The Quantum Threat to Bitcoin: How a Powerful Computer Can Steal Your Cryptocurrency in Under 10 Minutes

This series has been exploring the intersection of quantum computing and cryptocurrency, with a focus on the potential risks to Bitcoin. The first part delved into the basics of quantum computing, including its unique properties and capabilities. However, understanding how a quantum computer works is only half the story - the other half is knowing how it can be used to compromise Bitcoin's security. To grasp this, we need to examine the encryption methods that underpin Bitcoin and identify the vulnerabilities that a quantum computer can exploit. Bitcoin relies on a system called elliptic curve cryptography, which involves a pair of keys: a private key and a public key. The private key is a secret number, while the public key is derived from it through a mathematical operation. This operation is essentially a one-way function, meaning it's easy to generate a public key from a private key, but virtually impossible to do the reverse. The security of Bitcoin hinges on this one-way function, as it allows users to prove ownership of their coins without revealing their private key. However, a quantum algorithm known as Shor's algorithm can potentially break this one-way function, rendering Bitcoin's encryption vulnerable to attack. Shor's algorithm works by using the principles of quantum mechanics to find the period of a function, which is essential for breaking the elliptic curve discrete logarithm problem. This problem is the foundation of Bitcoin's security, and solving it would give an attacker access to a user's private key. The implications of this are profound, as it would allow an attacker to steal Bitcoin from a user's wallet. Recently, a team of researchers from Google, the Ethereum Foundation, and Stanford University published a paper that significantly reduced the estimated number of qubits required to run Shor's algorithm against Bitcoin's encryption. This development has brought the threat of a quantum attack on Bitcoin closer to reality. The researchers designed two quantum circuits that can implement Shor's algorithm, one of which requires approximately 1,200 logical qubits and 90 million Toffoli gates. They also introduced a practical attack scenario, which involves precomputing certain parts of the algorithm and then using a quantum computer to finish the calculation once a target public key appears. This attack scenario, known as the 'mempool attack,' gives an attacker a roughly 41% chance of deriving a private key and submitting a competing transaction before the original transaction confirms. The bigger concern, however, is the 6.9 million Bitcoin that are already vulnerable to an 'at-rest' attack, which can be carried out without any time constraints. As the development of quantum computers continues to advance, the risk to Bitcoin's security will only grow. The final part of this series will explore the practical implications of this threat and what it means for the future of cryptocurrency.