The first part of this series introduced quantum computers as fundamentally different from traditional machines, leveraging unique physical laws at atomic scales. However, understanding their operation is just the beginning; comprehending how they could potentially be used by malicious actors to steal bitcoin involves a deeper dive into bitcoin’s security mechanisms and vulnerabilities.
Bitcoin relies on elliptic curve cryptography for encryption, involving two keys: a private key (a secret 256-digit binary number) and a public key derived from it through mathematical operations on the ‘secp256k1’ curve. The relationship is expressed as K = k × G, where k is the private key, and K is the public key. This operation involves adding points along the curve rather than traditional multiplication.
The system’s security hinges on a one-way process: deriving K from k is straightforward, while reversing it to find k from K is theoretically impossible for classical computers, taking longer than the universe’s age according to current algorithms. Bitcoin transactions use private keys to generate digital signatures without revealing them.
In 1994, mathematician Peter Shor introduced an algorithm capable of breaking this security model by efficiently solving the discrete logarithm problem, turning a task that would take eons for classical computers into one manageable in polynomial time using quantum mechanics principles. The algorithm transforms the problem into finding the period of a function on an elliptic curve through superposition, entanglement, and interference.
Shor’s algorithm has been known for over three decades but remained theoretical due to hardware limitations. Google’s recent paper from its Quantum AI division, co-authored by Ethereum Foundation researcher Justin Drake and Stanford cryptographer Dan Boneh, suggests that fewer than 500,000 qubits might suffice, a significant reduction from earlier estimates.
The team designed circuits with approximately 1,200 to 1,450 logical qubits and millions of Toffoli gates. These gates operate on three qubits: two control and one target, where specific conditions must be met for the target to change states. Qubit instability necessitates redundancy, leading to a high ratio of physical to logical qubits.
Google’s research not only decreases required qubit counts but also redefines threat assessment by precomputing parts of Shor’s algorithm based on bitcoin’s fixed parameters. This allows quantum computers to be primed for specific public keys once they appear in transactions, completing the task within about nine minutes—a timeframe that overlaps with bitcoin’s average block confirmation period.
This creates a ‘mempool attack’ scenario where attackers have a 41% chance of intercepting funds before original transaction confirmations. While this is concerning, the larger threat lies with the approximately 6.9 million bitcoins already exposed on the blockchain, vulnerable to an ‘at-rest’ attack requiring no immediate action by the attacker.
Understanding which bitcoin assets are at risk and how quickly quantum technology might bridge existing gaps will be explored in the concluding article of this series.