses, making them susceptible to attack without the need for the nine-minute timeframe. The 2021 Taproot upgrade inadvertently increased the number of vulnerable wallets. While the bitcoin network would continue to function, the potential for private key derivation from public keys would undermine the ownership guarantees that make bitcoin valuable, posing a significant risk to users with exposed keys and potentially eroding institutional trust in the network's security model. The solution lies in adopting post-quantum cryptography, which would replace the vulnerable math with quantum-resistant algorithms, a migration that Ethereum has been working towards for eight years but has not yet begun for bitcoin.