The notion that a quantum computer can 'crack' bitcoin in nine minutes has garnered significant attention, but what does this actually mean in practical terms? To grasp the implications, it's essential to understand how bitcoin transactions work. When a bitcoin transaction is initiated, the sender's wallet uses a private key to sign the transaction, which is then paired with a public key. This public key is shared publicly and is temporarily stored in the mempool before being included in a block by a miner, a process that typically takes around 10 minutes.
The link between the private and public keys is established through a complex mathematical problem known as the elliptic curve discrete logarithm problem, which classical computers cannot solve efficiently. However, a sufficiently powerful quantum computer, utilizing an algorithm like Shor's, could potentially reverse this math problem.
The nine-minute timeframe comes into play when considering that a quantum computer could be pre-configured to solve parts of the attack that are not specific to any particular public key. Once a public key is visible in the mempool, the quantum computer would only need approximately nine minutes to derive the associated private key, potentially allowing an attacker to redirect funds before the original transaction is confirmed. This scenario is akin to a thief developing a universal safe-cracking machine that, once a new safe appears, requires only a few final adjustments to open it.
While this 'mempool attack' is alarming, it requires a quantum computer that does not yet exist, with estimates suggesting it would need fewer than 500,000 physical qubits, far beyond the capacity of today's largest quantum processors. A more pressing concern involves the approximately 6.9 million bitcoin that are already at risk due to permanently exposed public keys, including older bitcoin addresses and wallets that have reused addresses. These coins are vulnerable to being cracked by a sufficiently powerful quantum computer without any time constraints.
The 2021 Taproot upgrade inadvertently expanded the pool of vulnerable wallets by making public keys visible on-chain by default. The underlying bitcoin network would continue to function, as mining relies on a different algorithm that is not significantly sped up by quantum computers.
However, the ability to derive private keys from public keys would undermine the ownership guarantees that make bitcoin valuable, potentially leading to theft and a collapse of institutional trust in the network's security model. The solution to this issue lies in post-quantum cryptography, which involves replacing vulnerable math with algorithms that quantum computers cannot crack, a migration that Ethereum has been working towards for eight years, but bitcoin has yet to initiate.