The concept of a quantum computer deriving a bitcoin private key from a public key in approximately nine minutes has garnered significant attention. 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 uses a private key to sign the transaction, while also revealing the associated public key.
This public key is then broadcast to the bitcoin network, where it awaits confirmation by a miner. On average, this confirmation process 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 are unable to reverse within a practical timeframe. However, a sufficiently powerful quantum computer could potentially exploit this using an algorithm like Shor's. The notion of a nine-minute timeframe comes into play when considering that a quantum computer could be pre-programmed to perform the parts of the attack that don't depend on a specific public key. Once a public key is visible in the mempool, the quantum computer would only need about nine minutes to derive the private key, potentially allowing an attacker to redirect the funds before the original transaction is confirmed.
This scenario is often likened to a thief who has developed a universal safe-cracking machine that requires only minor adjustments to crack any safe, with these adjustments taking around nine minutes. While this 'mempool attack' is alarming, it requires a quantum computer that does not yet exist. A more pressing concern involves the approximately 6.9 million bitcoin that are already in wallets with permanently exposed public keys. These include older bitcoin addresses that used a pay-to-public-key format and wallets that have reused addresses, thereby revealing the public key for all remaining funds.
In these cases, an attacker with a sufficiently powerful quantum computer could derive the private keys at their leisure, without any time constraints. The 2021 Taproot upgrade inadvertently increased the vulnerability by making public keys visible on the blockchain by default. Although the bitcoin network would continue to function, as the mining algorithm is not susceptible to significant speedup by quantum computers, the ability to derive private keys from public keys would undermine the security model that makes bitcoin valuable. The solution lies in adopting post-quantum cryptography, which would replace the vulnerable mathematical algorithms with ones that are resistant to quantum computer attacks.
While Ethereum has been working towards this migration for eight years, bitcoin has yet to initiate this process.