The notion that a quantum computer could derive a bitcoin private key from a public key in approximately nine minutes has sent shockwaves through the crypto community. To understand the significance of this claim, it's essential to grasp the basics of bitcoin transactions. When a user sends bitcoin, their wallet uses a private key to sign the transaction, which is then broadcast to the network.
The private and public keys are linked 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 could potentially reverse this math using an algorithm called Shor's. The recent paper by Google's Quantum AI team revealed that a quantum computer could be 'primed' in advance by pre-computing parts of the attack that don't depend on a specific public key. Once a public key appears in the mempool, the machine would only need about nine minutes to derive the private key, giving the attacker a roughly 41% chance of redirecting the funds before the original transaction confirms.
This 'mempool attack' is alarming but requires a quantum computer that doesn't yet exist. A more pressing concern is the 6.9 million bitcoin that already sit in wallets with exposed public keys, which could be cracked at leisure by a sufficiently powerful quantum computer. The bitcoin network would continue to function, but the ability to derive private keys from public keys would undermine the security model, making anyone with exposed keys vulnerable to theft.
The solution lies in post-quantum cryptography, which would replace the vulnerable math with algorithms that quantum computers can't crack.