The notion that a quantum computer could derive a bitcoin private key from a public key in roughly nine minutes, as suggested by Google's Quantum AI team, has sent shockwaves through the crypto community. To understand the implications, it's essential to grasp how bitcoin transactions work.
When a bitcoin transaction is initiated, the wallet signs it with a private key, a unique secret number that verifies ownership of the coins. This signature also reveals the public key, a shareable address that is broadcast to the network and waits in the mempool until a miner includes it in a block, a process that typically takes around 10 minutes.
The link 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 in a practical timeframe but a sufficiently powerful quantum computer potentially could. The 'nine minutes' figure comes into play because a quantum computer could be pre-programmed to solve parts of the problem that don't depend on a specific public key. Once a public key appears in the mempool, the quantum computer would only need about nine minutes to derive the private key, giving it a roughly 41% chance of succeeding before the original transaction is confirmed.
This scenario is akin to a thief building a universal safe-cracking machine that, once a new safe appears, only needs a few minutes to crack it. However, this 'mempool attack' is theoretical and requires a quantum computer that does not yet exist, with estimates suggesting it would need fewer than 500,000 physical qubits, far beyond today's largest quantum processors. A more immediate concern is the approximately 6.9 million bitcoin, about one-third of the total supply, that are already vulnerable due to exposed public keys. These include early bitcoin addresses and wallets that have reused addresses, making them potentially accessible to an attacker with a powerful enough quantum computer without any time pressure.
The 2021 Taproot upgrade inadvertently expanded the pool of vulnerable wallets by making public keys visible on-chain by default. While the bitcoin network would continue to function, as mining uses a different algorithm that quantum computers cannot significantly speed up, the ability to derive private keys from public keys would undermine the ownership guarantees that give bitcoin its value.
The solution lies in post-quantum cryptography, which replaces vulnerable math with quantum-resistant algorithms, a migration Ethereum has been working towards for eight years but bitcoin has yet to initiate.